1/28 Fri Euchre - You hold the 2nd trick, now give your partner a chance to help.

[Dlan]

https://worldofcardgames.com/#!replayer ... %3A1%7D%5D

[Wes (aka the legend)]

https://worldofcardgames.com/#!replayer ... %3A1%7D%5D

Anyone who is convinced S4 misplayed this hand is wrong. And anyone who is convinced S4 played this hand correctly is wrong. We simply don't have enough evidence to draw a safe conclusion.

The question of course being, should S4 lead the Right on trick 2 to protect his effective tripleton offsuit ace? You certainly won't find a consensus among strong players on that--which is often the best recourse we have when we have no statistical backing.

I personally have wondered about this spot alot over the years. I would play the hand the way S4 played it but I have never been confident in that line.

And if we do test this spot and it turns out that leading the Right is wrong, I assume that means leading our off ace is best. Of course that claim would have to be tested against other junk leads too. But say it turns out leading our off ace is best would that still be true with a doubleton ace? A singleton ace? Or would leading the Right be better in those cases. I'm assuming leading the Right WOULD be better in those cases.

Worth noting, when I have R+1+a tripleton next ace--iow an effective quadrupleton offsuit ace--then I abandon the idea of protecting my off ace. In that special case I lead my extra dirty off ace on trick 2 hoping it brings out some trump. Maybe if we have a tripleton or effective tripleton off ace we should also abandon the idea of leading the Right to promote it. Idk

For now my take is, tripleton off ace or less, lead Right. This spot really needs to be tested. We'll never get satisfying answers otherwise.

[LeftyK]

My take is s1 should be leading trump because they are holding BOTH green aces AND they are singleton at that. Where does that fit into this Wes?

[raydog]

I finally had a chance to look at this. I simulated 1,000,000 hands, fixing the cards in the dealer's hand and the turn card. I looked only at hands where S4 won the first trick with the 9H (trump) - this was about 240,000 hands - and tested 3 different possible leads for the 2nd trick: JH (followed by AD, trick 3); AD (followed by JH, trick 3, if they win - a separate test showed this to be the best follow-up lead); and QC.

JH: (27,806 / 147,678 / 63,320) [2 pts / 1 pt / euchred] EV = +0.32
AD: (13,491 / 166,813 / 58,500) EV = +0.32
QC: (8,749 / 177,061 / 52,994) EV = +0.37

A rather interesting result! Here's my take: we actually win a point with this hand quite often, as we already have one trick and have another guaranteed trick with the R. Our Ace also looks very promising, but maybe our best asset (as Don alluded to) is our partner! So we shouldn't pray our Ace doesn't get trumped, or risk drawing out what may be our partner's only trump. Instead we should just lead garbage and see how things evolve. We should be looking to avoid euchres rather than win sweeps, and holding back with our best cards seems to be the best way to do this.
______________________

I looked a bunch of related hands as well.

First, I tried swapping the JH and the 9H (so JH already in S4's hand and the 9H turned). This resulted in S1 and S3 calling about 8% of hands (vs. 1.5% in the original scenario), and clearly their stronger hands, so the overall results improved for S4.
JH led: (31,874 / 147,474 / 50,302) EV = +0.48
AD led: (16,047 / 166,253 / 47,350) EV = +0.45
QC led: (10,438 / 176,009 / 43,302) EV = +0.48
More sweeps, fewer euchres, and a shift in best card to lead. But the results are very close, and leading garbage on the 2nd trick is still a good strategy.

The original scenario featured a doubleton next Ace - so only 3 other cards of that suit in the wild. What if those odds were different? I tried the following scenarios [1,000,000 hands; S4 hand shown, after discarding the 10S; only looked at hands where S4 is the declarer and has won the 2nd trick lead after winning 1st trick with 9H - always about 1/4 of total hands]:

1) J-9H + AD + Q-9C [singleton next Ace]:
JH led: EV = +0.47
AD led: EV = +0.51
QC led: EV = +0.45

2) J-9H + A-9C + QD [doubleton green Ace]:
JH led: EV = +0.38
AC led: EV = +0.47
QD led: EV = +0.43

3) J-9H + AC + Q-9D [singleton green Ace]:
JH led: EV = +0.56
AC led: EV = +0.67
QD led: EV = +0.52

4) J-9H + A-10-9C [tripleton green Ace]:
JH led : EV = +0.27
AC led: EV = +0.36

5) J-9H + A-10-9D [tripleton next Ace]:
JH led: EV = +0.22
AD led: EV = +0.26

All these results seem to show that is never a good idea to lead the R in an effort to make the Ace good. This may be because the downside (it's your last trump, and you may be drawing your partner's only trump, which may have been good for a trick) outweigh the benefits (your Ace may still not be good if an opponent has 2 trump AND is void in D). And there are of course all sorts of other scenarios which could play out. It seems generally best just to lead the Ace on the second trick; if it's a tripleton Ace then it probably won't win, but it still beats wasting your R bower first - and those are your only 2 options. The particular characteristics of the original hand make both the A lead and the R lead unfavorable, so a garbage lead is best (but there is not a huge difference in the results).

_______________________________

I was also curious how the dynamic would shift if S1 were given this hand (round 2), with the option of leading the Right and keeping a trump in reserve. So I tested the following 2 hands over 100,000 deals, looking only at those cases where S1 bid H, R2. [subsequent leads are also shown, in cases where the A wins]

1) S1 holds J-9H + A-10D + QC (9D turned)
lead JH (then AD): EV = +0.82
lead AD (then QC): EV = +0.43
lead QC: EV = +0.47

2) S1 holds JH + AD + A-QC + 9S (9D turned)
lead JH (then AC, then AD): EV = +0.35
lead AD (then AC, then JH): EV = +0.18
lead AC (then 9S): EV = +0.25

Leading the R is clearly best, even though the L is more likely to lie with partner than with either opponent (individually, if not in aggregate), and the Aces are more likely to win even without drawing trump (given that it is a 2nd round bid and the cards can be assumed to be distributed marginally more evenly - and dealer didn't get an opportunity to create a void). Even without having a second trump card in reserve in the case of the second hand (though having 2 Aces is a boon).

I confess that I find it hard to explain why it is so clearly better to lead the R in the second hand above (R as only trump + 2 aces, 2nd round bid from S1) vs. the second scenario at the top (R + 1 trump + doubleton green ace, 1st round bid from S4).

[Wes (aka the legend)]

I finally had a chance to look at this. I simulated 1,000,000 hands, fixing the cards in the dealer's hand and the turn card. I looked only at hands where S4 won the first trick with the 9H (trump) - this was about 240,000 hands - and tested 3 different possible leads for the 2nd trick: JH (followed by AD, trick 3); AD (followed by JH, trick 3, if they win - a separate test showed this to be the best follow-up lead); and QC.

JH: (27,806 / 147,678 / 63,320) [2 pts / 1 pt / euchred] EV = +0.32
AD: (13,491 / 166,813 / 58,500) EV = +0.32
QC: (8,749 / 177,061 / 52,994) EV = +0.37

A rather interesting result! Here's my take: we actually win a point with this hand quite often, as we already have one trick and have another guaranteed trick with the R. Our Ace also looks very promising, but maybe our best asset (as Don alluded to) is our partner! So we shouldn't pray our Ace doesn't get trumped, or risk drawing out what may be our partner's only trump. Instead we should just lead garbage and see how things evolve. We should be looking to avoid euchres rather than win sweeps, and holding back with our best cards seems to be the best way to do this.

So glad you did this work Ray. Amazing stuff. I'm definitely going with the garbage lead from this very specific hand configuration from now on.

I looked a bunch of related hands as well.

First, I tried swapping the JH and the 9H (so JH already in S4's hand and the 9H turned). This resulted in S1 and S3 calling about 8% of hands (vs. 1.5% in the original scenario), and clearly their stronger hands, so the overall results improved for S4.
JH led: (31,874 / 147,474 / 50,302) EV = +0.48
AD led: (16,047 / 166,253 / 47,350) EV = +0.45
QC led: (10,438 / 176,009 / 43,302) EV = +0.48
More sweeps, fewer euchres, and a shift in best card to lead. But the results are very close, and leading garbage on the 2nd trick is still a good strategy.

Wow, It never would've occurred to me to try this adjustment yet it absolutely is critical to test cuz changing the upcard (making it not the Right) does change enemy ranges significantly. Awesome. Leading garbage still holds up here so that's nice for the sake of consistency/simplicity.

The original scenario featured a doubleton next Ace - so only 3 other cards of that suit in the wild. What if those odds were different? I tried the following scenarios [1,000,000 hands; S4 hand shown, after discarding the 10S; only looked at hands where S4 is the declarer and has won the 2nd trick lead after winning 1st trick with 9H - always about 1/4 of total hands]:

1) J-9H + AD + Q-9C [singleton next Ace]:
JH led: EV = +0.47
AD led: EV = +0.51
QC led: EV = +0.45

2) J-9H + A-9C + QD [doubleton green Ace]:
JH led: EV = +0.38
AC led: EV = +0.47
QD led: EV = +0.43

3) J-9H + AC + Q-9D [singleton green Ace]:
JH led: EV = +0.56
AC led: EV = +0.67
QD led: EV = +0.52

4) J-9H + A-10-9C [tripleton green Ace]:
JH led : EV = +0.27
AC led: EV = +0.36

That's a big difference. So glad you tested this stuff Ray. Very compelling. At this point I think we have to conclude leading the off Ace is best except for the special case (the original hand)

5) J-9H + A-10-9D [tripleton next Ace]:
JH led: EV = +0.22
AD led: EV = +0.26

I'm just happy I was correct on one scenario!

All these results seem to show that is never a good idea to lead the R in an effort to make the Ace good. This may be because the downside (it's your last trump, and you may be drawing your partner's only trump, which may have been good for a trick) outweigh the benefits (your Ace may still not be good if an opponent has 2 trump AND is void in D). And there are of course all sorts of other scenarios which could play out. It seems generally best just to lead the Ace on the second trick; if it's a tripleton Ace then it probably won't win, but it still beats wasting your R bower first - and those are your only 2 options. The particular characteristics of the original hand make both the A lead and the R lead unfavorable, so a garbage lead is best (but there is not a huge difference in the results).

I wouldn't say never tho! I'm assuming when we are down 9-8 leading the Right--ie taking the line that leads to more sweeps--is now best. In this spot the math changes cuz getting euchred now only costs us 1 pt. Given this reality maybe it's best to always lead the Right whenever our opponents are at 9 except for the 9-9 scenario.

I was also curious how the dynamic would shift if S1 were given this hand (round 2), with the option of leading the Right and keeping a trump in reserve. So I tested the following 2 hands over 100,000 deals, looking only at those cases where S1 bid H, R2. [subsequent leads are also shown, in cases where the A wins]

1) S1 holds J-9H + A-10D + QC (9D turned)
lead JH (then AD): EV = +0.82
lead AD (then QC): EV = +0.43
lead QC: EV = +0.47

2) S1 holds JH + AD + A-QC + 9S (9D turned)
lead JH (then AC, then AD): EV = +0.35
lead AD (then AC, then JH): EV = +0.18
lead AC (then 9S): EV = +0.25

Leading the R is clearly best, even though the L is more likely to lie with partner than with either opponent (individually, if not in aggregate), and the Aces are more likely to win even without drawing trump (given that it is a 2nd round bid and the cards can be assumed to be distributed marginally more evenly - and dealer didn't get an opportunity to create a void). Even without having a second trump card in reserve in the case of the second hand (though having 2 Aces is a boon).

I confess that I find it hard to explain why it is so clearly better to lead the R in the second hand above (R as only trump + 2 aces, 2nd round bid from S1) vs. the second scenario at the top (R + 1 trump + doubleton green ace, 1st round bid from S4).

I like when you get curious! I'm glad you tested this additional S1-R2 spot. Leading the Right with those hands is how I'd play it. I'm glad that line turned out best. I'm not sure I can explain the difference in a satisfying way either but I'm not bothered by it. Since these are two very different spots (S4 vs S1) there is no apparent contradiction we need to explain away in my opinion. Perhaps it's as simple as this: when we call super-marginal from S1-R2--as we often have to do--it is more critical to lead that Right to possibly take out 2 enemy trump in one lead. The only additional hand I'd like to see tested from this S1 scenario would be Next calls when we have R+0 but only 1 off ace. For example (assume 9D turned)

S1:

I would call Next and lead the Right with that hand.

[Wes (aka the legend)]

My take is s1 should be leading trump because they are holding BOTH green aces AND they are singleton at that. Where does that fit into this Wes?

I somehow missed that this post was addressed to me. From this exact hand I would predict that leading trump is best. S1 has just a low trump with no voids. His trump is basically strategically useless if he doesn't lead it but if he leads it some good can happen: primarily, this lead will lower the probability of an enemy sweep.

That said, I wouldn't safely conclude leading trump is best here without an actual test. Because bad things also happen when we lead trump in this spot--we unguard our P, or we prevent our P from getting 2 tricks those times he has R+1--a test would be necessary to make sure leading trump is best.

Furthermore if that test shows that leading trump is indeed best we can't safely extrapolate from this specific hand to all other 1 trump, two green ace hand configurations. In some of those configurations we'll have a void + a high trump. Even with 2 green Aces it may be best to not lead trump, instead leading an off ace keeping that trump behind the maker hoping we can overtrump him later in the hand and force a euchre.

[raydog]

As for the lead by S1, I find the following (tested for 100,000 hands; when S4 declares, R1 [about 49,000 hands]; fixed cards in S1's hand + turn card):

lead AS: EV = -0.44
lead 10H: EV = -0.46
lead QD: EV = -0.59
[EV's from the perspective of S1]

So no great advantage to leading trump, but don't lead garbage.

[Wes (aka the legend)]

As for the lead by S1, I find the following (tested for 100,000 hands; when S4 declares, R1 [about 49,000 hands]; fixed cards in S1's hand + turn card):

lead AS: EV = -0.44
lead 10H: EV = -0.46
lead QD: EV = -0.59
[EV's from the perspective of S1]

So no great advantage to leading trump, but don't lead garbage.

This makes sense to me. Over the last 2 years, as a working hypothesis I have mostly abandoned leading trump out of this configuration vs a dealer call and I have been happy with the results. Nice to have some hard data backing that up. And it's worth driving home that this specific hand (low trump, no voids, two singleton green aces) would be one of the best hands to lead trump from in theory and YET leading an off Ace STILL wins out (or you could call it a statistical tie if we haven't reached a 95 CI). Either way, this is actually strong evidence that we should not be leading trump from these type of hands (1 trump + 2 aces) vs a dealer call.

[Tbolt65]

I would not ever be leading trump with 1 trump two aces against a dealer call unless I know it's a certain player , or two, or three. Then you almost have to. Other wise, I lead aces. Situation play against situation players. What i've always said. Certain play works the majority of the time except for special circumstances. Then you adjust for and to the play/players.

Tbolt65
Edward

[Wes (aka the legend)]

I would not ever be leading trump with 1 trump two aces against a dealer call unless I know it's a certain player , or two, or three. Then you almost have to. Other wise, I lead aces. Situation play against situation players. What i've always said. Certain play works the majority of the time except for special circumstances. Then you adjust for and to the play/players.

Tbolt65
Edward

Yeah if I had to map out the perfect time to do it, it would be when an aggressive player picks up a Jack and S1 has a hand like the one in the OP (1 low trump, no voids, 2 green aces). Since S4 didn't go alone you'd expect their range to be relatively weak with R+1+0 making up a significant portion of that range and that's the exact hand you're hoping S4 has when we lead trump from this hand configuration. Notice the EXACT ideal spot described happened here. An aggressive player DID just pick up a Jack and S1 HAS the hand type described above. And incidentally if S1 leads trump in this hand a euchre will be had. My understanding is Ray's simulation doesn't cover this specific spot. S1's hand is fixed to that ideal hand but S4's hand range is not fixed to just ordering up the Jack. He tested S1 leading trump from that hand against S4's entire calling range (all upcards included). So there's still hope that S1 leading trump from this specific hand is the right play against an aggressive S4 player who just picks up the Jack and that's what I would predict.

[irishwolf]

I am casting SKEPTICISM on the results posted to JH 9H AD 9D QC. Why questi9on this.
1) Of 1,000,00 hands tested there are 761,196 where one can statistically speculate of the combo's. For example S2 can have 2 trumps, 33.38 (33,380 hands). So did the Simulator Order with these hands? Which ones did the simulator Pass? [S2 JD/AH, JD/KH, JD/QD, JD/10H // AH/KH, AH/QH, AH/10H // KH/QH, KH/10H //QH/10H] At a score of 0 to 0, NEVER order the JH to your partner. And many other scores, even with 3 if behind in score. However, we can S2 does order with 3 trumps - 9.1% or 91,000 hands. So of course you MUST lead trump here. But what if Opponents hold 2 & 2 trumps, 2 & 0 or 1& 2 trumps or 2 & 1 trumps? And what if S2 has no trump - 15%? I contend that analysis MUST be broken down for further analysis.

But to continue, to stress my point is looking at when, as Ray did, the 9H is the up card. Now you can have S2 order with 2 trumps - 33.38% is a good Simulation or projection of what a good player would assist from S2. I am estimating that what was Posted when the 9H is up - at least a tie (between leading the JH or QC garbage) even when there are only 3 Unknown diamonds out. And when s2 has no trump you have no choice under those dire situations to lead trump, or even when s1/s3 has 2 & 1 trumps. When S1 or S4 has 4 trumps with the Left, should they not be ordering? If so then it's higher than 8%?

If you are going to post on residual hands, what is missing MAY be vital information to give a complete picture of the Universal set. 238,804 is just a subset. I could say a lot more about those missing, 761,196 hands but this is enough for now. It's all critical to the strategy one should use.

Then simulation with 9D down, giving S1 the hand that the Dealer had. Ray says, I cannot account for the Difference? Well of course not, because all those 33.38% hands that S2 had 2 Hearts are GONE because he would most likely have ordered. I suspect are now in S3 possession. I think it does impact the results.

So unless there is MORE information on those 761,196 - to each his own! But I am going to quit comment on the simulations, thank you!

IRISH

RAY'S RESULTS:

Post by raydog » Mon Feb 28, 2022 11:43 am
I finally had a chance to look at this. I simulated 1,000,000 hands, fixing the cards in the dealer's hand and the turn card. I looked only at hands where S4 won the first trick with the 9H (trump) - this was about 240,000 hands - and tested 3 different possible leads for the 2nd trick: JH (followed by AD, trick 3); AD (followed by JH, trick 3, if they win - a separate test showed this to be the best follow-up lead); and QC.

JH: (27,806 / 147,678 / 63,320) [2 pts / 1 pt / euchred] EV = +0.32
AD: (13,491 / 166,813 / 58,500) EV = +0.32
QC: (8,749 / 177,061 / 52,994) EV = +0.37

A rather interesting result! Here's my take: we actually win a point with this hand quite often, as we already have one trick and have another guaranteed trick with the R. Our Ace also looks very promising, but maybe our best asset (as Don alluded to) is our partner! So we shouldn't pray our Ace doesn't get trumped, or risk drawing out what may be our partner's only trump. Instead we should just lead garbage and see how things evolve. We should be looking to avoid euchres rather than win sweeps, and holding back with our best cards seems to be the best way to do this.
______________________

I looked a bunch of related hands as well.

First, I tried swapping the JH and the 9H (so JH already in S4's hand and the 9H turned). This resulted in S1 and S3 calling about 8% of hands (vs. 1.5% in the original scenario), and clearly their stronger hands, so the overall results improved for S4.
JH led: (31,874 / 147,474 / 50,302) EV = +0.48
AD led: (16,047 / 166,253 / 47,350) EV = +0.45
QC led: (10,438 / 176,009 / 43,302) EV = +0.48
More sweeps, fewer euchres, and a shift in best card to lead. But the results are very close, and leading garbage on the 2nd trick is still a good strategy.

[irishwolf]

The Wes says,

"This makes sense to me. Over the last 2 years, as a working hypothesis I have mostly abandoned leading trump out of this configuration vs a dealer call and I have been happy with the results. Nice to have some hard data backing that up. And it's worth driving home that this specific hand (low trump, no voids, two singleton green aces) would be one of the best hands to lead trump from in theory and YET leading an off Ace STILL wins out (or you could call it a statistical tie if we haven't reached a 95 CI). Either way, this is actually strong evidence that we should not be leading trump from these type of hands (1 trump + 2 aces) vs a dealer call."

I say, one has to remember the results is ONLY for the specific hand as Posted. AS QD 10D, AC 10H (JH up) and under the conditions whatever hands S2 ordered or passed in the Simulation? Did he order 2 trumps, (I suspect so, Ray would have to confirm.), and now those pulled out giving one more suit card to S2? And S1 has a doubleton Diamond to catch S4 AD/9D.

What about AC/xC, AS, 10H QD? Does your strategy still give the same results? And if S2 assists, then what will you do? If S2 does not order the Dealer with 2 trumps, what will you do? Is that not the same as S2 ordering weak?

You might be happy as you say, "abandoned leading trump out of this configuration."

But it makes me wonder.

IRISH


As for the lead by S1, I find the following (tested for 100,000 hands; when S4 declares, R1 [about 49,000 hands]; fixed cards in S1's hand + turn card):

lead AS: EV = -0.44
lead 10H: EV = -0.46
lead QD: EV = -0.59
[EV's from the perspective of S1]

So no great advantage to leading trump, but don't lead garbage.

[irishwolf]

WHAT SHOULD ELDEST LEAD?

Here is another post (SEE BELOW) I seriously question the Simulator is playing optimally when QD is led EV = -0.59 in favor of Dealer. If S1 leads QD, 61% of the time S3 can trump or over trump S2. From here it all depends on what is led. If clubs is led (has to be a 50% chance Clubs or Spades with 5 unknown - probably lead from 3 clubs/spade, etc.) S1 wins the trick. From here what is S1 now leading via Simulator. HE MUST LEAD ANOTHER DIAMOND, STILL HAS 10D. When S3 has two trump 39% and 3 trumps 11% it results in a Euchre. I will bet the simulator plays the AS not the 10D. One ends up a Euchre and the other a point for S4. No way should there be a EV = -0.59 for S1.

Should the Post to be definitive and accurate, post both ways of such a critical juncture?

Is it better than leading 10H or AS? I will leave that to ya'll to figure out! I conclude it's not JUNK with only 1 unknown diamond. Although, S1 does not know that Dealer has two diamonds - but he could if S1 has AS/AC.

IRISH

raydog wrote: ↑
Mon Feb 28, 2022 4:15 pm
As for the lead by S1, I find the following (tested for 100,000 hands; when S4 declares, R1 [about 49,000 hands]; fixed cards in S1's hand + turn card):

lead AS: EV = -0.44
lead 10H: EV = -0.46
lead QD: EV = -0.59
[EV's from the perspective of S1]

So no great advantage to leading trump, but don't lead garbage.

[Tbolt65]

The Wes says,

"This makes sense to me. Over the last 2 years, as a working hypothesis I have mostly abandoned leading trump out of this configuration vs a dealer call and I have been happy with the results. Nice to have some hard data backing that up. And it's worth driving home that this specific hand (low trump, no voids, two singleton green aces) would be one of the best hands to lead trump from in theory and YET leading an off Ace STILL wins out (or you could call it a statistical tie if we haven't reached a 95 CI). Either way, this is actually strong evidence that we should not be leading trump from these type of hands (1 trump + 2 aces) vs a dealer call."

I say, one has to remember the results is ONLY for the specific hand as Posted. AS QD 10D, AC 10H (JH up) and under the conditions whatever hands S2 ordered or passed in the Simulation? Did he order 2 trumps, (I suspect so, Ray would have to confirm.), and now those pulled out giving one more suit card to S2? And S1 has a doubleton Diamond to catch S4 AD/9D.

What about AC/xC, AS, 10H QD? Does your strategy still give the same results? And if S2 assists, then what will you do? If S2 does not order the Dealer with 2 trumps, what will you do? Is that not the same as S2 ordering weak?

You might be happy as you say, "abandoned leading trump out of this configuration."

But it makes me wonder.

IRISH


As for the lead by S1, I find the following (tested for 100,000 hands; when S4 declares, R1 [about 49,000 hands]; fixed cards in S1's hand + turn card):

lead AS: EV = -0.44
lead 10H: EV = -0.46
lead QD: EV = -0.59
[EV's from the perspective of S1]

So no great advantage to leading trump, but don't lead garbage.

When seat 2 does order regardless of the type of player they are. Leading trump is preferable. However leading the Ace with certain configuration and players can be used. Re: My opening leaded as s1 in the 9/10 diamond thread.

With the new configuration added for a s4 order. Lead your singleton Ace. Yes sometimes s2 does trump it. It sucks too.

If s2 calls light and doesn't order. Then S4 orders and calls light. I would advocate for a trump lead with your new hand configuration Irish and the original here.

Tbolt65
Edward

[Tbolt65]

I would not ever be leading trump with 1 trump two aces against a dealer call unless I know it's a certain player , or two, or three. Then you almost have to. Other wise, I lead aces. Situation play against situation players. What i've always said. Certain play works the majority of the time except for special circumstances. Then you adjust for and to the play/players.

Tbolt65
Edward

Yeah if I had to map out the perfect time to do it, it would be when an aggressive player picks up a Jack and S1 has a hand like the one in the OP (1 low trump, no voids, 2 green aces). Since S4 didn't go alone you'd expect their range to be relatively weak with R+1+0 making up a significant portion of that range and that's the exact hand you're hoping S4 has when we lead trump from this hand configuration. Notice the EXACT ideal spot described happened here. An aggressive player DID just pick up a Jack and S1 HAS the hand type described above. And incidentally if S1 leads trump in this hand a euchre will be had. My understanding is Ray's simulation doesn't cover this specific spot. S1's hand is fixed to that ideal hand but S4's hand range is not fixed to just ordering up the Jack. He tested S1 leading trump from that hand against S4's entire calling range (all upcards included). So there's still hope that S1 leading trump from this specific hand is the right play against an aggressive S4 player who just picks up the Jack and that's what I would predict.

That and also based on what S2 play calling is like, it may even make it more imperative to do so. However there will be times that one's assesment will be wrong/off on the holdings and when we do lead that trump. We risk losing out on our aces. Forget about euchring someone, we also lose out on a stopper. It's rare, but it does happen.

Tbolt65
Edward

[raydog]

My simulations hopefully shed some light, but obviously don't answer all questions, or give definitive answers (in many situations). My guiding principle in even endeavoring to create this program is that Euchre is a "solved" game - like Tic-Tac-Toe, checkers, Connect 4, backgammon, chess, and even poker (apparently). That is to say, there is a set strategy which will allow you to win in the long run.

From the above list, backgammon and poker include a component of chance (luck of the die or of card distribution), for which victory is never guaranteed, but involves probabilistic calculations. As in Euchre. And for the astute, these sorts of games allow for an added advantage, if you are able to ascertain how your opponent is likely to play in certain given situations (the proverbial "tells" in poker, or simply a tendency for tightness vs. aggressiveness).

Several very smart colleagues of mine have already highlighted the fact that a simple "one strategy fits all" approach may not be appropriate for Euchre, given that the proclivities of opponents (and even partner) are important factors to be considered. But I remain convinced that there is a strategy which will perform optimally, in the long-run, against ANY opponent, even a randomized one, even if there are ways of juicing short term gains with near certain knowledge [such deviations in play can always be adopted in live play].

I cannot "prove" this, nor can I aver that my approach is the right one [maybe what is required is an algorithm which adapts in real time based on the witnessed play of the other players in real hands]. Maybe I'm just lazy or rationalizing - I don't have the skills to create such a program! - or maybe I'm right; I'm sticking with the latter. At any rate, developing and tweaking this algorithm has revealed many interesting bids and plays to me, ones I would never have intuitively discovered. And I hope that, for you as well, the results I post will at least make you THINK about possibilities you had perhaps not previously considered. Even if you ultimately reject them.

Irish, I say again that your insights and comments are invaluable, if occasionally incomprehensible ["we can S2 does order with 3 trumps" ??] - if you were to take an extra few minutes to proofread before posting, we would all benefit. Thanks! I understand and agree with your comments which essentially point to the fact that my program is a "black box", and it's not easy for me to give a simple answer to a question such as "when does S2 bid?" Some queries I can easily address - and will - but others will just remain unknowns. I do not offer "truths", just "likelihoods" given certain parameters.

I think we've beat this horse [hand] enough, I'm ready to move on.

[irishwolf]

Ray,

This is how I see it. It is extremely frustrating, for example this hand and your Simulator Posts. Questions are asked that NEVER get answered. We probably differ on this but if a person posts they are obligated to answer the questions. If you don't know or not going to answer, state it!

1) This hand and your posts, as to how your simulator arrived at the EV and some of your conclusions. Questions go unanswered and you want to move on. For example, results of "leading garbage" the QD/10D combo. Your conclusion and how I think your simulator played that Hand from S1 (AS AC 10H QD 10D) arriving at an EV = - 0.59 is CLEARLY in error. In fact the QD/10D is not junk. When S3 is void in D's and leads a club it results in a Euchre most of the time. And so does leading the AS a good lead, but to arrive at the conclusion you did is not correct. It is disappointing in asking the question no answer was forth coming. The other questions on this hand I guess will not get reviewed by you?

2) The questions or skepticism I have pointed out about the present hand should be answered even though you are ready to move on. Don't leave such critical euchre strategy go unanswered. If you don't then "reader beware". Everything should always be "open" to comment and question. That is how one gets at the truth. And as you suggest, " I remain convinced that there is a strategy which will perform optimally, in the long-run, against ANY opponent, ...: That is a true statement.

3) I have asked numerous questions about how your Simulator arrived at the EV's, and most do not get answered. Or you admit in error did not know it could or should be played that way. That shows your inexperience in playing the game. Too bad you do not have a person to review the results before Posting. I think what I object to most is the results is not offered as a suggestion but this is the definitive answer. That might not be your intention but it is a Perception.

4) Your simulator, although valuable, is not the Holy Grail as most readers believe, I suspect. Invaluable in some simulations, for example, like on Donating in some situations. However, some of those simulations in controversial gray areas can be 'quick sand' and one has to be very careful then applying widely to similar situations. Euchre is dynamic and fluid and one always has to have their eyes peeled to adjust accordingly. It plays better than most players and is only as good as you are a player. So keep it up.

I do want to acknowledge your criticism of my proof reading. My weakness and I hate to proof read and correct. But you are justified and i want to acknowledge it.

I will stop being a thorn in your side, I bow out.

IRISH

P.S. (an Addendum)
I said I would bow out on commenting, (and I will), but I cannot in good conscience do that without concluding my comments about the results posted of Leading the JH vs QC (JH 9H QC AD 9D). When you know something, one should say it. And I know it here on this hand!

I am not sure what your Simulator is doing, but I suspect Ordering with two trumps with the JH up. I said not good strategy at that score unless at 8 or 9. Sometimes 7. If S2 does NOT order (with 2 trumps) the JH lead will out perform leading the QC (or leading the AD). It's not my duty to be guessing what your 'Black Box' is doing. And if it is true with 3 unknown D's, it is also true on all those other Ace combinations having 3 unknown cards out except an Ace triplet held by the Dealer. As bad as it may be, you have to pull 2 trumps from your Opponents.

I further suspect that what S2 is doing is CLOUDY the way this hand should be played. If you play that way, ordering with 2 trumps, probably then your post might be correct. And you can conclude that the QC out performs the JH. You are the programmer and MUST know what it is doing as this as I have said is critical to the results. For anyone who is my partner, you don't order a Jack with two trumps! Now I can move on!

[raydog]

Irish, I completely agree with what you've said. I didn't realize I was leaving you hanging and causing you must frustration, but now I see it. Apologies! I will try my best to do better going forward.
As for this hand, I'm about to jump on a plane, but will dive back in early next week and try to answer your questions - or say if I can't. We'll resolve this.
Ray

[raydog]

Irish, let me try to address your comments in an organized fashion.

1) My program only considers a select subset of hands.
This critique is sufficient to discredit all my results. Creating and optimizing my algorithm is a necessarily recursive process. I compare various bids to see which gives the best results ... dependent on how the hands are played. I compare playing different cards in various situations to see which gives the best results ... but that is dependent on how the other players bid (what subset of hands actually got me to that situation). There are chaotic systems which do not have any stable equilibrium based on the above recursive process, but I don't believe the play of euchre is one of them. So I have faith that my program is gradually approaching that stable equilibrium of "best practice" - though I can't handicap how close I am to that goal.
In addition, it is possible for astute partnerships to develop a style of play and an inherent understanding which allows them to further optimize their play, beyond the scope of what I am trying to achieve with my program. For instance, when you say "NEVER order up a bower when your partner is dealer at a score of 0-0", I patently disagree. I believe there are hands which warrant calling, because they virtually guarantee a point (or two), and the cost of giving up a potential 4-pt call by your partner (the dealer) is compensated for by guaranteeing dealer doesn't pass and give the opponents loads of extra points (via 1st or 3rd seat call, R2). At least that's what my algorithm tells me at this stage. BUT, it's a close call in many instances, and if the partnership has an understanding that 2nd seat will NEVER call in those situations, it opens up the possibility for dealer to make looser calls, and possibly compensate. [I'm not convinced it's the better strategy, but I have an open mind and cannot prove one way is better than the other].
The caveat here is: my program is not the HOLY GRAIL! I don't believe I ever touted it as such. It has proved very useful to me to understand the dynamics of the game, but please interpret its results with a healthy degree or skepticism.
All that said, let me try and salvage some credibility for my program. You cited certain specific hands, and I can tell you under what conditions S2 would call (according to my program), with 2 trump and a bower turned:
a) always with L + 1 trump, even with 9's and 10's as other cards;
b) often with A + 1 trump, but would need something like a green singleton A, two green K's, or perhaps AS + K-10C (if holding A-10 trump, H or D);
c) sometimes with K + 1 trump; would need singleton A + K-x in off-suits, both green;
d) never without any trump, even with Aces in all off-suits.
I think this is reasonable, but that is just my opinion. And I re-tested a bunch of these, and still found that calling was better than passing.
Regarding a couple other comments you made in the same vein:
a) I agree that trump should be led if S2 has 3+ trump, but unfortunately it's not possible to be sure of that (it will be a minority of cases);
b) when you listed the the possible split of trumps between the opponents, they are indeed all possible, but, again, no way to know. So my results are weighted by the possibility of each scenario (random card distribution). I don't understand how analyzing each scenario separately improves the simulation - it's just a weighted average of different possibilities;
c) according to my algorithm, S2 will never have 0 trump. How did you get 15% of the time?

1st installment. I will continue to cull through your comments.

[raydog]

Irish, looking at your next set of comments I confess to being very confused. Which is probably why I didn't address them (and that's unfair). So let me know ask you for clarification:

You said: "But to continue, to stress my point is looking at when, as Ray did, the 9H is the up card. Now you can have S2 order with 2 trumps - 33.38% is a good Simulation or projection of what a good player would assist from S2. I am estimating that what was Posted when the 9H is up - at least a tie (between leading the JH or QC garbage) even when there are only 3 Unknown diamonds out. And when s2 has no trump you have no choice under those dire situations to lead trump, or even when s1/s3 has 2 & 1 trumps. When S1 or S4 has 4 trumps with the Left, should they not be ordering? If so then it's higher than 8%?"

- my program never has S2 calling with no trump (and S1 could never know if that were the case);
- deciding to lead trump when the trump split is 2/1 between S1 and S3 [respectively?] may or may not be the best play, but S1 can never know if it's the case, so it's simply factored in to a probabilistic choice of leads.

You said: "I say, one has to remember the results is ONLY for the specific hand as Posted. AS QD 10D, AC 10H (JH up) and under the conditions whatever hands S2 ordered or passed in the Simulation? Did he order 2 trumps, (I suspect so, Ray would have to confirm.), and now those pulled out giving one more suit card to S2? And S1 has a doubleton Diamond to catch S4 AD/9D."

Is this just a very specific scenario? Once again, the way I handle these is that it will arise a certain percentage of the time, and if the results are favorable/unfavorable, they will be factored into the overall results with the appropriate weighting. Or, are you saying that you suspect my program is misplaying this particular scenario? That is quite possible - this is one of the prime ways you help me improve my program! If so, please tell me more directly. I'd love to delve deeper into such scenarios (which may well be generalized, to some extent). Ultimately, you have proven to me that you can help me improve my algorithm more than I can help you improve your play. But there are many others on this forum for whom the opposite is true.

You said: "What about AC/xC, AS, 10H QD? Does your strategy still give the same results? And if S2 assists, then what will you do? If S2 does not order the Dealer with 2 trumps, what will you do? Is that not the same as S2 ordering weak?"

- in the 1st two sentences, you introduce a related but different scenario. I didn't explore that avenue, with respect I will refrain from doing so even now. Sorry, just too many other avenues to investigate at the moment;
- I don't understand the 3rd sentence at all (does S1 know if S2 is "assisting"?);
- how does S1 know if S2 had 2 trump and didn't order the dealer? And if they can't know, why would they factor that into their decision making?

[raydog]

I didn't look at the original hand - I though S2 had ordered!

Let me look again at my analysis - please don't respond to what I previously posted!

[irishwolf]

RAY, I need to at least respond to your itemized list. My comments in 'blue'.

All that said, let me try and salvage some credibility for my program. You cited certain specific hands, and I can tell you under what conditions S2 would call (according to my program), with 2 trump and a bower turned:
a) always with L + 1 trump, even with 9's and 10's as other cards;
b) often with A + 1 trump, but would need something like a green singleton A, two green K's, or perhaps AS + K-10C (if holding A-10 trump, H or D);
c) sometimes with K + 1 trump; would need singleton A + K-x in off-suits, both green;...

I contend (strongly) a. b. & c., are ALL BAD assists except when you are at 8 or 9 points. Here is my reasoning.
Hopefully, we can agree with the JH as the upcard, of course S2 does not know what the Dealer holds. But he should know (as you have agreed and expressed before the Dealer should always Order the JH when he has 1 trump. CORRECT?
S2 does understand he has 2 trump and that there are 4 other trumps unknown. The Dealer has no supporting trump, statistically, 23.4%. With that being true, S2 is only making a good decision 23.4% and a bad decision 76.7% because the Dealer would have Ordered anyway. However, a good player will even pick it up with any two aces.
He might turn it down with a hand like this AD, 10D,9D JC JS. And if he does S2 may have had JD/AH, JD/KH, JD/QH, JD/10H OR JD/9H or even an Ace to boot. I contend even then, S4 is making a good decision. Other things to consider that I won't go into.


Okay you say, what is the harm? With 4 unknown trumps 47% of the time S4 has 1 trump, 25% of the time has 2 trumps and ~5% has 3. For sure you SPOILED HIS LONER ATTEMPT a minimum of 30%. And perhaps if he had 2 Ace doubletons with just one other trump - another 7 or 8%. Play the way you want but I do not want my partner ordering unless he has three trump or even then - LEAVE IT ALONE!

So that's my story on that and I am sticking to it.

Additionally, all those assisting that just disappeared? I suppose should have been included in this WHAT TO LEAD? 33% S2 has 2 trumps, of 1,000,000, will be 330,000 more hands that assuredly will go toward having a positive EV when leading the JH as S2 has two trumps. Perhaps, Sweeps 11% and the rest of the 330,000 1 pointers with a few euchres??? Will leading QC now overtake leading the JH? I doubt it. But the point is (my point) that EV you have for leading the JH is erroneous.

IRISH

If you see any grammar errors, fix em for me!

d) never [Never say never. I once at 9 to 6, ordered my WEAK partner with 3 aces, no trump. Afraid IT would turn down a bower. and he would have only the Jack And S1 had 3 and lead trump and we still made a point and S1 had a Next loner.] without any trump, even with Aces in all off-suits.
I think this is reasonable, but that is just my opinion. And I re-tested a bunch of these, and still found that calling was better than passing.

[raydog]

OK, let's start with your comments here.

1) Yes, my program has dealer picking up with any trump (J turned). That would give them 2 trump, including the R, in their hand.

2) My program currently has the dealer picking up a J with 3 off-suit aces, but not with just 2. I just tested this again, and found it was better to pass with no trump and just 2 off-suit aces, J turned, as dealer. *

3) I tested ordering from S2 with A-KS + A-KC + AD (JH turned), and found and EV of 0.56 if ordering and 1.01 if passing. * Glad it worked for you on the occasion you mention.

4) I find the same probabilities of S4 holding 1, 2 or 3 trump when S2 has 2 trump [just a simple probability calculation, but nice to verify my program is sufficiently random to arrive at the same result]. But you seem to posit that S4 should always declare alone with 3 trump, which I disagree with [you say that S2 is spoiling S4's loner attempt in all those situations]. Some percentage of those hands will be good loner attempts, but I contend that even MOST will not be - better to bid w/ partner (based on the results from my program). *

5) I did a simulation where I ran my program as it is currently configured, then ran the hands again with S2 NEVER calling with only 2 trump [JH was fixed as the turn card, all other cards random]. I ran this for 100,000 hands; about 30,000 were hands where S2 had 2 trump; about 7,200 of those hands that S2 currently bids. The results were enlightening.

When S2 calls with 2 trump (J turned):
EV = 1.17 [in about 5% of hands, S2 bid alone for an EV of 1.60; the rest had an EV of 1.15]

When those same hands are passed (and bid later):
EV = 1.20
(EV's from the perspective of S2/S4)

So, indeed, I find that it is better for S2 to NEVER declare with partner when holding only 2 trump and with a J turned [OK, never say NEVER - there may be certain hands and certain situations that warrant calling; but for the purposes of my program I do need some degree of generalization, and this seems like a good rule to adopt]. I believe it still makes sense to bid those rare, very strong hands where S2 bids alone, and also when a J is not turned. This is something I will change in my program (not currently taking into account the turned card, other than indirectly, as it does affect my calculated "strength of hand" and thus if S2's hand has enough strength to reach a threshold for bidding).

So once again you taught me something new, Irish!

As for all the * above, those just mean that my conclusions are based on the way my program currently bids and plays. Partnerships may develop other understandings, and there will certainly be instances where you can presume that a partner will be bidding sub-optimally and so you should adapt your own bidding criteria. I can't simulate those. As I keep tweaking my program I will need to revisit different scenarios, and may will arrive at different conclusions for some of them. That's the slow slog towards optimization.

So now I need to revisit my analysis of the hand. I'll post again when I manage to do that.

[irishwolf]

RAY,
Yes, (see below your statement) of course not all would with S2 having JH + 2 would be loner attempts, and I agree with your statement. I really did not intend to mean ALL when Dealer JH + 2. That said, certainly attempt with a doubleton or Ace + singleton which I suggest is a pretty worth while proposition and reason for S2 to pass. We could figure what that might be. Certainly not when Dealer has three (3) singletons and no Ace. Two kings is borderline, no attempt. However, just look at the percentage that the Dealer would . . . But the take away here is that S2 needs to be QUIET when the Jack is up except at close out (8 or 9)!

And when behind in score by 3 or more points, I want my partner to Pass, even with 3 headed by the Left.

You don't need to re-run the hand for me. I know what to do!

Irish

You said, 'But you seem to posit that S4 should always declare alone with 3 trump, which I disagree with [you say that S2 is spoiling S4's loner attempt in all those situations]. Some percentage of those hands will be good loner attempts, but I contend that even MOST will not be - better to bid w/ partner (based on the results from my program)."

[irishwolf]

I want to finish this discussion on this hand by saying with your recent Post we are in pretty close agreement (now). So peace Bro!

And to that Never say Never, I ordered with no trump, 3 aces. Diamonds JD was the up card. I would not order with a good partner, and it not always about the Math. There is another Dimension to Euchre, Intuition - at times, way stronger than Statistics. Ponder on that one for awhile because you can't program it!

On the S1 hand AS AC 10H QD TD - I will just let that one die on its own merits.

IRISH

[irishwolf]

Ray,

So let's examine in more detail, and more realistic loner attempts by S4. With the hands S4 JH up (random hand for S4), S2 has assists with 2 trumps (any two trumps but adding into the mix the 9H), with and without S2 having a side ace (4 unknown trumps):

S2 2 trumps with an ace.
I. S4 has only 1 trump (47%) + JH:
1) 2 Ace dblt
2) 1 Ace trip
3) 1 King trip
4) 1 Ace + King dblt

II. S2 same but without an Ace (s2)
(same list as I. above) but probabilities increase with one more Ace unknown.

One should also take note that when S4 only has the JH, S2 has 2 trumps, and S1 has three trumps, the chance of being Euchre increase when S1 has 3 trumps and leads trump.

III. S4 has 2 trumps + JH (25,5%), S2 has one ace:
1) 1 Ace dbl
2) 1 King dblt
3) 1 Ace + any sglt
4) 1 Queen dblt (could be the Queen of S2 Ace)
5) 2 Aces

IV. Same as list III. above S2 without an Ace - Probabilities go up for S4 holdings to go alone.

V. S4 has JH + 3 trumps (4.2%) Any Ace or any Singleton.

VI. S4 having JH + 4 trump. (1.6%)

With all these LONER ATTEMPTS the successful points from Loners will FAR exceed the points from S2 Ordering. Not all inclusive but just a quick list.

S2 not assisting with 2 trumps, changes the dynamics and conclusions drawn of WHAT TO LEAD by S4.

IRISH

[Wes (aka the legend)]

Irish, let me try to address your comments in an organized fashion.

1) My program only considers a select subset of hands.
This critique is sufficient to discredit all my results. Creating and optimizing my algorithm is a necessarily recursive process. I compare various bids to see which gives the best results ... dependent on how the hands are played. I compare playing different cards in various situations to see which gives the best results ... but that is dependent on how the other players bid (what subset of hands actually got me to that situation). There are chaotic systems which do not have any stable equilibrium based on the above recursive process, but I don't believe the play of euchre is one of them. So I have faith that my program is gradually approaching that stable equilibrium of "best practice" - though I can't handicap how close I am to that goal.

I'm bored so I thought I'd chime in. First off, I just wanted to reiterate that I love your simulator. I don't need it to be perfect or 100% accurate. I just need it to be useful and you have already demonstrated that it is VERY useful many times over. There's a lot of grey areas in this game, and I don't mind using your simulator as a tie breaker so to speak. As far as "stable equilibrium of "best practice" I think that's theoretically achievable but only after we specify the game texture. I am most interested in two game textures:

1) Me + 3 amateurs, I.E. an expert + 3 amateurs. This by default may be the most important game to "solve". Why? Becuz if one studies this game and plays everyday on their phones/computers, this is the type of game they will be in 95-99% of the time. Whether I play in my weekly tournament or on the app, I'm almost always in this type of game becuz most people simply don't take this game serious enough to move beyond what I refer to as amateur status.

2) 4 experts/strong players. It seems like your aim is to solve the game from this perspective which is fine although the utility of these findings won't be as profitable given how rare this game texture is. But thanks to ohioeuchre it's not THAT rare. Solving the game from this perspective will help players optimize their play in the Monday/Friday night games as all players I presume are experts or aspiring to be so. For me personally the insights from this angle will still be very useful as me and Edward play in one of the toughest euchre games on the planet every Thursday after the tournament. It's us vs a team that consists of a 4 time champion and a 3 time champion.

Also, I should add that solving the 4 expert game still will give us loads of insight on what's best in a "expert + 3 amateurs" game. Once one knows the correct strategy in a game with 4 experts it isn't hard to imagine adjustments for what to do against amateurs. For example, say it is slightly +EV to pass an ostensibly biddable hand from 3rd seat, 1st round in a game with 4 experts, a hand like Left+2+A. We can probably correctly infer that that same hand would be a call in an amateur game given that we can't count on our P to play the 2nd round correctly.

In addition, it is possible for astute partnerships to develop a style of play and an inherent understanding which allows them to further optimize their play, beyond the scope of what I am trying to achieve with my program. For instance, when you say "NEVER order up a bower when your partner is dealer at a score of 0-0", I patently disagree. I believe there are hands which warrant calling, because they virtually guarantee a point (or two), and the cost of giving up a potential 4-pt call by your partner (the dealer) is compensated for by guaranteeing dealer doesn't pass and give the opponents loads of extra points (via 1st or 3rd seat call, R2). At least that's what my algorithm tells me at this stage. BUT, it's a close call in many instances, and if the partnership has an understanding that 2nd seat will NEVER call in those situations, it opens up the possibility for dealer to make looser calls, and possibly compensate. [I'm not convinced it's the better strategy, but I have an open mind and cannot prove one way is better than the other].

I don't agree with the idea of the 2 seat never ordering up with 2 trump when his expert P has a bower up at a neutral score like 0-0. I know that's what we've all been taught, but that claim still demands to be tested. And I'm predicting that some 2 trump hand configurations will achieve +EV status vs passing.

The caveat here is: my program is not the HOLY GRAIL! I don't believe I ever touted it as such. It has proved very useful to me to understand the dynamics of the game, but please interpret its results with a healthy degree or skepticism.

I doubt this caveat is necessary. I'm assuming we all are aware that your simulator--all simulators--have inherent limitations. Again, all that matters is that this tool is useful, and you've demonstrated that in spades. Your simulator has changed my games in ways I likely never would have myself. I could care less that your simulator will sometimes pump out suspect results. Your simulator can often force me to look at a hand in a new way thus creating new insights allowing me another way to grow my game.

All that said, let me try and salvage some credibility for my program.

Credibility has already been firmly established for anyone that's been paying attention. Flaws and all, you probably have the best euchre simulator on the planet.

You cited certain specific hands, and I can tell you under what conditions S2 would call (according to my program), with 2 trump and a bower turned:
a) always with L + 1 trump, even with 9's and 10's as other cards;

With an amateur P who passes biddable hands like R+1 and doesn't go alone often enough this is a MUST call imo. The only possible exception would be if one is fishing hard for a loner cuz they are down a lot. With an expert P, I pass L+1+0, but this hand really should be tested before we act so certain on it. A good hand to test would be a hand where we don't block much in the 2nd round, a hand like this:

Upcard:

2S:

That's one of the best hands to test. If calling with that L+1+0 hand is not +EV than that should settle it on that hand configuration.

Beyond L+1+0, here's a 2 trump hand that I'm predicting will be a +EV call:

Upcard:

2S:

L+1+A hands should be tested too. In fact I would predict that this hand will be a +EV call assuming we block only 1 out of 3 in the 2nd rd:

Upcard:

2S:

b) often with A + 1 trump, but would need something like a green singleton A, two green K's, or perhaps AS + K-10C (if holding A-10 trump, H or D);

Once again, this hand will be an easy call with an amateur P imo. With an expert P, I suspect it's a pass. The hand to test would be a hand like this:

Upcard:

2S:

That's pretty much the best possible spot for this configuration given we block nothing in the 2nd round. If it's still a +EV pass than that will settle it for this configuration.

Also, what about when we have 2 off aces?!?! I bet this hand will be another +EV 2 trump call with an expert P:

Upcard:

2S:


If it is indeed a +EV call, then we'd have to test the worst hand from that configuration to see if all 2 trump + 2 ace hands are +EV calls. A hand like this:

Upcard:

2S:

c) sometimes with K + 1 trump; would need singleton A + K-x in off-suits, both green;

If I have K+1+A and I block nothing in the 2nd round, I'm calling this with an amateur P. That said, I would predict that all hands from this configuration would be a -EV call with an expert P. To test that out one would just need to test the very best from this configuration. A hand like this:

Upcard:

2S:

d) never without any trump, even with Aces in all off-suits.

I wouldn't say "never". For example. At 9-9, if you have no trump but 2 aces you gotta call this, even with an expert P imo. And I agree with Wolf that in close out situations we may have to make this loose call with an amateur P.

I think this is reasonable, but that is just my opinion. And I re-tested a bunch of these, and still found that calling was better than passing.

If you re-tested some of the hands above and found that calling is better than passing you need to take those results seriously imo. The adage "never order up your P's bower with 2 trump" is still primarily advice given to beginners like the adage "Never trump your P's ace". While very useful for beginners we should not expect that adage to always be true. It sounds like you already have compelling evidence that some two seat 2 trump hands are +EV calls with a bower up. Don't ignore it. This shouldn't be surprising. No adage is meant to hold up to this level of meticulous scrutiny. It would be shocking if such an adage held up 100%.

[Wes (aka the legend)]

Additionally, all those assisting that just disappeared? I suppose should have been included in this WHAT TO LEAD? 33% S2 has 2 trumps, of 1,000,000, will be 330,000 more hands that assuredly will go toward having a positive EV when leading the JH as S2 has two trumps. Perhaps, Sweeps 11% and the rest of the 330,000 1 pointers with a few euchres??? Will leading QC now overtake leading the JH? I doubt it. But the point is (my point) that EV you have for leading the JH is erroneous.

IRISH

I just want to point out that this isn't merely a theoretical issue. If one plays often whether on an app/website or in real life, they will be playing with an amateur P 95%+ of the time, and amateurs by definition pass biddable hands. So our 2 seat P will almost always have a stronger range after passing than any simulator can capture, meaning there's a greater chance that leading a bower on trick 2 is the best play even tho a simulator may say otherwise. A good way to test this would be to just have the 2S pass all 2 trump hands (except loners) and see if S4 leading the Right on trick 2 now wins out. Even if one disagrees with the strict 2 seat strategy Irishwolf has mapped out, doing this still approximates reality almost perfectly since most amateurs are surely passing all these candidate 2 trump hands the vast majority of time. So I agree with Wolf's sentiment that the simulator can't be trusted on this account becuz of how 2 seat players typically play in real life. If we do this--have 2S pass all 2 trump hands with bower up except loners--and leading the Right on trick 2 STILL ends up -EV when compared to other lines, that would be very strong evidence that leading the Right in that spot is incorrect.[/color]

[Wes (aka the legend)]

5) I did a simulation where I ran my program as it is currently configured, then ran the hands again with S2 NEVER calling with only 2 trump [JH was fixed as the turn card, all other cards random]. I ran this for 100,000 hands; about 30,000 were hands where S2 had 2 trump; about 7,200 of those hands that S2 currently bids. The results were enlightening.

When S2 calls with 2 trump (J turned):
EV = 1.17 [in about 5% of hands, S2 bid alone for an EV of 1.60; the rest had an EV of 1.15]

When those same hands are passed (and bid later):
EV = 1.20
(EV's from the perspective of S2/S4)

An EV of 1.15 vs 1.20 is pretty close, close enough where I think we can easily conclude that the claim "never order a bower with 2 trump at 0-0 with an expert P" is false. Given those close EV's I think we can safely infer many of the hands at near the top of the 2 trump range will indeed be +EV calls vs passing. And it isn't hard to guess which hands these will probably be. Hands like L+1+2A, and L+1+A and even 2 non bower trump + 2A spring to mind.

So, indeed, I find that it is better for S2 to NEVER declare with partner when holding only 2 trump and with a J turned [OK, never say NEVER - there may be certain hands and certain situations that warrant calling; but for the purposes of my program I do need some degree of generalization, and this seems like a good rule to adopt].

Yeah I agree it's a good general rule. It may be too much work with not much payoff to break this down further and have S2 playing every hand configuration correctly. I agree that having Seat 2 always pass 2 trump (except loners) will be a pretty good approximation of reality. But if it's not too much work to include some +EV 2 trump calls in Seat 2's range, I'd do it, but I don't think it's a big deal if you don't.

I believe it still makes sense to bid those rare, very strong hands where S2 bids alone

Yeah, the main question I would posit is, are all S2 L+1+AxXx+A hands worth going alone with the Right up. Becuz S2 starts off in a squeeze I wonder about some of the ones where we have a low trump. Keep in mind going set on this hand type is a mathematical tragedy given that we basically never go set and have a great chance of getting 2 points if we take our P along. It's clear to me that this is an obvious loner:

Upcard:

S2:

But what about the worst hand from this configuration:

Upcard

S2:

Is that still a loner? I suspect not, and if not, then what hand from this configuration reaches the point of indifference so to speak. Not asking you to figure this out. Just thinking out loud.

[Wes (aka the legend)]

And when behind in score by 3 or more points, I want my partner to Pass, even with 3 headed by the Left.

I love this idea. I would simply refine it as when down 3+ points S2 should never order up their P's bower unless they are going alone. Another condition I would need added here tho is that S4 can never pass a bower in this spot even if that's all he has. This condition prevents S2-S4's team from passing a biddable as a team and never passing R+0 shouldn't hurt their teams prospects too much as S2's passing range is now gonna be stronger than normal. The only caveat to worry about are those times S4 has R+0 but has a strong euchre hand if he passes. I think it's good to pass in that instance. That would be the only exception. I got Edward to agree to this strategy down 9-6/9-7 but he didn't like the idea down 0-3 altho I do. If we ever play together online, this is the convention we'll go by.

Devil's advocate take: In a tough game where players donate well, this strategy is basically dead on arrival and thus probably should be scrapped, but if S1 is an amateur then it's go time imo.

[raydog]

I checked out a few of the hands you suggested, Wes. Here's what my simulator yielded. (100,000 hands)

(In all cases, I'm looking at bids by S2, R1, with the JS turned)

JC + AS + 10-9D + 9H
S2 bids: EV = 1.21
S2 passes: EV = 1.20
Notes: 24K loners by S4 if S2 passes, 11,300 successful; 1275 euchred if S2 calls vs. 1850 euchred if S4 calls (R1 or R2); no bid for S2, R2; bids by S1 + S3 (R2) close to break-even in pts., so actually dilutive to S2/S4 score. This result is inconclusive: a toss-up whether to bid or pass (S2, R1).

9S + AH + AD + J-9C
S2 bids: EV = 1.30
S2 Passes: EV = 1.40
Notes: here's the exact breakout of results (S2 calls C, R2)
S2 bids, R1: 39,596 / 57,130 / 3,090 (2 pts / 1 pt / euchred)

S2 passes, R1: 8,004 / 6,041 / 50 // 29,510 / 32,354 / 497 (lone called // with partner; 2pt / 1pt / euchred outcomes) S4, R1
1,1198 / 1,505 / 176 // 781 / 3,550 / 3,983 (S1, R2)
4,646 / 6,739 / 638 (S2, R2 - only bids with p)
[hope this presentation is clear]
I think the difference here is that S2 has something to bid, R2, which tilts in favor of passing (having those 2 aces also gives a better chance of euchring S1 should they chose to bid, R2)

9S + 10-9H + AD + JC
S2 bids: EV = 1.18
S2 passes: EV = 1.15
Notes: the stats for bidding are slightly worse than in the previous scenario (understandably); if passing, the stats for S4 are slightly worse (less support), the stats for S1, R2, are slightly better, and, since S2 has no R2 bid, S3 also gets points for some R2 bids. Which render this scenario also a toss-up.

A-KS + 10-9H + AD
S2 bids: EV = 1.15
S2 passes: EV = 1.15
Notes: this hand is slightly worse than the previous scenario, in terms of S strength, but S2 has a decent bid in H, R2 [1,034 / 5,109 / 1,798], so it also ends up a dead heat.

A-KS + AH + A-KD
S2 bids: EV = 1.47
S2 passes: EV = 1.27
Notes: a stronger hand than the previous one, but not a stronger R2 bid by S2, which leads to a conclusion that it's better for S2 to bid, R1

I stopped there. Wes, you can investigate the other scenarios. There are just too many "what ifs" to justify exploring this in more detail with my simulator.

My simulator makes certain "assumptions": how other players will bid, and how the hands will be played. And those assumptions are assuredly biased (how detrimentally that affects the outcomes is still up for debate). BUT, at least those assumptions are consistent throughout all scenarios, so the relative hierarchy of strength of hands should stand: hands where I found it is better to bid are very likely much stronger bid candidates than those where the results were inconclusive. And there are likely hands where S2 has 2 trump (bower turned) where it is STILL better for S2 to call [if a table of expert players]. I will look into that.
____________________________________

As for having S2 NEVER call with 2 trump (except if calling alone), I did change my program to reflect that, and then reran the original hand. The EV's shifted, but the overall result was the same: leading the R was not as good as leading the "junk" QC. Once again, interpret this with the warranted skepticism [i.e. - what are my programs biases? At least they didn't change - same results if including S2 2-trump calls or not].

[Wes (aka the legend)]

I checked out a few of the hands you suggested, Wes. Here's what my simulator yielded. (100,000 hands)

(In all cases, I'm looking at bids by S2, R1, with the JS turned)

JC + AS + 10-9D + 9H
S2 bids: EV = 1.21
S2 passes: EV = 1.20
Notes: 24K loners by S4 if S2 passes, 11,300 successful; 1275 euchred if S2 calls vs. 1850 euchred if S4 calls (R1 or R2); no bid for S2, R2; bids by S1 + S3 (R2) close to break-even in pts., so actually dilutive to S2/S4 score. This result is inconclusive: a toss-up whether to bid or pass (S2, R1).

Nice work Ray! So it looks like we have a statistical tie here. The point I want to drive home tho is that these numbers prove--at least to me--that this is a MUST call for S2 with an unknown S4 P. Why? Becuz like 95%+ of unknowns pass R+1+0 and that reality changes everything. In addition unknowns do not go alone as often as they should so that also changes the math. IOW we only reach a statistical tie when S4 plays well, but 95-99% of the time we'll be playing with a P that DOES NOT play that well assuming one plays often with randoms.

With an expert P, I'm fine with passing. Obviously it doesn't matter much. If a player like Wolf or Edward want me to pass I'm cool with that. But I'm not always gonna obey their dictum. For example, say our team is up 7-0, I'm calling this from S2 just to control some variance as given that I only block 1 out of 3 2nd rd sounds I do not want the 2nd rd to ever happen in this spot. If I block my P's loner we're still up 9-0 with 99% equity. So even in that bad scenario I only cost my team 1% equity. So IMO with a big lead S2 should be ordering up even an expert P with this holding for variance controlling purposes (don't let the 2nd round happen). Of course that then begs the question, how big of a lead? IDK but I'd start getting tempted up even 3-0.

9S + AH + AD + J-9C
S2 bids: EV = 1.30
S2 Passes: EV = 1.40
Notes: here's the exact breakout of results (S2 calls C, R2)
S2 bids, R1: 39,596 / 57,130 / 3,090 (2 pts / 1 pt / euchred)

S2 passes, R1: 8,004 / 6,041 / 50 // 29,510 / 32,354 / 497 (lone called // with partner; 2pt / 1pt / euchred outcomes) S4, R1
1,1198 / 1,505 / 176 // 781 / 3,550 / 3,983 (S1, R2)
4,646 / 6,739 / 638 (S2, R2 - only bids with p)
[hope this presentation is clear]
I think the difference here is that S2 has something to bid, R2, which tilts in favor of passing (having those 2 aces also gives a better chance of euchring S1 should they chose to bid, R2)

This is a very surprising result for me. I would've bet some serious money that calling with this holding would beat out passing even with an expert P. But I buy the results and I agree with your explanation. S2 having a place to run to in the 2nd round (clubs) is important and having those aces also stops a lot of S1-R2 loners/2 pt sweeps and of course if S1 calls Next he's in deep trouble.

The same caveat for an unknown P still apply. In reality this S2 holding ends up clearly in the call bucket becuz his P will invariably pass too much and not go alone enough.

9S + 10-9H + AD + JC
S2 bids: EV = 1.18
S2 passes: EV = 1.15
Notes: the stats for bidding are slightly worse than in the previous scenario (understandably); if passing, the stats for S4 are slightly worse (less support), the stats for S1, R2, are slightly better, and, since S2 has no R2 bid, S3 also gets points for some R2 bids. Which render this scenario also a toss-up.

Yep looks like another statistical tie. Another MUST call with an unknown P.

A-KS + 10-9H + AD
S2 bids: EV = 1.15
S2 passes: EV = 1.15
Notes: this hand is slightly worse than the previous scenario, in terms of S strength, but S2 has a decent bid in H, R2 [1,034 / 5,109 / 1,798], so it also ends up a dead heat.

Same story as above: with an expert P, passing is defensible, but with a random P this is a must call.

A-KS + AH + A-KD
S2 bids: EV = 1.47
S2 passes: EV = 1.27
Notes: a stronger hand than the previous one, but not a stronger R2 bid by S2, which leads to a conclusion that it's better for S2 to bid, R1

This is another very surprising result for me. I mean the idea that calling beats out passing is not surprising. I would've predicted that, but the gap between EVs is stunning. So much so that EVEN IF an expert team had an agreement to not order up their P's bower with just 2 trump they should break their own rule and make this hand configuration the exception. That's just too big of a gap to ignore. And from that large gap I would extrapolate further and guess that even the worst hand from this configuration is a +EV call for S2:

Upcard:

S2:

If so this would be a pretty easy exception to remember for any expert team.

I stopped there. Wes, you can investigate the other scenarios. There are just too many "what ifs" to justify exploring this in more detail with my simulator.

You did great Ray. Only test hands you wanna test. I don't wanna burn you out. In fact I didn't expect you to test any of these hands so I'm very happy to have these results to look at.

My simulator makes certain "assumptions": how other players will bid, and how the hands will be played. And those assumptions are assuredly biased (how detrimentally that affects the outcomes is still up for debate). BUT, at least those assumptions are consistent throughout all scenarios, so the relative hierarchy of strength of hands should stand: hands where I found it is better to bid are very likely much stronger bid candidates than those where the results were inconclusive. And there are likely hands where S2 has 2 trump (bower turned) where it is STILL better for S2 to call [if a table of expert players]. I will look into that.

It's pretty clear to me that your "biased assumptions" are getting it right most of the time becuz the vast majority of time imo your simulator is producing good results. But it sounds like you're gonna keep tweaking it, making it better and better which is awesome.

As for having S2 NEVER call with 2 trump (except if calling alone), I did change my program to reflect that, and then reran the original hand. The EV's shifted, but the overall result was the same: leading the R was not as good as leading the "junk" QC. Once again, interpret this with the warranted skepticism [i.e. - what are my programs biases? At least they didn't change - same results if including S2 2-trump calls or not].

Good stuff. Yeah I think there's a great chance that leading the Right is not optimal but yeah we will probably never really know. Either way this is a spot I have never been happy about. Like there are many lines I feel so good about that I don't need a simulator to tell me what's right. It's obvious to my honed intuition what's right. But this spot has NEVER been intuitively obvious to me. I have never really been happy with my results in this spot. The only thing I felt sure about is that the competing lines must be close as is almost always the case when I can't safely reach a conclusion. So this spot has always been a grey area to me. I don't mind using your simulator as a tiebreaker for grey area spots. Even if it turns out our simulator is wrong due to "biased assumptions" it will likely be wrong by so little it won't really matter that much EV-wise.

Anyways back to the Irishwolf idea of never ordering your expert P's bower with 2 (excluding 8/9 scenarios). For the most part, I think the data you presented backs his case. After all some of the very best edge case 2 seat hand calls above still ended up with just a statistical tie with passing. The exception being the 2 trump+2 green ace hand. Based on this data I think you should have S2 pass on all 2 trump holdings except loners. While it's not 100% accurate it's close enough and of course I'm seduced by this simplicity. It would be preferable that you change the rules when your team has 8+ points as Wolf pointed out--in that case S2 should be much more aggressive--but if that's too complicated I wouldn't worry about it.

[irishwolf]

RAY

Back to the Original post, lead QC vs JH - I tested 300 hands played both ways and it was better to lead the JH. Fewer euchres and more Sweeps leading the JH. Still leaves me with Skepticism on how your Simulator plays. I will stick with my playing strategy on this one.

IRISH

"As for having S2 NEVER call with 2 trump (except if calling alone), I did change my program to reflect that, and then reran the original hand. The EV's shifted, but the overall result was the same: leading the R was not as good as leading the "junk" QC. Once again, interpret this with the warranted skepticism [i.e. - what are my programs biases? At least they didn't change - same results if including S2 2-trump calls or not]."

[irishwolf]

I suppose I should have clarified the statement NEVER assist from S2 when Jack is up. In euchre you can't play Stupid. The whole purpose of S2 passes is so the Dealer can go alone. There are 8568 hands from 18 unknown cards. Of course there are hands that S2 holds the statistically minimizes the probability that the Dealer can successfully go alone. Ray simulated AS KS AH AD KD that is not a pass hand, and the results of the simulator showed that. It far better with that hand to go for a Sweep because S2 has 2 of 3 aces. Statistically the Dealer has to have a hand that now will not be a successful loner.

Yes, there are other hands to that favor S2 going alone. But to put that in perspective with 8568 hands randomly dealt does favor the statement - Never (almost anyway for most players). JC 9C 9S AH AD is borderline hand that depends on the score. Even a hand like JS UP AH AD/KD AC XX might be an assist hand because the chance of the Dealer having a successful loner is LOW.

So I guess I should have said Never means ~95%. For most players it is Never. Most every Rule of Thumb in euchre has an exception.

You have to use your Brain!

Now to some of the simulator results that indicates Toss up. I suspect that your simulator is Passing when the Dealer has JS +0 (no clubs) with one green Ace. That is not a pass for S4. If you simulator is doing that, it now favors S2 EV results instead of Passing. I don't like Toss Up and quoting you, there is always a Best line of Statistical Playing. So I am looking closer at a couple of those, TBD.

IRISH

IRISH

[raydog]

Irish,

I respect your results [better to lead the JH in the original hand / scenario] and I am not going to try to dissuade you. You are a better player than I, my simulator has its flaws, and the results I arrived at did not show a huge difference. I am also NOT going to delve deeper into this to try to find out where we are diverging - I think there are some other more obvious tweaks I need to make to my program first. For me, the jury is still out, but I could see it going either way. At the moment, your experience trumps my work-in-progress simulator.

As for your question about whether my simulator passes:
"I suspect that your simulator is Passing when the Dealer has JS +0 (no clubs) with one green Ace."
There have been so many scenarios presented in this thread, I'm not sure which hand you are talking about [the original hand had JH turned, so not that one]. Do please specify, as I am eager to check out this particular scenario. Currently my program only bids with R as the only trump if they also have 3 off-suit aces, but you are insinuating that dealer should bid more aggressively. I'd like to know.
___________________

Wes,

I had a look at your "worst case scenario" of S2 going alone, holding 9S + AD + A-J-9C (JS turned), and found it was a toss-up between bidding alone and passing (EV 1.45 vs. 1.46). The obvious weakness here is that S2 has A+1 in next - a very short suit - so if S1 leads that suit, the Ace may get trumped. [on the flip side, if the A is NOT trumped, the 9 is more likely to win later]. So is my simulator playing optimally, specifically with regards to S1's first lead?

I tried forcing S1 to lead a C (if they had one) when S2 called alone. The results? The EV of S1/S3 improved by +0.03, quite paltry. Which for me still leaves it as a virtual toss-up.

[As an aside, I am considering 2 things when I interpret the results from my simulator: 1) are the results close enough that they could be possibly be reversed if I discover my program is playing sub-optimally?; and 2) even if the my results are 100% valid, is it worth delving into that degree of granularity to achieve perfect results? Given that the typical euchre player (partner or opponent) is not playing optimally? Here, I say "let it go"]

My program currently passes with this hand. But it is close to bidding. I do a point calculation of how strong the hand is, taking into account the obvious parameters, and this hand comes out at 16.2. 17.1 is the threshold for bidding alone. So this tells me I am on the right track. Give S2 the KC instead of the 9C, and the point threshold is reached - bid alone becomes the better option.

[irishwolf]

To your question (see below) was specifically speaking about this hand: JC 9C 9S AH AD JS UPCARD. (but also apply to AS KS AS 9H 10H AD as well as JC 9S AD 9H 10H). I am say what does you simulator do when the Dealer has ONE off suit ACE and no Trump? That is a Order in my book for the Dealer even though he has just the Right bower. But not when that ace is AC + 2 Clubs (a triplet) in next. If your simulator has the Dealer Pass it is to the Disadvantage of S2 passing. Skews the EV in favor of ordering. With four unknown trumps that reduces S4 passing from 23.4% with 2 unknown Aces by about 40 - 45% down to 14 - 16%. All those points go to Dealer ordering in the scenario of 2 trumps 1 ace for S2. Euchred occasionally but still the correct strategy, IMO.

IRISH

YOU ASKED, "As for your question about whether my simulator passes:
"I suspect that your simulator is Passing when the Dealer has JS +0 (no clubs) with one green Ace."
There have been so many scenarios presented in this thread, I'm not sure which hand you are talking about [the original hand had JH turned, so not that one]. Do please specify, as I am eager to check out this particular scenario. Currently my program only bids with R as the only trump if they also have 3 off-suit aces, but you are insinuating that dealer should bid more aggressively. I'd like to know. . ." YES THAT IS WHAT I AM SUGGESTING. I TESTED IT BUT ONLY WITH S2 HAVING 2 TRUMPS!

[irishwolf]

So what are some of those hands S2 should NOT order the Jack up (excluding at 8 or 9 on close out)? This is not all inclusive, must use your brain. As you increase the Aces to S2 you decrease Dealer chance of a successful loner - Increase Sweeps that nullifies passing.

DO NOT ORDER FROM S2:
Two trumps and NO ACES. (whole array of hands meet this criteria)
Two trumps and ONE ACE. (also many hands meet this requirement)

DO ORDER FROM S2:
Two trumps & 2 ACES (this probability is less than 5% with two trumps)
Two trumps & 3 ACES
Three trumps + ACE (depends on strength - might even go alone here)
Three trumps - NO ACE (depends on OFF SUIT as well as how badly you need 4 pts for Ordering/Passing)
Four trumps go alone


IRISH

[raydog]

OK, I need to break this down. I was actually asking for what hand S4 had, but I have tested a few.

My program currently has S4 passing if they only have 1 trump (the R which they pick up), unless they have all 3 off-suit aces. I tested the following hands, all with JS as turned card (card in [] is the card S4 discards when they pick up the bower):

K-[9H] + AD + K-9C:
pass: EV = -0.13
call S: EV = -0.36

K-Q-10-[9H] + AD:
pass: EV = -0.46
call: EV = -0.37

K-Q-10H + A-[9D]:
pass: EV = -0.25
call: EV = -0.53

AD + K-Q-10-[9C]:
pass: EV = -0.18
call: EV = -0.46

K-Q-10-[9H] + AC:
pass: EV = -0.48
call: EV = -0.64

And a 2-A hand:
A-9H + A-9D + [10C]:
pass: +0.02
call: -0.08

From these results, I am going to stick to my presumption that it is better for S4 to pass if their only trump is the R which they picked up, even if they have one off-suit Ace (green). In only 1 case was it better for S4 to bid - with arguably the best possible hand (singleton green A + 2-suited). I haven't tested enough hands here to make a definitive verdict on 2-Ace hands, but will do so shortly.

But if the prevailing opinion among expert players is that S4 should be picking up the bower in these situations. I WANT TO KNOW WHY! Maybe I am getting something wrong, and I'd like to correct my error. Let's forget the influence of score for the moment (imagine it's 0-0). How the other players bid is important, of course, especially S2, R1, and S1, R2. For the latter, I am hewing toward being rather aggressive here (based on feedback from this site), looking at relative score rather than absolute score; for the former, I want to figure out how S4 would bid first, then adjust the bids of S2 - seems the logical approach, though there may be a bit of back-and-forth to optimize. This will have an influence, but the discrepancies in score I found were appreciable. Play of the hand is of course another factor - hard to handicap that.

[irishwolf]

RAY,
I want to make sure I have this right to your tests: Dealer got the hands above, now 18 cards was randomly dealt to ALL 3 players & Stock. If so I think you have it exactly right.
That is different from the test I did giving S2 Two trumps + an Ace. I realize that the Dealer Never knows when S2 will Pass with two trumps + an Ace. I did the test to compare EV against S2 hand of JC 9C 9S AH AD JS UPCARD should Dealer order with R + off suit Ace.

I am good with what you have done! GOOD STUFF far better for S4 to pass unless he has R + 1 when considering 18 cards randomly dealt!

IRISH

From these results, I am going to stick to my presumption that it is better for S4 to pass if their only trump is the R which they picked up, even if they have one off-suit Ace (green). In only 1 case was it better for S4 to bid - with arguably the best possible hand (singleton green A + 2-suited). I haven't tested enough hands here to make a definitive verdict on 2-Ace hands, but will do so shortly.

But if the prevailing opinion among expert players is that S4 should be picking up the bower in these situations. I WANT TO KNOW WHY!

[raydog]

Yes, what you stated is correct.

The obvious trade-off here is S2 not wanting to take away a lone call by S4, but also not wanting S4 to pass when the combined S2/S4 hands could win a point.

Currently this is how my simulator bids, when S2 has 2 trump:
1) S2 will always pass if the R is turned, unless they have a loner hand. This is an approximation, and there may be 5% of hands which S2 should bid w/ p, but I'm happy to sacrifice optimization for complexity.
2) with R + 1, S2 will always call, sometimes alone.
3) with L + 1, S2 will sometimes call - it depends on voids, blocks, and if there is a viable bid, R2.
4) with A + 1 or K + 1, S2 will sometimes call - same caveats as above, but a bit more stringent.

I have not optimized FOR EVERY POSSIBLE HAND, but these general guiding principles seem to work, in most instances. It's a tussle between granularity and programability for me. I'd like to address the obvious mistakes, but can't address every possible hand.

With feedback from hands presented on this forum, I am working toward improvement - thanks!

As for the hand you specified in your test, Irish, I have:
S2: 9S + AH + AD + J-9C
S4: K-9H + K-QD + AC - AC is the only non-trump A left
JS turned

When I ran these hands through my simulator (all other cards random), I have both S2 and S4 passing, although they do have a decent S bid (sometimes these hands fall through the cracks).

The good news is that S2 has a good C call, R2, and S2/S4 have a good chance of euchring their opponents should S1 call something R2. The final EV for S2/S4 is +0.52. If S4 were to bid S, R1 - against the odds, their EV would be +0.96 - for this specific hand! So better - for this specific hand - but they would lose out in the long run.

[irishwolf]

You got it Ray. Good stuff!

IRISH