I have a dollar bet riding on this

[coolguy69]

Showing

Seat 1 has

Pass and go alone diamonds or order hearts alone right away?

Also, this happened in an alternate format, where if you go alone and LOSE, you give the other team 4 points - so bonus: if you can tell us whether to go alone on hearts, or pass to diamonds, or (possibly, not probably) don't go alone hearts or don't go alone on diamonds due to this punishment.

[XaviRonaldo]

Confused why you'd even consider diamonds without any off aces. Well I guess technically the becomes one but still I think you're better off in hearts. I'd definitely go alone in conventional rules. Depending on the score I'd go alone with this format though. Order up hearts and you know exactly where the danger Ace is. Lead 1 bower and if everyone shows a Trump lead the other. If someone shows void you go off suit to protect against the ace still being protected.

[irishwolf]

You said 'lose' if going alone but I think that would mean to get euchred. Getting one point is not losing.
Short answer is go alone Hearts, do not wait. Be as it may, below is a detailed breakdown of the justification.

Be as it may let's break it down as to which is better. This is basically a probability problem.

There are 3 unknown hearts, thus dealer could have 2 of those unknown hearts at about 16% and that would stop his lone try for 4 points and if the dealer's (side) then led diamonds or clubs instead of spades that would result in a euchre. If the dealer had all 3 of those unknown hearts, ~1.2% would result in a euchre. So the chance of getting euchred, call it approximately 17%.

Now if he waits on Diamonds, the chance it makes it back and all Pass on Hearts, either S2 or S4 ordering up the AH (assuming S2 would not order with two low hearts but S4 would make hearts is the same - about 17%. Thus about 83% chance back to S1 for a Diamond call. Assuming S4 is conservate caller, and if aggressive it be higher that 17% - perhaps 25%. So why take that chance?

For waiting, going alone in Diamonds: There are 5 diamonds unknown. It now requires any 3 to euchre S1 and either S2 or S4 having 3 or 4 Diamonds and not leading a heart or having AS to secure a euchre. I am saying, approximately 20% as stopper and perhaps slightly lower for a euchre depending what is led.
But take note that is 20% of 83% that it gets back to S1 to call Diamonds. So going alone is lower than going alone now in Hearts. Going alone in hearts (now)17% of 100% vs 20% of 83% that it gets back to S1. This is why going alone NOW is far better than waiting.

The chance that Eldest being successful with Spades flying is the same regardless going alone in Hearts vs Diamonds. So we can rule that as the same. Opponents are not going to slough the AS or having two aces is the same either way.

So Eldest, S1, has a significant advantage of going alone Hearts than waiting. Thus many hands scoring more points than waiting. And waiting does not guarantee a Euchre. The dealer most likely will have two or three trumps with one or two Aces. And what if S2 orders with 2 + an ace. You might get 2 points but no guarantee. You MUST strike when the iron is hot!

But let's complicate this what if that KH is a lower card? What would you do?
IRISH

[Tbolt65]

Showing

Seat 1 has

Pass and go alone diamonds or order hearts alone right away?

Also, this happened in an alternate format, where if you go alone and LOSE, you give the other team 4 points - so bonus: if you can tell us whether to go alone on hearts, or pass to diamonds, or (possibly, not probably) don't go alone hearts or don't go alone on diamonds due to this punishment.

I've played it both ways. It depends on the players, the situation and score.

Early in game with people who pick up light. I bag all day and if they pass I go alone in diamonds.

Late in the game where a loner would put you out I'd order up and go alone.

Tbolt65
Edward

[Wes (aka the legend)]

You said 'lose' if going alone but I think that would mean to get euchred. Getting one point is not losing.

Yep that's what he meant.

Short answer is go alone Hearts, do not wait. Be as it may, below is a detailed breakdown of the justification.

I'm not so sure.

Be as it may let's break it down as to which is better. This is basically a probability problem.

Yep.

There are 3 unknown hearts, thus dealer could have 2 of those unknown hearts at about 16% and that would stop his lone try for 4 points and if the dealer's (side) then led diamonds or clubs instead of spades that would result in a euchre. If the dealer had all 3 of those unknown hearts, ~1.2% would result in a euchre. So the chance of getting euchred, call it approximately 17%.

17% is what I got also. For those interested in the probability that the dealer has 3+ hearts here's the math:

Probability dealer has 3 trump:

(3C2 x 15C3)/18C5 = 15.93%

Probability dealer has 4 trump:

(3C3 x 15C2)/18C5 = 1.23%

Thus the probability dealer has 3+ trump is 15.93% + 1.23% = 17.16%

I'm not sure I follow you on this:

and if the dealer's (side) then led diamonds or clubs instead of spades that would result in a euchre.

If S1 goes alone in hearts he's obviously gonna lead both bowers first and if the AH doesn't come out of S4's hand then S1 is gonna try to play it safe by leading the KS. If S2 has the AS, S1 will make his point every time unless S2 has and leads the QS and S4 is smart enough to NOT trump that lead with his AH. I believe 2 experts can play that spot well and do just that but my assumption is that teams will botch that spot up most of the time but for the sake of argument and simplicity I am fine with assuming S2 will always lead the QS if he has it and S4 will always correctly NOT trump it with the AH. It goes without saying that if S4 has the AS in this specific scenario then S1 is euchred 100% of the time.

Bottom line: EVEN IF S4 has 3+ trump I think S1 is still a significant favorite to make a point becuz S1 still has semi-control of the hand on trick 3. This is an important distinction becuz when S1 instead goes alone in diamonds perfunctorily leading both bowers and then gets his boss KH trumped becuz S2 or S4 has 3+ trump, S1 has completely lost control of the hand at that point. At that point he can't manipulate the hand at all in his favor and must pray to the euchre gods he somehow escapes. IOW when S1 goes alone in hearts he will survive and get 1 point significantly more often than when S1 goes alone in diamonds. This factor is difficult to quantify on the back of an envelope but certainly goes in the ledger on the side of going alone in hearts.

Now if he waits on Diamonds, the chance it makes it back and all Pass on Hearts, either S2 or S4 ordering up the AH (assuming S2 would not order with two low hearts but S4 would make hearts is the same - about 17%. Thus about 83% chance back to S1 for a Diamond call. Assuming S4 is conservate caller, and if aggressive it be higher that 17% - perhaps 25%. So why take that chance?

If we assume S2 and S4 are good players than we can assume that both S2 and S4 are not passing with 3+ trump or 2 low trump + 2 aces. (Lets do this for the sake of argument. I'm not trying to be right on the internet here just trying to establish some objective reference point).

The 2 seat will have 3 trump or 2 trump plus 2+ aces 2.52% of the time. S4 will have 3+trump or 2 trump plus 2+ aces 24.51% of the time. Excluding overlapping hands, S2/S4's team will order hearts 2.52 +(1 - .0252)(24.51) = 26.41% of the time.

Work:

Probability S2 calls hearts: [(3C3 x 15C2)+(3C2 x 3C2 x 12C1)+(3C2 x 3C3 x 12C0)]/18C5 = 2.52%

Probability S4 calls hearts: [(3C2 x 15C3)+(3C3 x 15C2)+(3C1 x 3C2 x 12C2)+(3C1 x 3C3 x 12C1)]/18C5 = 24.51%

Probability S2/S4 calls hearts: 2.52 + (1-.0252)(24.51) = 26.41%

For waiting, going alone in Diamonds: There are 5 diamonds unknown. It now requires any 3 to euchre S1 and either S2 or S4 having 3 or 4 Diamonds and not leading a heart or having AS to secure a euchre. I am saying, approximately 20% as stopper and perhaps slightly lower for a euchre depending what is led.
But take note that is 20% of 83% that it gets back to S1 to call Diamonds. So going alone is lower than going alone now in Hearts. Going alone in hearts (now)17% of 100% vs 20% of 83% that it gets back to S1. This is why going alone NOW is far better than waiting.

My calculations on how often S2/S4 will have 3+ diamonds:

S2 will have 3+ diamonds 9.87% of the time. Work:

[(5C3 x 13C2)+(5C4 x 13C1)+(5C5 x 13C0)]/18C5 = 9.87%

Same above calculation goes for S4.

Probability somebody on S2/S4 will have 3 diamonds is:

9.87 + (1-.0987)(9.87) = 18.77%

So if S1 goes alone in diamonds he will run into 3+ diamonds 18.77% of the time. If S1 goes alone in hearts he will run into 3+hearts 17.16% of the time. Going alone in hearts is ostensibly slightly better on this front but as discussed above running into 3+ hearts should get S1 euchred significantly less often than running into 3+diamonds. So the small gap is somewhat illusory.

So Eldest, S1, has a significant advantage of going alone Hearts than waiting. Thus many hands scoring more points than waiting. And waiting does not guarantee a Euchre. The dealer most likely will have two or three trumps with one or two Aces. And what if S2 orders with 2 + an ace. You might get 2 points but no guarantee. You MUST strike when the iron is hot!

But let's complicate this what if that KH is a lower card? What would you do?
IRISH

Just wanna make a correction to the above: Waiting actually DOES guarantee a euchre 100% of the time assuming S1 plays the hand well. If S2 calls hearts, all S1 has to do is Lead his bower(s) until S4's AH comes out and there's the euchre. When S4 calls hearts, all S1 has to do is lead the right and then play his offsuit leaning on the maker to endplay him for the last 2 tricks (this works whether the maker has 3 trump or 4 trump). This is perhaps an important point in this argument. When S1 chooses to sandbag and go alone in diamonds he will euchre a competent team 26.41% of the time. I understand that sometimes S1 bagging will cost him a 4 point loner in hearts but overall I think it's safe to assume there is still gonna be significant net value to sandbagging hearts. Enough to overcome the fact that going alone in hearts is a little better than going alone in diamonds? IDK. At that point I think we need a simulation.

Also, this happened in an alternate format, where if you go alone and LOSE, you give the other team 4 points - so bonus: if you can tell us whether to go alone on hearts, or pass to diamonds, or (possibly, not probably) don't go alone hearts or don't go alone on diamonds due to this punishment.

For now, I'll wait to share my thoughts on this.

PS: Hi Tom!

[irishwolf]

WES,
I think you have overlooked some facts. Not sure you even made a determination and committed which is better?

For example, you said, Just wanna make a correction to the above: Waiting actually DOES guarantee a euchre 100% of the time assuming S1 plays the hand well. I TAKE ISSUE WITH THE 100% NUMBER. IF S4 HAS 3 HEARTS WITH AS. LEADS BACK HIS AH THEN HAS QS OR A DIAMOND OR A CLUB - THOSE ARE NOT EUCHRES WHEN WAITING. If S2 calls hearts, all S1 has to do is Lead his bower(s) until S4's AH comes out and there's the euchre. When S4 calls hearts, all S1 has to do is lead the right and then play his offsuit leaning on the maker to endplay him for the last 2 tricks (this works whether the maker has 3 trump or 4 trump)."

You also stated, So if S1 goes alone in diamonds he will run into 3+ diamonds 18.77% of the time. If S1 goes alone in hearts he will run into 3+hearts 17.16% of the time. Going alone in hearts is ostensibly slightly better on this front but as discussed above running into 3+ hearts should get S1 euchred significantly less often than running into 3+diamonds. So the small gap is somewhat illusoryy. I disagree with your conclusion here. You overlooked that having 4 or 5 Diamonds exceeds the Dealer having 3 Hearts. Those are mostly Euchres going alone in Diamonds except leading low spade and the AS is buried or with S3.

Thus, the rate of getting euchred going alone in Diamonds will be at least double going alone in Hearts. Those are mostly - 4 pointers when going alone in Diamonds but mostly 1 pointers for S1 going alone in Hearts. Success of going alone in Hearts will exceed waiting on Diamonds.

It is a FACT, you will score more points going alone in Hearts and not waiting. A simulator is not needed to figure this out.

I stand by what I said in my original post except what percentage S1/S4 orders the Heart. I said possibly 25% but that depends on too many variables as to how S2/S4 plays euchre to settle on one number. A range is better, however, all those all detract from the rate of going alone in Diamonds vs Hearts. And that AS is the same for both to spoil his march.

But if Ray wants to run the simulations, I welcome it.

IRISH

[Wes (aka the legend)]

WES,
I think you have overlooked some facts. Not sure you even made a determination and committed which is better?

I'm actually the one who bet the dollar against the OP. I bet that Hearts is the better call. I'm not sure if he thinks diamonds is the better call tho. He told me to pick the suit I'd bet on and he'd take the other side.

For example, you said, Just wanna make a correction to the above: Waiting actually DOES guarantee a euchre 100% of the time assuming S1 plays the hand well. I TAKE ISSUE WITH THE 100% NUMBER. IF S4 HAS 3 HEARTS WITH AS. LEADS BACK HIS AH THEN HAS QS OR A DIAMOND OR A CLUB - THOSE ARE NOT EUCHRES WHEN WAITING.

No reason to take issue in this spot. This is one of those situations where it really doesn't matter what one feels or thinks. It is simply a fact that S1 will get the euchre 100% of the time unless he massively butchers the hand. It does not matter what S4 or S2 holds. Give them any hand you want assuming the AH is always the upcard. S1 should still get the euchre. I actually think you're having a brainfart here Wolf.

S1 has in trump. The is in the dealer's hand on S1's right and he knows that's where it is becuz it was the upcard. So if the Dealer gets in a spot where they lead trump, all S1 has to do is play under with the KH for the automatic euchre, or if the Dealer leads the AH then S1 will just play over for the automatic euchre. If there's a situation where S2 has the lead and the dealer trumps in then S1 can just overtrump with the KH for the automatic euchre. If the dealer trumps in with the AH then S1 can just overtrump with one of the bowers for the automatic euchre. The only way for S1 to mess up this easy euchre opportunity vs a dealer call would be to inexplicably lead the KH (something only an extremely drunk person would do) or if S1 leads both bowers not realizing they can just endplay the maker for the automatic euchre--a poor play an amateur will sometimes make.

You also stated, So if S1 goes alone in diamonds he will run into 3+ diamonds 18.77% of the time. If S1 goes alone in hearts he will run into 3+hearts 17.16% of the time. Going alone in hearts is ostensibly slightly better on this front but as discussed above running into 3+ hearts should get S1 euchred significantly less often than running into 3+diamonds. So the small gap is somewhat illusoryy. I disagree with your conclusion here. You overlooked that having 4 or 5 Diamonds exceeds the Dealer having 3 Hearts. Those are mostly Euchres going alone in Diamonds except leading low spade and the AS is buried or with S3.

I did not overlook it. I said that S2 will have 3+ diamonds 9.87% of the time. That includes S2 having 4 and 5 diamonds. Here's my calculations on that again:

My calculations on how often S2/S4 will have 3+ diamonds:

S2 will have 3+ diamonds 9.87% of the time. Work:

[(5C3 x 13C2)+(5C4 x 13C1)+(5C5 x 13C0)]/18C5 = 9.87%

Same above calculation goes for S4.

Probability somebody on S2/S4 will have 3 diamonds is:

9.87 + (1-.0987)(9.87) = 18.77%

The 5C3 represents three diamonds, 5C4 = four diamonds, and 5C5 = five diamonds. And obviously S2 and S4 can't both have 3+ diamonds at the same time as there are only 5 diamonds in play. S4 or S2 can only have 3+ diamonds the 90.13% of the time their partner has 2 diamonds or less hence the final calculation factoring in this conditional probability: 9.87 + (1-.0987)(9.87) = 18.77%

Thus, the rate of getting euchred going alone in Diamonds will be at least double going alone in Hearts.

Not according to my math. It's possible I made a mistake but I don't see it.

I stand by what I said in my original post except what percentage S1/S4 orders the Heart. I said possibly 25% but that depends on too many variables as to how S2/S4 plays euchre to settle on one number. A range is better, however, all those all detract from the rate of going alone in Diamonds vs Hearts. And that AS is the same for both to spoil his march.

For the sake of this discussion I'm gonna assume S2 and S4 are competent players and thus they will call hearts around 26.41% of the time if S1 passes. I guess what I'm trying to say here is: my first priority is finding out if Hearts alone is better than diamonds alone assuming competent opponents. Once that is established I can calculate the rest or deduce the rest based on different player reads. I think this should be our starting point anyways given that Ray's simulator also approximates competent play.

But if Ray wants to run the simulations, I welcome it.

IRISH

You may welcome it but I desperately need it! I can't win my dollar unless Ray's simulator says Hearts is better. As you already know, I got kids to feed!

[irishwolf]

LOL, I AM SURE IT'S COMING!

IRISH

irishwolf wrote: ↑Sun Mar 12, 2023 12:55 am
But if Ray wants to run the simulations, I welcome it.

IRISH

You may welcome it but I desperately need it! I can't win my dollar unless Ray's simulator says Hearts is better. As you already know, I got kids to feed!

P.S. -
You should have asked Richard!

[raydog]

I had a look at this one.

My base case (how my simulator plays) is that S1 calls alone in H. The results:
(34,037 / 62,347 / 3,616) [4pts / 1 pt / euchred] EV = +1.91

The first thing that pops out is the low euchre rate: only 3.6%. The predictions were for this to be at least 17%. Why the difference?

S1 starts by playing both their bowers for 2 quick tricks. Then, if the AH has dropped, leads the KH to score at least a point. If the AH hasn't been played [S4 has 3 or 4 trump], S1 leads the KS. At this point, S1 still has a very good chance of winning another trick. Far better than what was estimated. That KH is a very powerful card, especially given that S1 will often have the option of playing it or not (they are seated AFTER the AH).

There are only 2 ways of getting euchred:
1) S4 wins with the AS, then leads the AH (drawing out the KH), then leads the QS or a D or C;
2) S2 has the the AS and the QS, or the spades split 2-2 between S2 and S4 [rare].

So S4 having 3 trump isn't sufficient. They also need to have the AS [or the very rare case where S2 has the AS and all the other spades are perfectly distributed].

Please let me know if I have made a mistake in my analysis, but I had look at how several hands were played out, and this situation became obvious to me. So I am happy with the lower euchre rate of 3.6%.

An EV of 1.91 is hard to beat. But I had a look at S1 passing.

- S2 calls 1,229 hands (out of 100,000) and is always euchred;
- S3 calls 101 hands and makes 2 pts;
- S4 calls 23,954 hands (7% of the time alone) and gets euchred every time;
- S1 calls the rest of the hands, alone in D, and scores (21,770 / 46,861 / 6,085).

The net EV for S1 is +1.72. (I looked at S1 calling D, R2, with partner, and the EV fell to +1.06 - getting euchred even more often!)

One thing to note here is that S2 and S4 will ALWAYS get euchred if they call H (and S1 plays correctly). S2 is never going to call with just one trump (K or lower), so suffice to say that S1 can just lead the bowers and the AH will drop in the first 2 tricks. If S4 calls, they could have 4 trump, and also the AS - the worst case scenario. Here, S1 leads the R (1 trick), then leads the KS when S4 doesn't play the AH (1 trick for the opposition). This is where S4 gets stuffed: if they lead the AH, S1 overtrumps with the left, and their KH wins a third trick. If S4 plays a low trump, S1 wins with the KH and the L wins their 3rd trick.

If there is a situation where S4 can avoid a euchre, please let me know.

So I show a total of 25,284 hands which are bid R1, all of them resulting in 2 pts. for S1/S3. For the 74.7% of hands that make it to S1 for a 2nd round of bidding, S1 calls D alone, but can't achieve a high enough success rate to beat the 1.91 EV bogey.

So for me, it's clear that the best bid in this situation is S1 bidding H alone, R1.
____________________________________

The other question was the odd rule that a lone-caller loses 4 points if they don't win all 5 tricks. This all but requires a success rate of 50%+ [actually even more, given the pts that could be scored taking partner along]. Under this draconian rule, loners would be very rarely called, and certainly not in this situation (neither H in R1 nor D in R2).

I tested S1 calling with partner, R1:
(28,253 / 68,693 / 3,054) EV = 1.19

Then I tried passing, and calling D with partner, R2:
Ev = +1.07

A close call, but even with the added euchres (for 2 pts) a quarter of the time, diamonds is just not as strong a suit as hearts, so still better to call R1. But in my mind this is all forgettable, because playing with this rule takes a lot of drama (fun) out of the game, which is why it is rarely encountered. And my simulator isn't considering this absurd rule when deciding how players bid, so my results are of questionable accuracy.

[irishwolf]

RAY

Thanks for running this. Couple comments. Yes, brain fart no way of 17% euchre rate on hearts. Meant to mean stopping a loner. I agree with 3.6% euchre rate you have. But I also said later the Euchre rate for Diamonds would be double, which it is (8.1%).

For euchring Dealer can have 3 hearts but with AS, leads back AH to get the KH. Then any suit lead. But S2 & S4 couild have all 4 spades and accomplish a euchre with S4 having 3 hearts as well. Even with 4 trumps S4 has to lead back the AH and have AS or void in spades. I think we are in agreement.

But this is not close on the EV Hearts vs Diamonds. I get different values. Hearts EV = +1.84 (14.4 negative points from 3.6 euchres, I think you used 8?) and R1 pass then going alone even with all 2 pointers with R1 calls by S2/S3 OR S4 EV = +1.59. This is factoring in the negative 4 points for being euchred on a loner. I calculated all points based on 100,000 hands simulator post both ways using your numbers.

Not sure many would go alone without both bowers (7%). ALL DEPENDS. But that's okay.

If I mis-calculated let me know. We are in total agreement - go alone in Hearts. No sense waiting.

And now Wes can feed those Boys! A dollar must go further in Vegas than here! Can't even get a cup of coffee for that. lol
IRISH

[raydog]

I didn't personally calculate the EV's, it's done automatically. Here's the math (just verifying).

When calling H alone:
[(34,037 x 4) + (62,347 x 1) - (3,616 x 2)] / 100,000 = 1.91

When calling D alone, R2:
[(1,229 + 101 + 23,954) x 2 + (21,770 x 4) + (46,861 x 1) - (6,085 x 2)] / 100,000 = 1.72

As for going alone without a bower, I have found it makes statistical sense when you have 4 trump + a good off-suit, or maybe 3 trump and A+A or A-K or similar. Enough rare situations to total to 7%, even if in this particular case you get slammed! And note that I meant 7% of calls, or only about 1,700 hands out of 100,000.

Wes, this is no way to feed your kids!

[irishwolf]

Using the rules the play by - 4 pts for a euchre makes this even more favorable going alone R1 in Hearts. Not a close call by my standards.

I didn't personally calculate the EV's, it's done automatically. Here's the math (just verifying).

When calling H alone:
[(34,037 x 4) + (62,347 x 1) - (3,616 x 2)] / 100,000 = 1.91

When calling D alone, R2:
[(1,229 + 101 + 23,954) x 2 + (21,770 x 4) + (46,861 x 1) - (6,085 x 2)] / 100,000 = 1.72

[Wes (aka the legend)]

Thus, the rate of getting euchred going alone in Diamonds will be at least double going alone in Hearts.

Not according to my math. It's possible I made a mistake but I don't see it.

This was a misstep on my part. My math said nothing about the euchre rate, only that the probability of running into 3+ trump was similar for both strategies. Going alone in hearts: 17.16% vs Going alone in Diamonds: 18.77%. And as I alluded to before, it would be dangerous to extrapolate from those close numbers and conclude that the euchre rates of each strategy will also be close:

Bottom line: EVEN IF S4 has 3+ trump I think S1 is still a significant favorite to make a point becuz S1 still has semi-control of the hand on trick 3. This is an important distinction becuz when S1 instead goes alone in diamonds perfunctorily leading both bowers and then gets his boss KH trumped becuz S2 or S4 has 3+ trump, S1 has completely lost control of the hand at that point. At that point he can't manipulate the hand at all in his favor and must pray to the euchre gods he somehow escapes. IOW when S1 goes alone in hearts he will survive and get 1 point significantly more often than when S1 goes alone in diamonds. This factor is difficult to quantify on the back of an envelope but certainly goes in the ledger on the side of going alone in hearts....

So if S1 goes alone in diamonds he will run into 3+ diamonds 18.77% of the time. If S1 goes alone in hearts he will run into 3+hearts 17.16% of the time. Going alone in hearts is ostensibly slightly better on this front but as discussed above running into 3+ hearts should get S1 euchred significantly less often than running into 3+diamonds. So the small gap is somewhat illusory.

RAY

Thanks for running this. Couple comments. Yes, brain fart no way of 17% euchre rate on hearts. Meant to mean stopping a loner. I agree with 3.6% euchre rate you have. But I also said later the Euchre rate for Diamonds would be double, which it is (8.1%).

Good work irishwolf on showing the differing euchre rates. Thank you.

Using the rules the play by - 4 pts for a euchre makes this even more favorable going alone R1 in Hearts. Not a close call by my standards.

I didn't personally calculate the EV's, it's done automatically. Here's the math (just verifying).

Yep. I agree. The 4 pt rule doesn't make this close. Going alone in Hearts is much better than going alone in Diamonds.

I had a look at this one.

My base case (how my simulator plays) is that S1 calls alone in H. The results:
(34,037 / 62,347 / 3,616) [4pts / 1 pt / euchred] EV = +1.91

The first thing that pops out is the low euchre rate: only 3.6%. The predictions were for this to be at least 17%. Why the difference?

Thank you for doing this simulation Ray. Always appreciate the time you take to do this stuff. I know it can be tedious. As Wolf pointed out, the 17% only really had to do with the chances of running into 3+hearts from the dealer, not the euchre rate. I accept the 3.6% heart euchre rate although I must say my intuition was very off on this. I would've guessed that the euchre rate for going alone in Hearts was significantly higher, maybe around 10%. Your reasoning is perfect:

S1 starts by playing both their bowers for 2 quick tricks. Then, if the AH has dropped, leads the KH to score at least a point. If the AH hasn't been played [S4 has 3 or 4 trump], S1 leads the KS. At this point, S1 still has a very good chance of winning another trick. Far better than what was estimated. That KH is a very powerful card, especially given that S1 will often have the option of playing it or not (they are seated AFTER the AH).

There are only 2 ways of getting euchred:
1) S4 wins with the AS, then leads the AH (drawing out the KH), then leads the QS or a D or C;
2) S2 has the the AS and the QS, or the spades split 2-2 between S2 and S4 [rare].

So S4 having 3 trump isn't sufficient. They also need to have the AS [or the very rare case where S2 has the AS and all the other spades are perfectly distributed].

Excellent stuff Ray. I agree that option 2) is so rare we can almost discount it by 100%. Not only is that spot rare but EVEN IF it happens I would guesstimate that 95% of euchre teams would still screw it up. Either S2 would not lead the QS on trick 4 or S2 makes that correct lead but S4 mistakenly burns his AH on that QS. So it's quite the parlay for that spot to even fully materialize.

Also another way to explain why the euchre rate for Diamonds must be significantly higher than Hearts:

When one goes alone in hearts and runs into 3+ trump they will still have the advantage of the lead + 1 trump on 3rd street. When one goes alone in Diamonds and runs into 3 trump they will have lost the lead and have no trump after their 3rd street lead of the KH. That's a big difference which is manifested in Irishwolf's numbers.

The other question was the odd rule that a lone-caller loses 4 points if they don't win all 5 tricks. This all but requires a success rate of 50%+ [actually even more, given the pts that could be scored taking partner along]. Under this draconian rule, loners would be very rarely called, and certainly not in this situation (neither H in R1 nor D in R2).

I tested S1 calling with partner, R1:
(28,253 / 68,693 / 3,054) EV = 1.19

Then I tried passing, and calling D with partner, R2:
Ev = +1.07

A close call, but even with the added euchres (for 2 pts) a quarter of the time, diamonds is just not as strong a suit as hearts, so still better to call R1. But in my mind this is all forgettable, because playing with this rule takes a lot of drama (fun) out of the game, which is why it is rarely encountered. And my simulator isn't considering this absurd rule when deciding how players bid, so my results are of questionable accuracy.

I think you're right Ray. My guess would've been that under the 4 pt loner euchre rule just calling Hearts would be best becuz if one calls hearts they always have the option of playing their hand in such a way as to guarantee a point. For example, Let's say S1 calls hearts and leads the Right, and both S2 and S3 show void in trump and S4 plays a low trump. S1 can immediately recognize the danger of such a situation--that S4 may be loaded--and simply lead his offsuit to set up an unstoppable end play for 2 more tricks. Having the privilege to always avoid a euchre is very nice and valuable.

[Wes (aka the legend)]

And now Wes can feed those Boys! A dollar must go further in Vegas than here! Can't even get a cup of coffee for that. lol
IRISH

Wes, this is no way to feed your kids!

I did indeed bet on hearts and am now $1.00 richer! But here comes the plot twist. I made that bet at the end of the night, after that hand had been played. In the actual hand I was in S1 and I passed on Hearts and went alone in diamonds....and I got euchred!

The sick part is I have played probably around 40K games of online+live euchre and I have ALWAYS went alone in Hearts in this spot. So this was the first time I tried something different. Why did I do it? Well that's the ironic part. I got rattled by the 4 pt euchre possibility. Seeing the AH upcard and knowing that if the dealer had 2 more hearts I could be in trouble and knowing how devasting getting euchred is in this dumb -4pt format coupled with the fact that I've been running bad over the last 10 months in the tournament and have actually gotten euchred twice in almost this exact same spot + I have seen Edward choose the diamond route before so it seemed plausible = I made the fateful split second decision to go alone in Diamonds figuring the EVs probably weren't that much different anyways (which obv isn't true). So the supreme irony of course is that I choose diamonds becuz I feared getting euchred in hearts but the euchre rate of diamonds is way worse than hearts! Again tho, in normal euchre I always go alone in hearts. The 4 pt euchre rule got inside my head and somehow made me make an even worse decision. Sigh.

[irishwolf]

LOL
FUNNY STORY!

[raydog]

I misunderstood the 4-pt. euchre rule: I thought if you call alone and don't win all 5 tricks, the other team gets 4 pts. Not just when you get euchred. Obviously a big difference. Now I see how it just tightens up lone calls a bit but doesn't shut them down the way my interpretation of the rule would.
______________________________

Also, Wes brings up a good point: it's possible to avoid getting euchred at all (calling H alone from S1), in the same way it's possible to euchre S2 or S4 is they call H [two sides of the same coin]. The issue is that S4 will often have 2 trump and the AS will be with S3 or buried, such that leading that second bower on trick 2 draws out the AH and sets up a 4 pt. sweep.

So the aggressive move is to play the 2nd bower on trick 2, hoping the AH drops (plus a few other ways to sneak out a 3rd trick if S4 has 3 or 4 trump). This opens you up to getting euchred (3.6% of the time), for a deficit or 3 pts. (-2 vs. +1 pt). But it also gives you a decent chance of getting a sweep, for a 3pt. benefit (+4 pts. vs. +1 pt). Is it worth doing?

I compared the two approaches:
Aggressive: (33,928 / 62,439 / 3,633) EV = +1.91
Avoid euchre: (21,523 / 78,477 / 0) EV = +1.65

So it's clearly better to risk a few euchres in pursuit of quite a few more 4 pt sweeps. Not so hard to predict, given that it works whenever S4 has exactly 2 trump AND neither opponent has the AS [I'm not considering a few other rare scenarios that have to be played perfectly], which happens more than 3.6% of the time. But it's nice to test if my simulator is spewing out decent results.

[irishwolf]

It is easy to TOTALLY reduce the threat of being euchred in Hearts under that -4 rule.

What you do is lead JH to trick one. If S2 has no trump, now lead KS to trick 2. There is no way possible to get euchred as you have JD/KH even if Dealer has 4 trumps with AS or any other holding. You now have 12 cards unknown with 2 unknown trumps (if AH did not fall). But this more than doubles the chance S4 has 3 or 4 hearts to start the hand.

And if the AH falls (35%) then proceed accordingly and success rate is 44.4% for a sweep. I like this approach under the - 4 rule.

Anyway. you do reduce successful loner attempts but not by that much but Totally reduce the Euchre. If S2 has no trump (35%) then the Dealer is likely to to have Ah + 2/3 trumps. Playing both bowers still makes you vulnerable to that 3.6% euchre.

It's just a matter of how aggressive you want to be if S2 has no trumps.

Irish

P.S.
Now we have all these Simulations on how to play various hands. The trick now is to retrieve these from memory when playing. lol

[coolguy69]

I owe wes $1 thanks everyone

[Tbolt65]

Don't play scared euchre. That's the absolute worst mistake you can make when determining which line of play to take.

Its one thing if you make a logical assessment and line of play and find out that your wrong.

But just don't play scared euchre. This will eventually go away. You just got to be proactive about it.



Tbolt65
Edward

[Wes (aka the legend)]

Congratulations on Ray getting 2nd place in our weekly Vegas tournament with 61 points (in 6 games). It's actually kinda a bad beat he didn't get first. Somebody got 63 pts. Last year Ray got first. He's gotten over 60 points in both times he's been in our tournament. Excellent stuff!!

[Tbolt65]

Congratulations on Ray getting 2nd place in our weekly Vegas tournament with 61 points (in 6 games). It's actually kinda a bad beat he didn't get first. Somebody got 63 pts. Last year Ray got first. He's gotten over 60 points in both times he's been in our tournament. Excellent stuff!!

Grats to Ray.

Tbolt65
Edward