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This post is over 3 years old, but it showed up as related to a more recent post, and asks an excellent question. So it deserves a response.

Always bid from S4 (as dealer) if you have 3 trump. In the worst possible scenario you will have Q-10-9 of trump, with two random 9's, and will get euchred A LOT. But you will still be better off than if you pass, because passing allows S1 (the player to your left, and the first person to bid in Round 2) to pick their best trump suit and potentially win 2 or even 4 pts.

Just suck it up and bid, knowing the expected value of your hand (EV) will be negative (more points to the opponents than to you), and take some solace when the player on your left says, "Damn! I had a loner in Hearts!", which will happen more often than you think.

Bidding with 3 trumps of any size has been a RULE OF THUMB in Euchre. However, that has to be qualified based on the Score. (Such as 8 to 8.) Probability of taking a euchre vs opponents scoring 1 point needs to be carefully evaluated.

IRISH

raydog wrote: ↑

Tue Jan 11, 2022 3:41 pm

This post is over 3 years old, but it showed up as related to a more recent post, and asks an excellent question. So it deserves a response.

Always bid from S4 (as dealer) if you have 3 trump. In the worst possible scenario you will have Q-10-9 of trump, with two random 9's, and will get euchred A LOT. But you will still be better off than if you pass, because passing allows S1 (the player to your left, and the first person to bid in Round 2) to pick their best trump suit and potentially win 2 or even 4 pts.

Just suck it up and bid, knowing the expected value of your hand (EV) will be negative (more points to the opponents than to you), and take some solace when the player on your left says, "Damn! I had a loner in Hearts!", which will happen more often than you think.

Good stuff Ray. Another important question tho is how to play Richard's hand. Specifically, what should Richard lead after he takes the first trick with a trump. E.G. say 1st seat leads the AC and everyone follows suit and Richard trumps in. Should he now lead trump or lead his offsuit? This website recommends leading offsuit in this spot those times we don't have an off ace to promote like in this hand. That used to be my position. Now my updated position is if I started with Kxx or Qxx in trump I will lead trump in this spot on 2nd street. If I started with Axx or Lxx in trump I will lead offsuit on 2nd street. The idea being that when we have low trump it's more critical we try to take out two enemy trump with one lead.

As far as I know, the above claims haver never been tested. When you get the chance can you tell us what your simulator says as far as what Richard should lead on 2nd street assuming he trumps the first trick. And furthermore, if Richard started with



Am I right that he should now lead offsuit on 2nd street?

Again, assume S1 led the AC and everyone followed suit until Richard trumps in. BTW this is a pretty important spot due to the fact that it comes up relatively often.

I tried different 2nd trick leads for this hand (S4, D trump, 1st trick won w/ 9D):



lead QD: (3,734 / 40,687 / 26,156) [2 pts / 1 pt / euchred] EV = -0.059
lead 10H: (2,375, 43,075 / 25,127) EV = -0.034

lead QD: (3,807 / 40,674 / 26,402) EV = -0.064
lead QH: (2,449 / 42,974 / 25,460) EV = -0.043

lead QH (2,285 / 42,858 / 25,337)
lead 10H: (2,283 / 42,870 / 25,327)
just 28 pts separate these last two, or 0.0004 of EV

It seems drawing trump leads to more sweeps but also more euchres, and since the latter is 3 times worse than the former is good, it's better to just lead the off-suit.

In all these hands the decision got to S4 about 70% of the time, and S4 won the first trick with the 10D about 50% of those times. I would suggest leading your worst card, but I can't guarantee my program is playing the hands optimally.
_____________________________________

I tried different 2nd trick leads for this hand (S4, D trump, 1st trick won w/ 9D):



lead 10D: (4,100 / 41,825 / 24,524) [2 pts / 1 pt / euchred] EV = +0.014
lead 10H: (2,845 / 44,709 / 22,895) EV = +0.065

lead AD: (4,174 / 40,494 / 25,736) EV = -0.037
lead 10H: (2,845 / 44,709 / 22,895) EV = +0.061

I come to the same conclusion as above. Slightly better overall outcome due to having a slightly better hand.
____________________________________

Given these results I thought I'd also try:



Same set up as above; I replaced H with C to avoid having a better bid in H. 9S turned, about 29,000 situations tested each scenario.

lead 10D: (4,259 / 43,739 / 25,564) EV = +0.015
lead 10C: (3,262 / 48,560 / 21,740) EV = +0.158

lead jH: (4,536 / 43,520 / 25,812) EV = +0.013
lead 10C: (3,136 / 48,838 / 21,894) EV = +0.153

Here there seems to be even a stronger case for playing an off-suit. My conclusion would be that it is only better to draw trump if you have the boss card in an off-suit. At least for hands of this strength.

raydog wrote: ↑

Mon Jan 17, 2022 4:47 pm

I tried different 2nd trick leads for this hand (S4, D trump, 1st trick won w/ 9D):



lead QD: (3,734 / 40,687 / 26,156) [2 pts / 1 pt / euchred] EV = -0.059
lead 10H: (2,375, 43,075 / 25,127) EV = -0.034

lead QD: (3,807 / 40,674 / 26,402) EV = -0.064
lead QH: (2,449 / 42,974 / 25,460) EV = -0.043

Great stuff Ray. Man that's close tho. This work makes me want to formulate a hypothesis: Firstly, If you are playing with a good partner, leading offsuit on 2nd street from this configuration is most likely the best play. We can safely conclude that from your work. However, I suspect this hand is highly sensitive to how one's P plays. For example, say S1 leads the AC on 1st street, everyone follows suit and S4, the maker, trumps in and takes the first trick. Then on 2nd street S4 leads the TH and say S2 takes the trick and at this point lets assume S2 has no trump. On 3rd street it is ABSOLUTELY critical that S2 be a good enough player to KNOW that spades is now the unequivocal best lead as leading a non-fresh heart or club in that spot is super toxic. IF S2 is not good enough to know this I would hypothesize that leading trump on 2nd street will actually end up being the best play for S4. Given how close your results are, a bad P, could easily swing it the other way.

raydog wrote: ↑

Mon Jan 17, 2022 4:47 pm

lead QH (2,285 / 42,858 / 25,337)
lead 10H: (2,283 / 42,870 / 25,327)
just 28 pts separate these last two, or 0.0004 of EV

This makes sense. There should be no discernable difference becuz QH and the TH are connected, I.E. they are equivalent. This specific test would be more relevant with QcTc or KhTh.

raydog wrote: ↑

Mon Jan 17, 2022 4:47 pm

It seems drawing trump leads to more sweeps but also more euchres, and since the latter is 3 times worse than the former is good, it's better to just lead the off-suit.

In all these hands the decision got to S4 about 70% of the time, and S4 won the first trick with the 10D about 50% of those times. I would suggest leading your worst card, but I can't guarantee my program is playing the hands optimally.

Can you test one more hand from this configuration just to make sure:



I think there's a chance leading trump on 2nd street could be best with that specific hand. The idea being with the 3 lowest trump there are now more higher trump in the wild thus there is more value to to leading trump on 2nd street and potentially taking out 2 enemy trump with one lead.

raydog wrote: ↑

Mon Jan 17, 2022 4:47 pm

I tried different 2nd trick leads for this hand (S4, D trump, 1st trick won w/ 9D):



lead 10D: (4,100 / 41,825 / 24,524) [2 pts / 1 pt / euchred] EV = +0.014
lead 10H: (2,845 / 44,709 / 22,895) EV = +0.065

lead AD: (4,174 / 40,494 / 25,736) EV = -0.037
lead 10H: (2,845 / 44,709 / 22,895) EV = +0.061

I come to the same conclusion as above. Slightly better overall outcome due to having a slightly better hand.

It's nice to see that my instinct was right that one is better off leading offsuit when we start with Axx in trump vs Kxx in trump. Cool. Awesome stuff.

raydog wrote: ↑

Mon Jan 17, 2022 4:47 pm

Given these results I thought I'd also try:



Same set up as above; I replaced H with C to avoid having a better bid in H. 9S turned, about 29,000 situations tested each scenario.

lead 10D: (4,259 / 43,739 / 25,564) EV = +0.015
lead 10C: (3,262 / 48,560 / 21,740) EV = +0.158

lead jH: (4,536 / 43,520 / 25,812) EV = +0.013
lead 10C: (3,136 / 48,838 / 21,894) EV = +0.153

Here there seems to be even a stronger case for playing an off-suit.

This is the only one I would've predicted with great confidence. Can't break up that guarded Left on 2nd street after getting the first trick. Since that guarded left is basically equivalent to 1 trick and S4's team already got the first trick, his team only needs one more trick to scratch a point. This is a classic spot where S4 needs to go fishing by leading his offsuit.

raydog wrote: ↑

Mon Jan 17, 2022 4:47 pm

My conclusion would be that it is only better to draw trump if you have the boss card in an off-suit. At least for hands of this strength.

I'm not sure if we can safely draw this conclusion. I think we can when our offsuit is Qx or lower, but I'm not so sure when our offsuit is Kx. Your results are so close that perhaps when we have Kx in offsuit, the small but significant percentage of time your off King is boss will be enough to make leading trump on 2nd street best.

I would test these hands just to see:







If relevant you could also test whether it's better to lead the TH vs the KH on 2nd street. According to this site, it's best to lead the TH to try to promote the KH to boss status but that concept has never been proven.

So the setup is that S4 picks up the 9D, discards the 9S, and is left with the given cards. They win the first trick with the 9D, what do they lead trick 2?


lead 10H: (223 / 3,686 / 3,002) EV = -0.27
lead 10D: (403 / 3,603 / 2,905) EV = -0.20


lead 10H: (244 / 4,327 / 2,503) EV = -0.027
lead QD: (423 / 4,185 / 2,466) EV = -0.014


lead 10H: (414 / 4,919 / 1,919) EV = +0.263
lead KD: (548 / 4,629 / 2,075) EV = +0.217


lead 10H: (304 / 4,503 / 2,220) EV = +0.095
lead 10D: (462 / 4,306 / 2,259) EV = +0.101


lead 10H: (173 / 3,808 / 2,910) EV = -0.24
lead 10D: (356 / 3,865 / 2,672) EV = -0.11

So your theory appears correct, Wes, except for the A-K-9 trump holding. That's why I tried the A-10-9D holding, which reverts back to what you predicted (better to lead trump). Perhaps leading the K trump does too much harm by not allowing a later overtrump of the 10 or Q?

RAY, i HAVE A QUESTION about how your Simulator plays, where the low off suit doubleton (10H & 10S) is led. When S3 win the trick with the AH, KH or a trump and now leads an off suit to trick 3. What does your simulator do? Does it Duck or Trump? I suspect it trumps, but I suggest it should Duck!
With the Queen doubleton, if the AH & KH (or AS/KS in those other hands) does not both fall, I would Duck (slough the QH or 10H which ever applies).

Can you clarify, or even have it your simulator Duck as an Option to see the results? I think it might be significant here?

IRISH

raydog wrote: ↑
Mon Jan 17, 2022 4:47 pm
Given these results I thought I'd also try:



Same set up as above; I replaced H with C to avoid having a better bid in H. 9S turned, about 29,000 situations tested each scenario.

RAY

WHOA! What is occurring with these hands to account for the differences in results? We need to dig into the differences?

IRISH

So the setup is that S4 picks up the 9D, discards the 9S, and is left with the given cards. They win the first trick with the 9D, what do they lead trick 2?


lead 10H: (223 / 3,686 / 3,002) EV = -0.27 0.07 SIGNIFICANT LEAD TRUMP
lead 10D: (403 / 3,603 / 2,905) EV = -0.20


lead 10H: (244 / 4,327 / 2,503) EV = -0.027 0.013 NOT SIGNIFICANT
lead QD: (423 / 4,185 / 2,466) EV = -0.014


lead 10H: (414 / 4,919 / 1,919) EV = +0.263 .046 LEAD LOW 10H
lead KD: (548 / 4,629 / 2,075) EV = +0.217


lead 10H: (304 / 4,503 / 2,220) EV = +0.095 NOT SIGNIFICANT
lead 10D: (462 / 4,306 / 2,259) EV = +0.101

ALSO:
Did you know that with 100,000 hands, differences become STATISTICALLY SIGNIFICANT AT EV = +/- 0.02 or greater. Less than this is NOT SIGNIFICANT.
I don't know off hand what it is for 10,000 hands but could test if needed. But higher for sure.
IRISH

Ray,

For STATISTICAL SIGNIFICANCE at 10,000 hands, EV needs to be equal to or greater than +/- 0.04. For 100,000 EV equal to or greater than +/- 0.02. I estimated the standard deviation to get that.

Less than those numbers, one can say trending (or chance, but not STATISTICALLY SIGNIFICANT.

IRISH

I re-ran the following hand 100,000 times:


lead 10H: EV = -0.015
lead QD: EV = +0.026

This may now be on the cusp of statistical relevance, and does highlight how a sample size of 10,000 hands is not large enough here. But there is something else going on.

For this same hand I looked at occasions where S3 won the 1st trick with a H, and then led a black suit on trick 2. My program does indeed trump in from S4 on these occasions, so I set it up to throw off instead (KH in this instance). I tested this for 100,000 hands, 71,133 of which were bid by S4. The situation came up 2120 times, and the results were as follows:

don't duck (play trump): EV = +0.033
duck (don't play trump): EV = +0.028
there was no change in sweeps, but ducking led to 112 more euchres.

On the surface this result seems to NOT be statistically significant. But then I tweaked my program to look ONLY at those 2000 odd hands in which the play of the hand was altered. The results changed dramatically:

for the 2,056 relevant instances (out of 100,000 total hands played):
don't duck: (0 / 746 / 1310) EV = -0.91
duck: (0 / 632 / 1424) EV = -1.08
Suddenly the results seem statistically significant! Because they aren't being diluted by all the extraneous data. It would appear that once S3 wins the first trick with a H, S4 is already on the road to getting euchred 2/3 of the time. And it is important to trump in on a black card lead to reduce the number of euchres.

What I like about running these scenarios is that they give insight into what may usually happen in very specific and uncommon situations, and it is sometimes not completely intuitive. But I must always keep in mind the limitations of my program (non-optimized) and the statistical significance of the results (not always straightforward to assess!)

RAY,

WOW! Now this is exciting. The Nitty Gritty details!

1.08 - 0.91 = 0.17 is a Statistical Significant difference! Most likely because it was the AH or QH if AH is buried and now the KH is boss card. So that throws the advantage to trumps S3 off suit lead. Cool! However, now I wonder if it makes a difference of the size of that lead by S3? If it is a low Spade (for example) vs AS or KS (on Ducking)?
This type of hand comes up frequently, like Wes says.

Thanks for looking at this!

IRISH

... the 2,056 relevant instances (out of 100,000 total hands played):
don't duck: (0 / 746 / 1310) EV = -0.91
duck: (0 / 632 / 1424) EV = -1.08
Suddenly the results seem statistically significant! Because they aren't being diluted by all the extraneous data. It would appear that once S3 wins the first trick with a H, S4 is already on the road to getting euchred 2/3 of the time. And it is important to trump in on a black card lead to reduce the number of euchres.

raydog wrote: ↑

Tue Jan 18, 2022 11:55 am

So the setup is that S4 picks up the 9D, discards the 9S, and is left with the given cards. They win the first trick with the 9D, what do they lead trick 2?


lead 10H: (223 / 3,686 / 3,002) EV = -0.27
lead 10D: (403 / 3,603 / 2,905) EV = -0.20


lead 10H: (244 / 4,327 / 2,503) EV = -0.027
lead QD: (423 / 4,185 / 2,466) EV = -0.014


lead 10H: (414 / 4,919 / 1,919) EV = +0.263
lead KD: (548 / 4,629 / 2,075) EV = +0.217


lead 10H: (304 / 4,503 / 2,220) EV = +0.095
lead 10D: (462 / 4,306 / 2,259) EV = +0.101


lead 10H: (173 / 3,808 / 2,910) EV = -0.24
lead 10D: (356 / 3,865 / 2,672) EV = -0.11

So your theory appears correct, Wes, except for the A-K-9 trump holding. That's why I tried the A-10-9D holding, which reverts back to what you predicted (better to lead trump). Perhaps leading the K trump does too much harm by not allowing a later overtrump of the 10 or Q?

This is wonderful stuff man. IMO it would've been almost impossible or at least highly impractical for one to test this spot doing a kitchen table sample. The EV's are too close so it would take forever to reach a 95% CI the low tech way. Your work is invaluable.

Now we can take this data and formulate some global strategies, again assuming S4 takes the first trick by trumping in:

1) If one starts with QT9 in trump they should lead trump on 2nd street no matter what their offsuit is.

2a) If one starts with Kxx in trump, they should lead offsuit on 2nd street if their offsuit is Qx or worse. Hypothesis: If, however, one does not trust their P to give them good leads later in the hand, it possibly could be best to lead trump anyways.

2b) If one starts with Kxx in trump and their offsuit is Kx or better, they should lead trump on 2nd street.

3) If one starts with Axx in trump, they should lead offsuit on 2nd street whenever they have Kx or worse. For the very worst Axx trump (AT9), leading offsuit was a statistical tie:

lead 10H: (304 / 4,503 / 2,220) EV = +0.095
lead 10D: (462 / 4,306 / 2,259) EV = +0.101

Extrapolating from that, I'm assuming for any better Axx trump combo leading offsuit will be best. Therefore for the sake of simplicity I would go with the recommendation of always leading offsuit when one starts with Axx.

4) If one starts with Lxx in trump, always lead offsuit on 2nd street when one has Kx or worse. This is the only configuration we probably didn't need a simulation to feel confident about as it almost just seems logical that we shouldn't break up our guarded left in that spot after our team has already won 1 trick.

That said there are some Lxx combos that I would say are controversial, those Lxx hands where we have an offsuit suited ace. We have two conflicting desires with this hand configuration: 1) lead trump to promote one's ace & 2) lead offsuit cuz we don't wanna risk breaking up our guarded Left. Well we can't do both so we have to choose. For example, with this hand I believe leading the AC unpromoted on 2nd street is best:



After taking the first trick with the 9D I believe leading the AC on 2nd street is the best play. I think it's too risky to break up our guarded Left in that spot. I would make the same claim for this hand (lead the off ace on 2nd street):



However before we could even get to testing that claim, we have to first confirm that hand is not a loner. I always go alone with that hand when not at 8/9 pts, but I've never been sure if that is correct. So in actuality I'm usually not in that spot to lead an off Ace on 2nd street.

Speaking of loners here's a claim I believe to be true that could easily be wrong:

It is +EV to go alone with this hand:



That hand may seem too weak to go alone with but I believe the value of having an offsuit suited ace with no gaps pushes it to loner status.

Conclusion, before we can test whether it's best to lead the off ace on 2nd street from this configuration: L-X-X + suited Ace, we have to first prove calling is better than going alone. If going alone is best then what to lead in 2nd street obviously becomes moot.

Ray, I have another Question on the play of this hand, and all the other related combinations as well.
Say the Dealer on 2nd trick leads 10H. S2 wins the trick with the AH or KH (if AH is buried). What does you simulator lead to the 3rd trick? It should NOT lead trump unless it is the JD. How does your simulator lead in this situation if S2 does have a trump card? Nor should a heart be led.
More importantly for the Club doubleton as it applies, since there is one more club.

IRISH



lead 10H: (223 / 3,686 / 3,002) EV = -0.27 [0.07 advantage)
lead 10D: (403 / 3,603 / 2,905) EV = -0.20