3rd trick lead

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raydog
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3rd trick lead

Unread post by raydog » Sat Apr 01, 2023 3:43 pm

You are in S1 and hold K-JS + AH + AD + JC, with the 9S turned.
You call S alone and lead the JS. S2 plays the 9H, and S4 plays the 9S.
You lead the JC on the 2nd trick, S2 plays the 9C, and S4 plays the 10S.

What do you lead on the 3rd trick? Imagine the score is 0-0, and you are just trying to maximize your EV.



sdu754
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Unread post by sdu754 » Sat Apr 01, 2023 5:16 pm

you lead one of the two Aces just in case the third seat has the Ace of Spades.

irishwolf
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Unread post by irishwolf » Sat Apr 01, 2023 9:40 pm

This is about maximizing points - 10,000 hands. So you Must lead the KS on trick 3.

So what is the reason? It is just as likely that S4 has QS as he would the AS. So every time he has QS and you lead one of the ace, it might get trumped. You still have two Aces of which opponents will end up leading to one of them. If S4 has 4 trumps, low chance he still has to lead and will most likely to one of your aces. This is only if S4 plays 10S in sequence.

But what if S1 had A/K? Forced to lead one of these on trick 3.

IRISH

THIS IS AN ADDENDUM AS I WILL ASSUME S4 IS 'SMART'.
If he had the QS as well as the 10S, he would have played (QS) it instead of the 10S to trick 2. Thus either he has the AS or no more trump! So leading an ace is better!

raydog
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Unread post by raydog » Sun Apr 02, 2023 10:24 am

I am currently working on optimizing my simulator for play of the hand when a player calls alone. That's how I came across this scenario.

As initially (and currently) coded, my simulator plays conservatively and leads the AH on the 3rd trick. The AS (boss trump) is still out there somewhere (though possibly buried), so the best way to avoid getting euchred is to play a boss off-suit A, which will either win the 3rd trick or draw out S4's trump.

But now I wonder if that is the best play. If S4 had only the 9 and 10 of trump, S1 gets the sweep no matter what he leads. If S4 had the 4 remaining trump, both the AS and QS will win tricks. So what about those times that S4 holds the 9-10-QS initially? Leading the KS would guarantee the sweep here, and not allow S4 to trump the AH. But if S4 has the AS (but not the QS), they can trump the 3rd trick and potentially win the last 2 tricks, resulting in a euchre. If the base case is winning 1 pt, getting a sweep is worth +3 and getting euchred is worth -3. So which case arises more often?

I have of course run the simulation on this, but will wait a couple of days to post the results, in case someone else wishes to chime in.

As for Irish's very clever and rational addendum, I would counter that in a game where all players are "smart" and perfectly logical (like you find in many a logic riddle), S4 would know how S1 is analyzing the situation, and that, when holding just the 9-10-Q of trump, S1 would expect them (S4) to play the Q on the 2nd trick. They would therefore play the 10, tricking S1 into thinking S4 held the 9-10-A of trump. But S1 in turn knows that S4 is analyzing how they (S1) is assessing the situation, and realizes S4 will try to deceive them. Thus, the play of the 10S will be interpreted as S4 holding the 9-10-Q of spades. This circular reasoning continues, such that S4 can, in fact, be sure of nothing, except that S4 originally held at least the 9-10S.

irishwolf
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Unread post by irishwolf » Sun Apr 02, 2023 12:24 pm

I will say this - IT'S NOT CLOSE (ASSUMING QS IS STILL IN PLAY) THAT S1 SHOULD LEAD HIS KS TO TRICK 3.

Without doing the math there are only 11 unknown cards that QS & AS could be available to S4. Estimating that the QS is 28%. If could have it and if an AH or AD is led S4 would have to have a void even if he had QS to trump it. That chance is around 6 to 7%, a third of 28% at best (or worst). Still does not guarantee a euchre either.

And if S4 had the QS leading the KS, all those are 4 pointers.

And suppose S4 had the AS and KS is led. He also has to have two winning Clubs (S2/S4) off suit cards to get a Euchre. That as well will be around 5 to 7% (estimating) euchre rate.

What if the score is 6 to 9 their favor? What are you going to do.

I do hope others weigh in their thoughts.
IRISH

raydog
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Unread post by raydog » Tue Apr 04, 2023 2:03 pm

All simulations are over 100,000 hands.

1) In the first scenario, I gave S1 the K-JS + AH + AD + JC, and made the 9S the turn card. I then looked only at hands where S2 had no trump (34,898).

When leading the KS on trick 3 (instead of the AH), sweeps increased from 25,756 to 27,265 [+1,509] and euchres increased from 410 to 2,439 [+2,029]. Leading the AH is slightly better.

2) In the 2nd scenario, I did the same as in 1) but additionally gave S4 the 10S. (48,220 hands counted)

When leading the KS on trick 3 (instead of the AH), sweeps increased from 27,107 to 32,419 [+5,312] and euchres increased from 1,458 to 5,817 [+4,359]. Leading the KS is better.

3) In the 3rd scenario, I did the same as in 2) but additionally gave S2 the 9H and 9C. This scenario most closely matches the exact situation I described in my initial problem. (62,696 hands counted)

When leading the KS on trick 3 (instead of the AH), sweeps increased from 34,995 to 41,732 [+6,737] and euchres increased from 2,038 to 7,351 [+5,313]. Leading the KS is better.

I also tried giving S2 the 9-10C or the 9-10H, and the results were very similar.

4) Finally, I simply set the cards in S1's hand and the turn card, and nothing else. And I looked at all 100,000 hands.

When leading the KS on trick 3 (instead of the AH), sweeps increased from 85,716 to 87,177 [+1,461] and euchres increased from 431 to 3,697 [+3,266]. Leading the AH is better.

The reason I tested these 4 different scenarios is to show how the details matter A LOT. It's not just the hand that S1 holds and the turn card that matter, but what cards are played by S2 and S4 on the 1st 2 tricks. If you're not paying attention to what is being played (4th scenario), it's better overall to lead the AH on the 3rd trick. If you only notice that S2 is void in trump (1st scenario), it's still better overall to lead the AH on the 3rd trick. If you notice that S2 is void in trump and that S4 plays the 9 and 10 of trump on the 1st 2 tricks (2nd and 3rd scenarios), it's better overall to lead the KS on the 3rd trick.

Why the differences? I examined 3 different possible card distributions in detail.

A) S4 has all 4 remaining trump
- S1 will ALWAYS get euchred if S4's 5th card is a C
- if S1 leads the AH on the 3rd trick and S4 has a red card, S1 will always get 3 tricks and a point (either
on the 3rd trick, if S4 has a H, or on the 5th trick, if S4 has a D)
- if S1 leads the KS on the 3rd trick, S4 will win with the A and lead back a trump, forcing S1 to discard
one of his aces. This means some chance (up to 50%) of saving the wrong A and getting euchred.
So in this case, it's better to lead the AH on the 3rd trick.

B) S4 has Q-10-9 trump
- S1 will ALWAYS get a sweep if he leads the KS on the 3rd trick
- if S1 leads the AH (AD) on the 3rd trick, he will get the sweep if S4 holds any H (D) (27 - 40% odds, depending on
what S2 discarded on the first 2 tricks - S1 should lead the red Ace from the longest remaining suit)
So in this case, it's better to lead the KS on the 3rd trick, though about a third of the time S1 will still
get a sweep if he leads an Ace


C) S4 has A-10-9 trump
- S1 will ALWAYS get a point if he leads and Ace on the 3rd trick
- if S1 leads the KS, he will always be euchred if S4 holds 2 clubs, will always get a point if S4 holds 3 red
cards, and risks getting euchred if S4 holds a C and a red card (if the C is played first and S1 discards
the wrong A)
So in this case, it's better to lead the AH on the 3rd trick.

What's ultimately important is how often each of these 3 distributions occur (relative to one another) and how badly they hurt S1 if he makes the less optimal play. It's the former that changes among the 4 scenarios I described at the beginning of this post. While Irish was confident that the answer to my problem was obvious and not even close, I would be surprised if someone could accurately assess all 4 scenarios I presented and determine the correct card to lead. Maybe Irish has a good gut feeling based on countless hours of play, but these differences seem subtle and difficult to weigh against each other.

A couple more thoughts. Irish asked what the play would be if S1/S3 were losing 9-6. In that case, the euchres can be discounted to -2pts vs. the base case of scoring 1 pt [once you've lost 1 pt you've lost the game], while the sweeps are still worth +3 pts. So as long as the increase in euchres is 2/3 or less than the increase in sweeps, it would be better to play the KS and increase sweeps.

Irish also mentioned the case where S1 holds A-KH rather than AH + AD. This would affect how badly S1 gets hurt by making the less than optimal lead (as per my detailed descriptions of the card distributions above), since S4 is more likely NOT to hold a H in their hand. I would predict on that on balance it would swing the pendulum toward making the conservative play of leading the AH on the 3rd trick, but I'd have to do the simulation to be sure (and I'm not going to).

irishwolf
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Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Tue Apr 04, 2023 4:19 pm

RAY

I am having difficulty understanding your conclusion that AH is better here:

When leading the KS on trick 3 (instead of the AH), sweeps increased from 25,756 to 27,265 [+1,509 = 6036 pts] and euchres increased from 410 to 2,439 [+2,029 = -4058 pts][/b]. Leading the AH is slightly better.

Leading KS scores +6036 pts to -4058 euchres? Almost 2000 more points! (A 5.8% increase in euchres 2029/34,898.) S2 having no trump 35% as Hal hit on the nose. Thurs S2 65% (of 3 unknown) he has 1 or more.

What am I missing that AH is better?

IRISH

raydog
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Unread post by raydog » Tue Apr 04, 2023 5:50 pm

Sorry for the confusion, I didn't post the full results. Since both sweeps AND euchres are increasing, something must be decreasing. In fact, it's hands where you score 1 pt. 1,509 + 2,029 = 3,538 hands where you no longer score a point, so -3,538. All told, you score 1,560 fewer pts over ALL hands when you lead the KS.

Similar logic for the other hands: base case is scoring a pt, and extra sweep is worth +3, and extra euchre is worth -3.

sdu754
Posts: 42
Joined: Sat Jan 23, 2021 3:15 am

Unread post by sdu754 » Tue Apr 04, 2023 6:00 pm

irishwolf wrote:
Sat Apr 01, 2023 9:40 pm
This is about maximizing points - 10,000 hands. So you Must lead the KS on trick 3.

So what is the reason? It is just as likely that S4 has QS as he would the AS. So every time he has QS and you lead one of the ace, it might get trumped. You still have two Aces of which opponents will end up leading to one of them. If S4 has 4 trumps, low chance he still has to lead and will most likely to one of your aces. This is only if S4 plays 10S in sequence.

But what if S1 had A/K? Forced to lead one of these on trick 3.

IRISH

THIS IS AN ADDENDUM AS I WILL ASSUME S4 IS 'SMART'.
If he had the QS as well as the 10S, he would have played (QS) it instead of the 10S to trick 2. Thus either he has the AS or no more trump! So leading an ace is better!
What if the seat that has the ace of Spades is two suited and the non-Trump suit is one that you don't have an Ace in. You would then get Euchred.

sdu754
Posts: 42
Joined: Sat Jan 23, 2021 3:15 am

Unread post by sdu754 » Tue Apr 04, 2023 6:07 pm

raydog wrote:
Tue Apr 04, 2023 5:50 pm
Sorry for the confusion, I didn't post the full results. Since both sweeps AND euchres are increasing, something must be decreasing. In fact, it's hands where you score 1 pt. 1,509 + 2,029 = 3,538 hands where you no longer score a point, so -3,538. All told, you score 1,560 fewer pts over ALL hands when you lead the KS.

Similar logic for the other hands: base case is scoring a pt, and extra sweep is worth +3, and extra euchre is worth -3.
Great simulation, as always. Once again, my gut feeling was right. It is better to risk only scoring one point than getting euchred.

irishwolf
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Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Tue Apr 04, 2023 9:31 pm

sdu, did you read the results of what Ray said?

3) In the 3rd scenario, I did the same as in 2) but additionally gave S2 the 9H and 9C. This scenario most closely matches the exact situation I described in my initial problem. (62,696 hands counted)

When leading the KS on trick 3 (instead of the AH), sweeps increased from 34,995 to 41,732 [+6,737] and euchres increased from 2,038 to 7,351 [+5,313]. [color=#FF0040]Leading the KS is better[/color]. :lol:

IRISH

irishwolf
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Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Tue Apr 04, 2023 11:53 pm

RAY,

I don't agree with your math. You are deducting 1509 twice - once on loners then again for the euchres?

25,756 to 27,265 // +1,509 x3 + 4527 pts He would have +1 had he led AH. Not decreasing 1509 but adding +3 for each loner. Thus this is not a decrease but an additional + 4527 points. The euchre points stay the same -4058. So that is 4527 - 4058 = +469 leading the KS.

IRISH

raydog
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Joined: Thu Sep 16, 2021 6:56 pm

Unread post by raydog » Wed Apr 05, 2023 2:09 pm

Here is the full data set (1st scenario):

34,898 hands counted (ones where S2 has no trump)
lead AH, 3rd trick: (25,756 / 8,732 / 410) [sweep / 1 pt / euchred] EV = +3.18
lead KS, 3rd trick: (27,265 / 5,194 / 2,439) EV = +3.13

irishwolf
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Joined: Tue Apr 24, 2018 9:33 pm

Unread post by irishwolf » Wed Apr 05, 2023 3:49 pm

THANKS!

IRISH

sdu754
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Joined: Sat Jan 23, 2021 3:15 am

Unread post by sdu754 » Fri Apr 28, 2023 11:53 pm

irishwolf wrote:
Tue Apr 04, 2023 9:31 pm
sdu, did you read the results of what Ray said?

3) In the 3rd scenario, I did the same as in 2) but additionally gave S2 the 9H and 9C. This scenario most closely matches the exact situation I described in my initial problem. (62,696 hands counted)

When leading the KS on trick 3 (instead of the AH), sweeps increased from 34,995 to 41,732 [+6,737] and euchres increased from 2,038 to 7,351 [+5,313]. [color=#FF0040]Leading the KS is better[/color]. :lol:

IRISH
I did read the scenario; it is only when Raydog added Trump to the fourth seats hand that leading the King of Spades was better. When he ran the simulation with the fourth seat having random cards rather than predetermined cards, it was better to lead one of the two Aces. In the totally random scenarios (which was scenarios one and four) leading an Ace was best.

Tbolt65
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Location: Las Vegas

Unread post by Tbolt65 » Wed Jun 21, 2023 12:14 am

Regardless of what was posted by Ray on his simulataor over all I would lead the Ace. very rarely would I gamble and lead the King. I have and it has worked out but the majority I am personally leading an Ace.


Tbolt65
Edward

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