Any thoughts?

https://worldofcardgames.com/#!replayer ... %3A1%7D%5D
Unread post by Dlan » Wed Jan 19, 2022 11:44 pm
Unread post by RedDuke » Thu Jan 20, 2022 8:27 am
Unread post by LeftyK » Fri Jan 21, 2022 5:50 pm
Unread post by raydog » Sat Jan 22, 2022 4:33 pm
Unread post by irishwolf » Sat Jan 22, 2022 6:38 pm
Unread post by Wes (aka the legend) » Sun Jan 23, 2022 2:04 am
Really good stuff Ray. This is a spot I've always wondered about and it's also a spot that's too tedious--at least for me--to test at the kitchen table. I've played it both ways--trumping in with the Right in that spot and playing off--and I never really developed any good intuition on it. Seemed like I always chose wrongly no matter what I did in this spot. Your work shows a pretty decent gap in EV between playing the Right vs playing off. That's really strong evidence that playing the Right here is best.raydog wrote: ↑Sat Jan 22, 2022 4:33 pmI tried a simulation of this hand. I fixed the cards for S2 + the turn, and gave S1 the AH. All other cards randomized. Here's what I found:
100,000 hands; 49,795 bid by S4 (alone or w/partner); 23,779 where S1 leads the AH. S2 plays:
JC: (3,545 / 16,349 / 3,885) [2 pts/ 1 pt / euchred] EV = +0.66 [perspective of S2/S4]
10S: (803 / 17,817 / 5,159) EV = +0.38
JD: (804 / 17,728 / 5,247) EV = +0.37
It seems that S2/S4 do best if S2 trumps with the R on the 1st trick. The advantages are:
- S4 knows where the R is;
- S2/S4 win the first trick if S4 happens to NOT be void in H.
While S2 would like to be able to lead the R early in the game and draw out enemy trump, it's unlikely they will ever get the lead and the chance to do so.
I tried replacing the R with the AC, then with the 9C, then tried giving S2 2 trump (9C + QC, no 10S); in all these cases, trumping on the first trick gave a better outcome.
What if S1 leads a non-A H? I first examined only a KH lead. I made sure S1 had the KH (all other cards random), but it was rare that S1 decided the KH was the best lead.
100,000 hands; 39,663 times trump called by S4 (with partner); 2,618 times KH led:
S2 plays trump: (227 / 1993 / 398) EV = +0.63
S2 plays 10S: (225 / 1968 / 425) EV = +0.60
This difference is perhaps too small to be statistically significant, but it does look like playing trump leads to a couple more sweeps and less euchres.
I then tested if S1 led ANY H other than the A, and didn't seed S1's hand with any particular cards.
100,000 hands; 37,556 times trump called by S4 (with partner); 6,261 times a non-A H led by S1:
S2 plays trump: (741 / 4,657 / 863) EV = +0.70
S2 plays 10S: (748 / 4,642 / 871) EV = +0.70
The KH was likely led very rarely, so we are looking at mostly Q or lower leads. Both sweeps and euchres rise slightly if trump is not played, so the results here are truly ambivalent.
From these tests I would conclude that it is best for S2 to trump an A lead by S1, even if that means using the Right bower. It's possible this also holds true for a K lead, but for Q and lower leads it is not clear if it is better to trump or duck. Reasoning? If an A is led and S2 ducks, the trick can only be won if S4 trumps. If a lower card is led, the trick can be won by S4 trumping but also by S4 having the highest in the led suit, hence the disappearance of the advantage of S2 trumping.
Unread post by raydog » Sun Jan 23, 2022 8:36 pm
Unread post by Wes (aka the legend) » Sun Jan 23, 2022 10:49 pm
There's some problems here. First off, if S1 leads a non-Ace, S2 should not trump in with the Right in that spot no matter what his offsuit is. S2 should always throw off. That is so fundamental that even if a simulator suggested otherwise I wouldn't believe it. I would assume there's something wrong with the simulator.raydog wrote: ↑Sun Jan 23, 2022 8:36 pmIrish introduces a couple of unique twists:
1) If S2 has an off-Ace, I think that supports trumping, in order to lead the ace - let me know if I have misunderstood (an important consideration, just not undermining the prerogative to trump in this situation).
2) If S2 has a singleton, especially an off-suit, that could argue for playing off: if S4 is able to trump the 1st trick, they should view partner's discard as voiding themselves in a suit - very powerful. It's parlaying one void for a potential second winning void.
So I tested an initial hand of![]()
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with
turned. S4 calls C trump, and when S1 leads a non-A heart, S2 plays off with their KD to create a void in D (hoping S4 can win the 1st trick and lead back a D).
Here's what I found:
100,000 hands played; 36,476 called by S4; 7,257 a heart lead by S1 (non-A) and won by S4; 4,267 times S4 could lead back diamond [important to pay attention to the relative rarity of this particular sequence of events].
[note: the following is based on the instances of an non-A heart led by S1 and won by S2: 7,257 hands]
S2 wins with trump, leads KD: (1,033 / 4,716 / 1,508) EV = +0.52
S2 plays off (KD), S4 wins (higher H or trump) and leads back a D (when possible): (931 / 5,441 / 885) EV = +0.76
This gets rather confusing, but the idea is to isolate instances where 1) S4 calls C as trump; 2) S1 leads a non-A heart; and 3) S2 has the choice of trumping or discarding their KD [in the latter case, if S4 wins, they lead a D when possible]
It appears better for S2 to discard their singleton D rather than trump. This is really getting into the nitty gritty, as it is a rare choice for an equally rare hand, but it does validate Irish's intuition.
Unread post by raydog » Mon Jan 24, 2022 8:55 am
Unread post by Wes (aka the legend) » Mon Jan 24, 2022 8:06 pm
You're not missing anything. There's isn't much value to S2 creating a void in this spot. This is partially why I'm betting that trumping an Ace lead with the Right is best even if S2 can create a void. The other reason I'm betting trumping in is best in this scenario is I just think the gap in EVs your work has already shown suggests to me our other offsuit is not gonna matter.raydog wrote: ↑Mon Jan 24, 2022 8:55 amVery good analysis, Wes; I learned something. But if S4 is always going to lead back trump if they win the first trick (either with the highest card or with trump), and S2 only has 1 trump, what's the value in S2 getting void in a suit?
Perhaps S3 wins the first trick, and leads the suit S2 just voided herself in. But then we're back to the same decision as on trick 1: trump with the R or not? Let me know what I'm missing.
Unread post by irishwolf » Mon Jan 24, 2022 8:26 pm
Unread post by raydog » Tue Jan 25, 2022 10:23 am
Unread post by Wes (aka the legend) » Tue Jan 25, 2022 11:52 am
Yep, that's how I'd program it. And I wouldnt worry that there could possibly be some rare combos where this play is incorrect. Those hands would be so rare it wouldn't matter.raydog wrote: ↑Tue Jan 25, 2022 10:23 amI have a question for the experts:
Say S4 calls trump in R1. My program currently generally trumps in from S2 on the first lead, when possible, even with a lone bower (their only trump). I'm getting the impression this is not ideal, but I'd like to know the parameters I should test.
My current thinking is along these lines:
1) OK to trump with a bower (only trump) if an Ace is led because it shows partner where the bower is, almost certainly assures winning the trick, and avoids wasting the bower if S4 were to otherwise win 1st trick and lead back the other bower;
This possibility should never exist as the simulator should have S2 calling every time he has R+1. The exception to the rule--hands like #7 in my quiz--are so rare they just don't matter.
Yep. Perfect. Always play off with the Right in that spot.
Unread post by irishwolf » Tue Jan 25, 2022 7:31 pm
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