Round 2, Board 13

[Mbodell]

FWIW I'm in the process of single dummy simulating this using Jack.  My early too small sample size suggests that this still grossly underestimates the chances of 9 tricks in nt and overestimates the chances of 10 tricks in diamonds.  It will take quite a while though as single dummy is super slow, so I might not update results until Monday.

Well I've finished a run of the single dummy test - and inquiry's later estimates have the same answer even if they arrive at it slightly differently. I was using Jack 4.01 on championship mode (AKA the highest settings and also set playing MP) and it takes around 2 minutes a hand. I was trying to sim the play after the unopposed auction 1♦-1nt-3♦-3nt. There were no explicit rules about points or shape for E/W, just that they had to be hands that Jack would decide to pass with. Now even though the hands were generated ahead of time with Jack agreeing with this auction, when run through the simulator occasionally Jack bid 1♦-1nt-3♦-5♦ so I picked up a few 5♦ hands as well and tracked how many tricks they made. For the 3nt I tracked the leads, for the 5♦ I didn't.

 

Now this will be, probably, slightly unfair to 3♦ and 1nt as defending against 1♦-1nt will be harder as the auction gives less away and it is less clear that you are especially trying for 8 tricks (those would also be harder to sim as even on hands that Jack would pass on the 3nt auction, he'd tend to bid on 1♦-1nt and 1♦-3♦(inverted) if passed out based on my early testing). You can see that occasionally Jack goes for the contract at risk of the 8 sure tricks, where in 1nt you might just cash out. Also, none of these test 1nt or 3nt from the long diamond side, which is worse on spade leads (but better on club leads) which may not work out the same.

 

3nt was bid 446 times
3nt made the following number of tricks:
5 tricks: 1 times
6 tricks: 3 times
7 tricks: 20 times
8 tricks: 284 times
9 tricks: 99 times
10 tricks: 34 times
11 tricks: 5 times
Spades were lead 48 / 446 times (0.10762331838565)
When spades were lead the contract made 48 / 48 times (1)
Hearts were lead 377 / 446 times (0.845291479820628)
When hearts were lead the contract made 74 / 377 times (0.196286472148541)
Clubs were lead 21 / 446 times (0.047085201793722)
When clubs were lead the contract made 16 / 21 times (0.761904761904762)

5d was bid 54 times
5d made the following number of tricks:
8 tricks: 2 times
9 tricks: 7 times
10 tricks: 40 times
11 tricks: 5 times

 

As you can see hearts were lead even more than Inquiry thought, however ~20% of the time 3nt still makes on a heart lead. That means 3nt makes around 31% of the time which is close to Inquiry's suggested values.

 

The 5♦ simulation is a smaller sample size, but suggest that in this smaller sample Inquiry's ~80% estimate of making 10 tricks was pretty good. Now this might be an overestimate as the sample size is small and against 4♦ or 3♦ the defense might be different as the defense might have blown the 4th trick to guarantee the 3rd trick when defending against 5♦.

[gnasher]

As you can see hearts were lead even more than Inquiry thought,

I'd have expected it be even higher. Can you give some examples of hands where a heart wasn't led?

however ~20% of the time 3nt still makes on a heart lead.

Sorry if I'm being dense, but how? So far as I can see, 3NT can make legitimately only if one hand has all of the long hearts, ♠A and ♣KQ, but didn't bid; or if the hearts are blocked. I'd guess that those add up to much less than 5%, so your figure of 20% suggests that either Jack doesn't defend very well or I don't analyse very well.

[Mbodell]

As you can see hearts were lead even more than Inquiry thought,

I'd have expected it be even higher. Can you give some examples of hands where a heart wasn't led?

however ~20% of the time 3nt still makes on a heart lead.

Sorry if I'm being dense, but how? So far as I can see, 3NT can make legitimately only if one hand has all of the long hearts, ♠A and ♣KQ, but didn't bid; or if the hearts are blocked. I'd guess that those add up to much less than 5%, so your figure of 20% suggests that either Jack doesn't defend very well or I don't analyse very well.

I can when I get home tonight and have access to the details on the hands. Based on the couple I saw it was as awm suggested early on this thread:

 

There's even enough discarding pressure on the running diamonds that you could conceivably make nine tricks on a heart lead!

 

Not that it always happens, but that it sometimes happens. I checked out one of the hands where 3nt made and it seemed that the spade A was on side and hearts were 5-4 and led with the K in the opening leaders hand, declarer holds up and then wins the A but might still have, from RHO perspective, the heart K. LHO pitches some spades and clubs on the run of diamonds, and when we exit with a spade from the board RHO has only seen 4 points from the declarer and doesn't know if his partner still has the ♠K or the ♥K or either or both and ducks his ♠A.

 

I do know it is a lot harder to defend single dummy than double dummy, and in a real matchpoint game ~1 in 5 people making on a heart lead doesn't seem that unreal.