[JLOGIC]

I have that 4 people were in 3D, 8 1N, 8 3N, 1 5D.

So 3D should get: (.56*8)+(.7*8)+(.5*3)+1=12.58

1N should get (.5*7)+(.7*8)+(.44*4)+1=11.86

3N should get (.3*4)+(.3*8)+(.5*7)+1=8.1

5D should get 0

Converted to a 12 point scale that is:

3D=7.55
1N=7.12
3N=4.86

With rounding that is:

3D=8
1N=7
3N=5

The 2 errors i found with your method were 1N was not getting .7 vs 3N, and 1N was only getting .3 vs 1N when it should get ,.44 (it wins the 30 % of the time 1N makes 3, and wins the 20 % of the time 3D makes 3).

[inquiry]

JLOGIC, on Aug 29 2010, 03:19 PM, said:

3N now scores higher than 1N?

It seems like your formula is off. You make 1N>3D only 30 % of the time. However, as far as I can tell, 1N is better than 3D the 30 % of the time it gets a spade lead, plus the 20 % of the time that 3D only makes 3.

So if my math is right, 1N>3D 44 % of the time.

Also, 1N should get a point 70 % of the time vs 3N, and 100 % of the time against 5D.

This surpised me too, but I didn't double check it. It turns out that I left off the scores for 1NT beating 3NT when 2NT is the limit

For 1NT, it gets 1/2 point for all other 1NT's, there were 8 in all, so that is 3.5 matchpoints. It gets 1 point for the 5D contract, that is 4.5. It gets 30% of a full point for each 3D/2D contract when it makes 3 (.3x4 = 1,2), plus it gets .18% of a full point for each diamond contract where 3D is the limit, but correcting for when 9 tricks make because that has already been factored in, so it will be 70% of .18x4 or 0.504 pts. In addition, it beats 3NT 70% of the time, so .7*8 = 5.6. Totally those up you get 3.5+1+1.2+0.5+5.6 = 11.8.

11.8/20 is 0.59 and 59% of 12 is seven.

So on this hand, both 1NT and 3D will get a SEVEN now. Up until someone shows another major flaw.

I will post a corrected score and list of who is where now

[awm]

I do not understand your "4♦ makes in the 80% range."

If the ♠AQ are both behind the KJx, then a spade lead sets 4♦ off the top. That by itself seems to reduce 4♦ below the 80% range, even double-dummy.

Suppose a heart lead against 4♦. If both spade honors are onside then you can obviously make. Otherwise you need to establish a club trick. So you pull trumps and lose a club trick. Now opponents cash a heart and a spade is lead through dummy. You have to guess which spade honor is onside, and if you go wrong you'll be down.

In practice, I'd say that 4♦:

(1) Always goes down if ♠AQ are both offside (25%)
(2) Makes if both ♠AQ are onside, assuming we play for that (25%)
(3) When one spade honor is onside (50%), makes if we can establish a club trick (75%) and we guess which spade honor is onside (roughly 50% of the time).

Adding these up I get around 25% + (50% * 50% * 75%) < 44% for 4♦ making. Perhaps we can add a little because our spade guessing ability is better than 50%, and add a little because the opening lead might be a club. But I also assumed that we can always decide correctly which of ♠AQ on or ♣ trick to play for, which might not be true at the table either.

I just can't fathom 4♦ being remotely close to 80% at the table (more like 50% or a bit below). Your double-dummy simulator is overestimating the odds of 4♦ making by almost a factor of two by assuming that we always get the guess right on the spade suit.

[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.

[gnasher]

I'm a bit puzzled by all this talk of nine tricks in notrumps. If the bidding starts
  1♦ pass 1NT pass
It seems to me overwhelmingly likely that West will lead a heart.

The possible explanations for East's failure to overcall are:
- He doesn't have five hearts. Then West has five hearts, and will lead them 100% of the time.
- East has five hearts but a poor hand. However, that would usually give West a takeout double of 1NT, so can almost be ruled out by the bidding.
- East has five poor hearts in a moderate hand. That will probably make a heart lead automatic from the West hand. What would you lead after this start from AQxx KJ9x xx xxx?

(Edited to (1) correct my confusion about East and West, and (2) make the example more believable.)

This post has been edited by gnasher: 2010-August-30, 04:36

[Mbodell]

Mbodell, on Aug 29 2010, 01:22 PM, said:

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]

Mbodell, on Aug 30 2010, 01:06 PM, said:

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?

Quote

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]

gnasher, on Aug 30 2010, 05:15 AM, said:

Mbodell, on Aug 30 2010, 01:06 PM, said:

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?

Quote

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:

awm said:

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.