What is the best line in 7NT?

[Jlall]

Bid em up, when you play them for 2 cards it becomes less likely because of empty spaces.

[jdonn]

Actually the odds one player started with KJ is (exactly) 24%. So relying on a finesse is slightly better than relying on one or the other player to have KJ.

 

Think of it another way. If west has KJ both succeed, if west has J and east has K they both fail. So you are weighing K with west and J with east vs KJ with east. In either case east has the jack. If east has the jack it's 12/25 east has the king but 13/25 west has the king. Therefore a finesse is better.

If you say so.

 

As far as I can tell, there are only 4 relevant holdings, and the last time I checked, each is equally likely.

 

K♦ - J♥

K♦J♥ - neither

J♥ - K♦

Neither - K♦J♥

 

With the finesse you win in 2/4 cases, diamond King with West (50%) and the other way, you still win in 2/4 cases (KJ with East or West), same 50%.

 

Excuse my math, but I am too dumb to understand anything else.

But they aren't equally likely, regardless of when you last checked.

 

The first and third are 26%. The second and fourth are 24%. Therefore diamond king with west is 50%, but KD JH in the same hand is 48%. I know it's a small difference, but since it's provable it matters. It is a grand slam after all.

 

Sorry I don't feel like excusing your math since your math is wrong.

[dellache]

My first thought was to vienna coup the ace of diamonds, then cash two hearts, (unblocking the ten) and then cash black suit winners ending in the south hand. If the K of diamonds, or a heart, has not appeared then you need to read the position. west could be 1363 or 1453.

This is essentially the same as my given line, however, you do not cash the 2nd heart early in the hand, but instead at trick 11.

 

The fact that the diamond finesse is 50% in your line B is an illusion.

 

K - J

KJ - -

J - K

- - KJ

 

In your given line B (with the finesse), you win whenever West started with the K (50%). In (our) line A, you win if West started with KJ (25%) or East started with KJ (25%) which is the same combined 50% of the cases, just in a different manner. In Line A, it doesn't matter how many hearts or diamonds the hand started with, as long as both honors are in the same hand, but I think you stated that it does matter in your line B.

This is not true.

On this deal, the squeeze is rather useless (but stylish, you can still play for the squeeze after cashing 3 Hearts when West has shown Jxxx) when West has the 4 Hearts, and clearly inferior when East has the 4+ Hearts.

 

Clearly, when East has 4 Hearts (not mentionning 5), the diamonds are 7 to West, 2 to East, making the ♦finesse a 78% bet, and a squeeze... a 22% bet. Actually, The non diamond lead even increases this percentage by some (uncomputable but probably significative) margin, because West *may* have led a diamond from xxxxxxx(7) instead of a Club.

 

The a priori distribution of the ♦K-♥J is irrelevant. It doesn't take into account what you learn from hand (spade distribution), or what you infer from other suits (including Hearts) when you have to decide for the right handling of the diamonds.

 

Cheers.

[manudude03]

Once you know that say East holds the !♦K, there is only 12 spaces left to put the ♥J as opposed to 13 in the West hand, hence the probability that East has the J if he has the King is 12/25 (48%). You need to half that because of the assumption that he had the King in the first place.

[Jlall]

Yes, everyone who is thinking "vienna coup" is not thinking rationally about the hand once LHO shows up with 1 spade and 3 clubs, they are just regurgitating some vague concept they read in a book once.

[eyhung]

Actually the odds one player started with KJ is (exactly) 24%. So relying on a finesse is slightly better than relying on one or the other player to have KJ.

 

Think of it another way. If west has KJ both succeed, if west has J and east has K they both fail. So you are weighing K with west and J with east vs KJ with east. In either case east has the jack. If east has the jack it's 12/25 east has the king but 13/25 west has the king. Therefore a finesse is better.

If you say so.

 

As far as I can tell, there are only 4 relevant holdings, and the last time I checked, each is equally likely.

 

K♦ - J♥

K♦J♥ - neither

J♥ - K♦

Neither - K♦J♥

 

With the finesse you win in 2/4 cases, diamond King with West (50%) and the other way, you still win in 2/4 cases (KJ with East or West), same 50%.

 

Excuse my math, but I am too dumb to understand anything else.

That's like saying that if you buy a lottery ticket, one of two outcomes must occur:

 

1) you will win the lottery

2) you will not win the lottery

 

Under your reasoning, there is a 50% chance that you will win the lottery.

This reasoning is clearly flawed because the chance of the second case is not equal to the chance of the first case.

 

Similarly, saying that

 

KJ void

K J

J K

void KJ

 

are equally likely is false. The 1-1 breaks are slightly more likely. Say you knew that the King was held by West, and that was the only information you had. The chance of the jack being in the same hand is now 12/25 because there are 12 chances for West to hold the jack, but 13 for East. So the 1-1 breaks occur 26% of the time, and the 2-0 breaks occur 24% of the time.

 

KJ void 24%

K J 26%

J K 26%

void KJ 24%

 

There are four cases but each case is not equally likely, so the 1-1 break is 52% and the 2-0 break is 48%. And that's why it's mathematically odds-on to drop a king instead of finessing with 11 cards.

 

The logic is the same when deciding whether to drop or finesse a queen with 4 missing, or to drop or finesse a jack with 6 missing. You cash your extra high honors and lead up to the tenace. Your 2nd-hand opponent plays the last small card. At this point, it's 52% to drop, 50% to finesse. So barring any extra information, it's correct to play for the drop.