[ahydra]

I had to play this suit combination (trumps) for one loser:

3 (dummy) opposite KQT8652 (hand)

Clearly any 4-1 or 5-0 break is hopeless, so we can focus on the 3-2 breaks. When I led the 3 from dummy RHO followed small.

Do I put up the K or the T?

There are the following cases:

Jx / Axx (3), play K then Q
xx / AJx (3), play T
Ax / Jxx (3), play T or K then small
AJ / xxx (1), play K then Q

Axx / Jx (3), play T or K then Q
Jxx / Ax (3), play K then small

(The case AJx / xx is hopeless, and the case xxx / AJ isn't relevant because RHO followed small)

So playing K then Q wins in 7 cases, K then small in 6, and T in 9. Or considering only the current trick, putting the K up wins in 13 cases and putting up the T in 9 cases. Hence, I should put the K up, right? That's what I thought (after a very messy attempt at calculating this at the table), but both BridgeHands and SuitPlay suggest the T is right - what did I miss?

Thanks,

ahydra

[johnu]

If you play the king, you have to guess whether to play queen or low on the next trick in the suit since you can't do both. You have to guess better than the odds for playing the 10 first.

[Stephen Tu]

You don't get to pick up ax offside by playing k. Lho won't duck.

[The_Badger]

johnu, on 2018-November-30, 03:55, said:

If you play the king, you have to guess whether to play queen or low on the next trick in the suit since you can't do both. You have to guess better than the odds for playing the 10 first.

That's it in a nutshell: the raw statistics versus the guesstimate. With the possibility of two potential losers, and only one opportunity to finesse, the finesse of the ten is best. (And trust me, I would have probably done the same as you, trying to work it out at the table and come to the wrong decision too.)

[mikeh]

As Stephen noted above, you cannot win by playing low to the K or Q if LHO has Ax: he simply wins all the time.


If you play low to the K:


LHO has Ax: he wins, and your play fails

LHO has AJ: he wins and you have no choice next time

LHO has Axx: he ducks and you have to guess next time.

LHO has Jx: he ducks perforce and you have to guess next time

LHO has Jxx: he ducks perforce and you have to guess next time.

Assume you guess right half the time. We can then assess the possibilities as being half the actual case number. There are 3 Axx combinations, but you will get them right only half the time, so it counts as 1.5 cases.

You win 1 case of AJ tight, 1.5 cases with Axx, 1.5 with Jx and 1.5 with Jxx. For a total of 5.5 winning cases.

Compare to low to the 10.

This wins every time RHO has Jx or Jxx or AJx. There is no subsequent guess.

There are 3 Jx combinations, 3 Jxx combinations and 3 AJx combinations.

Thus there are 9 combinations where low to the 10 wins, and (superficially) 5.5 cases where low to the K will lead, on average, to a win.

However, in real life some LHOs, either because they don't know any better or because they are not focused, will win from Axx when we lead low to the K/Q, leaving us with no play other than other top honour. Depending on the calibre of one's LHO, then, the winning cases for low to the K/Q may be as high as 7! That is still far short of the 9 winning cases for low to the 10.

The biggest difference, and the easiest to identify at the table is AJx onside: 3 cases where low to the 10 wins. AJx offside is hopeless, so the comparable is AJ offside, 1 case, where low to the K/Q wins.

[gszes]

In your original logic you had Ax Jxx as winning when you played the T OR (K or Q) then small. This might be messing with your thinking since when u play the (K or Q) on the first round the A wins and the remaining Jx will eventually score up a second trick

[sfi]

You don't need to go through all the combinations to show that low to the 10 is right. Assuming a 3-2 break, low to the 10 is 50%.

Compare that to low to the King and then playing the Queen. That relies on the Jack being doubleton, which is 40% (choose 2 of the 5 cards to put in the short hand). Low to the King and a low card next is even worse - you are basically playing for Ax onside (20%) or AJ offside. Clearly neither line is better than a finesse.

[ahydra]

Right, so my error in logic was assuming I would always guess correctly on the second round. Makes sense, and I'll be sure to revisit this combination once my transformation into Jeff Meckstroth is complete Thanks all for the explanations and apologies for the mistake re. Ax with LHO.

The actual layout was in fact Ax/Jxx, so I went one down but still won IMPs after the other table was unwisely in 3NT.

ahydra

[PhantomSac]

Your error is akin to thinking AJxx opp KT9x is 100 % to be picked up, so maybe you are transforming to meck!