[cherdano]

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You play in a trump suit, have plenty of extra trumps, and you can eliminate all side suits.

So which endplay do you pick in the suits? (Assume the suit doesn't break 5-1 if you want.)

Assume expert defenders. What if LHO had a chance to play a heart through earlier?

Arend

[SoTired]

With endplay, small to 10:

Without the endplay, the normal play is finesse the 8 which works about 40% of the time when LHO has the 9 + an honor.

The endplay changes things. Finessing the 8 gives you a 50% chance that the 9 is onside for the endplay to succeed. But small to 10 gives you more chances. If the 10 loses to an honor, and opp plays a small card back, then you must decide whether to play for split honors or KQ offside. Playing for split honors gives you better chances. I checked the odds and (unless I made a mistake):

(some plays always succeed like KQ-stiff, honor-stiff, or H9 onside. Or honor-stiff offside because the endplay will succeed)

Small to 8 =55%
Small to 10 and play J if small comes back = 59%
Small to 10 and play small if small comes back = 69%

You can estimate this at the table with the following logic: Finesse the 8 = 50%. But finesse 10 works 25% when KQ onside + 25% when KQ offside + H9-stiff offside has to be more than 50%. When 10 finesse loses to honor and small comes back, restricted choice rule is to play for split honors so duck.

[david_c]

It seems to be really close between leading the jack (if it's covered, cross back to hand and finesse the eight) and playing small to the ten (planning to play low from hand if RHO wins and plays a small one back). I think that a priori leading the jack is better, the difference being the probability of 9x with RHO, minus the probability of singleton K or Q with LHO. (All other layouts are exactly symmetric - the cards you want LHO to hold if playing small to the ten are the cards you want RHO to hold if leading the jack).

But this is so close that if LHO had the chance to lead a suit, and you don't have any other useful information, I think small to the ten becomes the favourite. This is because one of the losing cases for small to the ten (KQx(x) with RHO) is made less likely. [Also KQ9(x) is less likely, but both plays pick that up.]

[FrancesHinden]

edit: ignore rubbish I wrote

[han]

Ok, there are 3 lines.

A) Low to the 8.

B ) Low to the 10, low if east wins and a low comes back.

C) Lead the jack, if covered later low to the 8.

Low to the 10 and then playing the jack is clearly wrong so I won't consider it.

A and B both win when the 9 is right, so those probabilities cancel eachother. In addition B wins when wests has H9 (A also wins in that case but it is already counted), and when west has KQ9 (again, we shouldn't recount that possibility for A). A wins when west has KQ tight or stiff honor, and I think that that those are the only holdings where it differs. Both 3 holdings but the A holdings are less likely so B wins.

David is wrong that C wins when east has 9x, not against perfect defenders. Compared to A leading the jack only wins when east has stiff 9, but it loses when west has a stiff honor. So C is inferior to A and B wins.

Conclusion: B > A > C, unless I forgot some holdings. One really should use paper and pen when doing this.

[kenrexford]

Ace and out. I'm playing for KQ tight, or Kx-Qxxx/Kxxx-Qx or Qx-Kxxx/Qxxx-Kx.

Actually, I like this line best for the story.

[han]

I was so far off that I might switch to Tic-Tac-Toe. Apologies to David.