[Fluffy]

A1076

985


you run the 9, wich loses, run the 8 wich loses, and finally lead the 5, LHO playin 2, 3 and 4.

What is the percentage for drop vs finese? Assume for the shake of arguments that RHO never wins King then Jack, but any other combo is possible, (JQ, JK, QK, QJ or KQ)

wich combos are different between them?

[WellSpyder]

Simplest to forget the order or exact cards played by RHO. There are 3 doubleton honour combinations he could have held and one tripleton honour, so the third-round finesse is 75% on to win.

[JLOGIC]

Yes in a theoretical vacuum this is 3:1, a little less since KQJ tight is more likely than an individual 4-2 combo.

In practice since they can't win the K and then from the jack from KJ doubleton so it's a little bit different.

[Fluffy]

my intuition tells me that winning Jack then King seems more forced (there are no options with KJ tight) than winning the queen first for example, is this wrong?

[hanp]

The odds are still 3:1. (yes, a little bit less than that)

[JLOGIC]

Fluffy, on Sep 14 2010, 01:17 PM, said:

my intuition tells me that winning Jack then King seems more forced (there are no options with KJ tight) than winning the queen first for example, is this wrong?

This is wrong because they can just adjust by never playing the K then J from KQJ.

[ceeb]

JLOGIC, on Sep 14 2010, 01:42 PM, said:

Fluffy, on Sep 14 2010, 01:17 PM, said:

my intuition tells me that winning Jack then King seems more forced (there are no options with KJ tight) than winning the queen first for example, is this wrong?

This is wrong because they can just adjust by never playing the K then J from KQJ.

Yes, but maybe worth noting that the adjustment is a little intricate:

KQJ can follow 5 ways: KQ QK QJ JQ JK
KQ can follow 2 ways: KQ QK
QJ can follow 2 ways: QJ JQ
KJ can follow 1 way: JK

So if KQJ chooses each play with probability 1/5, then JK would be 5:1 to be a doubleton and other plays would be 5:2. In order to get the same 3:1 always, KQJ must give 2 "shares" to JK, playing JK 1/3 and other combinations 1/6.

(Alternatively you can (I think) make a rule to always play upwards and choose to hide each card from KQJ with probability 1/3. That means you select your first play with relative probabilities 4:2:0 for J, Q, K.)

If considering all 5 carding orders, ideally select the first play with relative probabilities 3:2:1 for J, Q, K (then after the J, be 2/3 to next play the K). It may be unrealistic to imagine that defenders actually come close to this. In particular if you think your RHO opponent is even 1/3 to play the K first from KQJ, then when you see KQ played on the first two tricks it might be right, if there is a modest additional clue, to spurn the third round finesse.

[Fluffy]

This problem happened to a friedn at a local club, he had all the stoppers and entries neccesary to try the triple finese for the overtrick instead of the 3-3. He losed to KQJ.

RHO was very nice to tell him: Nevermind, the cards will be offside for everyone