Spot the fallacy.

[mikeh]

I don't think Mikeh's post is the entire picture.

 

It is absolutely correct that if we never play the ten from QT76 and sometimes play from T76, then a finesse of the 8 is correct as there is the inference that the ten might have been played from T76.

 

However suppose that you actually hold QT76, then you know looking at dummy that if you follow the never play the ten strategy declarer will deduce that the percentage play is to finesse the 8 and therefore you are always going to lose.

 

Look at the implications if we suppose that we play

the T a fraction y from QTxx

and a fraction z from Txx.

 

Then ignoring shape considerations if the play proceeds K629, 37..

 

The 8 is correct if LHO QT76 = (1-y) combinations

The J is correct if LHO Q76 = 1/2 combination (restricted choice on T9)

The A is correct if LHO T76 = (1-z) combinations

 

However if the play were to proceed K629, 3T... Then:

 

The J is correct if LHO is QT6 or QT76 = 1/2 + y combinations (assuming RC on 97)

The A is correct if LHO is T76 = z combinations

 

The natural strategy suggested in Mikeh's post (y=0, z=1/2) presents declarer with a guess when the ten is played and makes the 8 the correct play if the 7 is played.

 

However we could adopt an alternate strategy of:

y=1/2 and z=1 ( play T half the time from QTxx and always from Txx)

Here we again have a guess when the T is played, but we also have equal odds of the Jack or 8 being correct when the 7 is played.

 

So whats the best bet for declarer when the 7 is played?

- Proabably the 8

when LHO has little clue z rates to be greater than equal to y

when LHO is fairly decent he might tray making z=1/2+y, in which case probability the 8 is right = (1-y)/((1-y)+1/2+(1-z) = (1-y)/(2-2y) =1/2

 

Whats the best strategy in defence?

Well if you're an evil genius and you decide that everyone else is playing some kind of z= y+1/2 strategy, you might try inserting the T always from QT76 safe in the knowledge that declarer will view this as a guess. Meanwhile you can now just play low from T76 and watch declarer get it wrong every time.

 

Sometimes bridge is just amazing

I started my post by saying that you should consider playing the 10 from 1076 'at least quite often'. I used that language precisely because, on a theoretical basis, the best line is some form of mixed strategy. In the real world, these situations come up infrequently, and you are unlikely to be met with this combination and the same opp very often... so when you and the opp are unknown quantities, as far as each is concerned, you are probably well advised to 'always' play the 10, but NOT if rho is known to be good and known or suspected to think that YOU are good :huh: But this was a B/I thread, so I omitted this part

[Simplicity]

Apologies to mikeh, i had meant my post as an expansion rather than a rebuttle, but rereading it didn't matierialise as such.

 

Admittedly the application of game theory in these situations isn't particularly BIL stuff, but i do find these situations interesting and somtimes make plays based purely on whether i think the opponents are good or if they rate my play.