phil_20686, on 2011-January-16, 10:37, said:
i think the point is that if you know rho *always* plays his lowest card then me must have Q4 T4 or QT4, so now cashing is equal to finesseing.
There is more to it than this but you are on the right track. If RHO has Q4 or T4(let's ignore QT4 since we can't pick it up), that gives LHO T32 or Q32. This might mean there is restricted choice on LHOs second play which makes the drop 2:1.
HOWEVER, if LHO knows that we know that RHO always plays his smallest card, and he plays perfectly and we play perfectly, he does NOT have restricted choice as he must play the 3 and the 2 when his partner plays the 4 as he is known to have those cards. This means that this scenario is different for LHO than if he had T42 and his partner had played the 3 (since the location of the 4 is not known). So, LHO does not have theoretical restricted choice.
Also, there is the matter of QT32 to be accounted for. The possibility of QT32 and a double finesse means that LHO cannot be falsecarding the ten too often, both in this scenario and the T42 scenario, since he would never play the ten with QT32 (because if we happened to play the jack, he blew a trick).
An interesting phenomenon is the opposite of this, say you're playing against "experts" who always drop the ten. RHO drops the ten under the ace to "trick you" into thinking he must have QT, and RHO plays low then ten with Txx to "trick you" into thinking he has QTx. Against these people, what do you do if all the small cards appear (ace small small, low towards dummy and small). One possibility is that RHO has QTx and LHO 2 small and there's nothing we can do. The other is LHO has QTxx, and RHO has a stiff. Accordingly you should play the 9 against these people which shows the error of their strategy as a whole.
Now let's apply that to this situation, say LHO is actually playing the ten 50 % and the 3 50 % of the time, and the 3 100 % of the time from QT32. Now if he plays small then small, he has 50 % of his T32's and 100 % of his QT32's. Accordingly, we should play the 9 when it goes small then small, and the king when it goes small then ten. The amount of times they have to be falsecarding the ten by mistake to make this a worthwhile strategy is very small, probably something like 10% of the time, because remember there are as many combos of QT32 and stiff 4 as T32 and Q4 (1 lol), the difference is just that 1 3-2 break is a little more likely than 1 4-1 break.
All of this means that:
In theory it is 50/50 whether to play for the drop or not given RHO playing the lowest spot 100 %.
In practice, it is a little better to play for the drop because LHO will err sometimes and falsecard the ten thinking he can play either of his "spots" and must sometimes falsecard >0 % of the time.
However, if this is much greater than 0 % like 15+ % of the time, we should play low to the king if he plays the ten on the 2nd round, and low to the 8 if he plays low the second round.
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