[neilkaz]

Of course most players at this level are familiar with the basic restricted choice with a 9 card fit. https://www.larryco....nter/detail/103 Cohen goes on to say "Furthermore, many theorists and bridge mathematicians say all this "restricted" talk is hogwash. They say it is simple math: J98 or Q98 is twice as likely to have been originally dealt than 98 doubleton."

But what about when there's an 8 card fit. Today, late in a very successful session I had in trumps AKT9 in dummy and PD declaring had xxxx. When he played the Ace the Queen fell from my LHO. PD had plenty of entries back to hand to then take two trump finesses against my RHO's remaining Jxx without harming his hand for later in the play.

However, PD said that a 32 split is considerably more likely than a 41 so he played for QJ doubleton to my left. I thought that restricted choice still applied.

I'll let the experts and math guys here tell me who's right on a percentage basis. There was no opposition bidding to give any clues as to distribution of other suits.

Thx .. neilkaz ..

PS .. yeah yeah..I need to learn how to work out probabilities of possible distributions in a suit.

[smerriman]

(ignore me)

[johnu]

The same basic argument for playing for singleton queen applies for the case when you are missing 5 cards. Similarly,

AK109

xxx

missing 6 cards and the ace drops the queen on the first round, etc. Of course, with an 8 card fit, sometimes other considerations may come into play and you may have to play for the drop, e.g. you have to ruff in the high trump hand so you can't pick up a 4-1 break.

[neilkaz]

smerriman, on 2016-June-25, 21:53, said:

I think the big difference here is that it's not just a case of deciding between Qx and QJ - any defender will also drop an honour from QJx.

With 8 trumps a trick will of course always be lost when QJx are offside and will always be lost once the ace is played. Qx is irrelevant isn't it and why would my LHO drop the Q from Qx when she knows from the bidding we are in an 8 card fit or even if she has no idea how many trump are in the closed hand? My question remains as to what the best percentage odds are with an 8 card fit xxxx opposite AKT9 and many entries back to hand to take two finesses vs RHO's presumed remaining Jxx?

Regarding dropping an honor from QJx offside this is a common ploy to induce declarer to use (hopefully wasting) an entry to finesse again but that is off no concern here nor to my question.

Thx .. neilkaz ..

[Stephen Tu]

Yes, restricted choice principles still apply. For me, the easiest way to do these problems is just to look at the initial probabilities and tally up which holdings you are picking up:

1. 8 card fit.
If you play for QJ tight when an honor drops offside, you are picking up 1/10 of the 2-3 breaks (10 ways to choose 2 cards out of 5). 1/10 * 1/2 * 67.83% = 3.39%
If you hook if an honor appears, you are picking up 2/5 of the 1-4 breaks. 2/5 * 1/2 * 28.26% = 5.65%

2. 9 card fit.
QJ tight is 1/6 of the 2-2 breaks. 1/6 * 40.7 = 6.78%
honor stiff is 1/2 of the 1-3 breaks 1/2 * 1/2 * 49.74% = 12.44%

The main time you should be playing for the drop in these restricted choice situations is a suit like xx opposite AKQ9xx where you would get owned by someone who is capable of playing an honor from JTx offside on occasion if you decided you were going to try to hook instead. Most other cases finessing tends to work out better.

[Phil]

Yes, its 2:1 the finesse works relative to QJ off but don't be surprised if you've wasted a vital entry trying to pick it up only to find QJx off.

[kenberg]

neilkaz, on 2016-June-25, 21:47, said:

However, PD said that a 32 split is considerably more likely than a 41 so he played for QJ doubleton to my left. I thought that restricted choice still applied.

There are 3-2 splits where the Q will be played and 4-1 splits where the Q will be played. The point being that we are no longer interested in simply comparing the frequency of 3-2 splits to the frequency of 4-1 splits. We are interested in 3-2 splits where his rho would play the Q, and 4-1 splits where his rho would play the Q.

IF we assume that declarer's rho would only play a Q or J when he holds QJ tight, then restricted choice, however one thinks of it, still applies. If he had the Q he had to play it, if he had QJ tight he could play either, so it is more likely that the Q was played because of restricted choice.

As has been noted, if declarer's rho has QJx, he can safely play the Q since the AKT are in plain sight. This is an extra wrinkle. He could be hoping declarer will use up his entries. Or show more of his high cards. Another possibility is that with QJx he hopes, by playing the Q, he can get declarer to play restricted choice and then, after defnder gets his J, he can play a third round of trump. Or he can attack in another suit. Had he played x from QJx, declarer had the option of playing another high trump and then leaving a trump outstanding whille developing the rest of the hand.

So the Q could easily be a false card from QJx. But if it is simply a matter of picking up the suit then ignore the falsecard possibility and go with restricted choice.

[Fluffy]

It still applies, but as Stephen Tu explained in detail, the 2/1 ratio doesn't hold anymore and it gets closer.

Just out of curiosity, the most common restricted choice scenario is not with 9 trumps, it happens anytime you play towards AJ10 and lose the first finesse.