BBO Discussion Forums: Principle of Restricted Choice - BBO Discussion Forums

I put this in the wrong category Sorry!
Anyway,I've often seen this referred to in bridge books
but never fully understood the concept. So what does it really mean?
Does it imply a 'forced play' ? I need enlightenment.

This post has been edited by PhilG007: 2018-June-05, 04:48

A forced play is involved, yes. The Principle of Restricted Choice applies in a lot of situations, but is usually explained when there is a 9-card suit missing QJxx. When a high card is played and the Q or J appears, we know that a person who holds both could have played either one. However, if she held a singleton honour, her choice would have been restricted to playing that one card. Therefore, other things being equal, she is twice as likely to have a singleton honour than a doubleton QJ.

To be more precise, about 65%.
But only assuming that she is equally likely to play either Q or J when holding both, an assumption that is unlikely to be true.

https://en.wikipedia...stricted_choice

There is a good treatment of this subject in "Bridge Odds for Practical Players" Kelsey & Glaubert.

It is one of those subjects that you do need to spend a little bit of time studying, because it can be counter-intuitive and you need to trust the underlying principles, but it is a powerful way of understanding how bridge odds change as our knowledge changes.

It is also worth using the search functions on this site as we have discussed PRC several times.

Basically it means that when an opponent drops an honor, that is one of equal rank to another honor(s) missing, it is more likely that the opponent was forced to play it (he had only that honor of those equals), than that he had both of those honors and chose to play the one he actually did.

So the usual card position it is introduced with is xxxx vs. AKT9x. You play the ace and the Q or J falls on the right, behind the AK. Should you finesse or drop the next round? Basically there are two ways to think about it:1. You look at the card played. Say the Q fell. So RHO either had the stiff Q (which he is forced to play 100% of the time he has stiff Q). Or he had QJ and chose to play the Q (which he should ~50% of the time, but could be in reality more or less, doesn't matter unless he gets ridiculously extreme about always or never playing it). He is dealt stiff Q 6.22% of the time. He is dealt QJ 6.78% of the time. So as long as he plays the Q less than 6.22/6.78 = 91.7% of the time, finessing the 2nd round is better.

2. You decide to look at all the possible situations, treating the missing honors as amorphous "quacks". A drop strategy whenever you see either honor works only when RHO holds QJ (6.78% originally). A finesse works when RHO holds EITHER stiff Q or stiff J, 6.22 *2 = 12.44% originally. So finesse works 12.44/(12.44+6.78) = 64.7% of the time vs. 35.3% for the drop.

Generalizing to more cases, it basically means when looking at suit probabilities, for cases where RHO has more than one equal honor and drops it, you divide that holding by the number of equal honors since he might have chosen a different one. Or you use approach 2 and look at all the cases and develop an overall strategy looking at all the honor dropping cases.

But be careful not to apply it incorrectly to situations like xx vs AKQ9xx; if RHO drops the J or T he might be fooling around from JTx trying to induce a finesse. Restricted choice correctly tells you that if the J fell, stiff J is more likely than JT doubleton, so against an RHO incapable of dropping an honor from JTx, finesse is right. But if RHO knows to play an honor from the JTx enough times, it tilts the drop back to being best.

Tramticket, on 2018-June-05, 08:18, said:

Glauert (I happen to be reading it on recommendation of this forum)

pescetom, on 2018-June-05, 06:03, said:

While it's unlikely to be true, it doesn't change the overall odds (other than increasing them in your favour if you are aware of the opp's flaw and want to exploit it).

smerriman, on 2018-June-05, 14:26, said:

Yes and no.
So long as she makes some attempt to randomise play from QJ then the odds do not change much.
But taking it to extreme then they do.
If for instance she always plays Q from QJ then the impasse will be 100% if the J drops.

pescetom, on 2018-June-06, 05:52, said:

But then you'll see the J fall a lot less often. Your overall success rate if you continue to just finesse when an honor drops is still 64.7%, choosing not to exploit; you win anytime there is stiff honor which is independent of how often they are choosing a particular honor from QJ doubleton. Now you can try to exploit and increase your success rate to up to 67.6% (if opp always drops Q) by playing for the drop when the Q appears, but if you are wrong about your opponent and they are actually randomizing, your rate drops to 50%. Since your gain is relatively small vs. your loss if wrong, it's right to just play the normal way unless you are very sure your opponent is not randomizing nearly at all. I doubt one ever gets enough sample size against a particular opponent to be sure enough to make the exploitative play correct.

To understand the concept of Restricted Choice, you should first address the concept of False Carding.

In bridge you see other players' actions and deduce their holding to form a picture of the actual hand and play accordingly.

The other players (try to) do the same. So you might design your actions to cater for opponent's expected conclusion (and reaction).

A player who doesn't falsecard will always play "forced" cards in the sense that his holding dictates his play (usually lowest if can't win the trick, perhaps signalling if he/she knows about it).

But when you suspect your opponent to be able to falsecard, you should mentally place yourself in his seat. Would you play the queen from QJ or not? Always? Sometimes? Why? Would your opponent do the same?

The math of Restricted Choice comes in once you have answered these questions.

You might conclude that you have no idea how the opponent would act. Then you should fall back on standard handling of the situation.

But if you think your opponent would act in some predictable way, you may (try to) improve on standard and exploit an eventual weakness. This is an important aspect at higher levels. When doing so, you should estimate what you win if you're right and what you lose if you're wrong to conclude whether you should take the risk.