Principle of Restricted Choice

[Califdude]

I'm under the impression that many bridge players who are less that experts either don't know of the Principle of Restricted Choice, or are not comfortable with applying it in their play. Perhaps I'm dead wrong. I thought it might be interesting to run a poll on the subject.

 

I've never tried to run a poll before, so if I've screwed that up in some way, please bear with me. Thanks.

[vuroth]

For years, I wasn't aware of how to apply the general mathematic principle to bridge. I think I understand the basic idea, and have played based on RC once or twice now. Still, I strongly suspect that the majority of club/BIL players aren't familiar with RC.

[matmat]

okay.

so

do you really expect people to own up to not knowing restricted choice?

 

this poll sounds, pretty much, like:

 

"

you are stupid if you have not heard of restricted choice.

do you know what restricted choice is?

 

[ ] yes, I am not stupid

[ ] no, I must be stupid.

"

 

if you are going to ask people about this use a declarer play problem...

sheesh

[han]

I completely understand the math but don't always know when to use it. Do you?

[Mbodell]

In a live field of normal non-life masters for the most basic restricted choice issue (9 card fit missing QJ where honor appears on first round) I'd say that 80+% of the field will not finesse but will instead use the 9 never rule and play for the drop.

 

But in most live open club games around me the numbers are nearly reversed with that vast majority of the field playing for the restricted choice play.

 

I'm not sure if people understand why and/or could apply restricted choice in harder situations, but I'd say more people know how to play on the basic restricted choice pattern than know how to run a basic squeeze play, for instance.

[barmar]

I have sympathy for people who don't always employ it. No matter how many times the math is explained, and even if you totally believe the math, it still "feels strange" and it's hard to go against intuition.. It's kind of like special relativity.

[NickRW]

I have sympathy for people who don't always employ it. No matter how many times the math is explained, and even if you totally believe the math, it still "feels strange" and it's hard to go against intuition.. It's kind of like special relativity.

I think it is hard on the intuition because some of the texts don't explain it very well. I'll try to do it well:

 

[hv=n=s9762hkq8daq64c76&s=sajt85ha75dk5c953]133|200|Contract 4♠.

 

Lead ♣K[/hv]

 

You have no problem generating enough tricks, but you have 2 club losers and at least one spade. The hand comes down to the question of how best to avoid a second spade loser.

 

Eventually you gain the lead and call for a spade, RHO plays a low one and you elect to finesse. LHO wins with the king. Then, back in dummy again on the next trick you call for a spade again and RHO again plays low. The true moment of decision has arrived. Do you play the finesse again? Or do go up with the Ace and hope to drop the queen?

 

Some people think it is a 50/50 guess and reason that the two critical distributions are:

 

1) LHO = KQ, RHO = xx

2) LHO = K, RHO = Qxx

 

Indeed, some people say (somewhat correctly) that any specific 2-2 distribution is (slightly) more likely than a specific 3-1 case, so playing for the drop is marginally the better play. This reasoning is flawed.

 

The true situation is that before you started playing spades the principle interesting distributions were:

 

1) LHO = KQ, RHO = xx

2) LHO = K, RHO = Qxx

3) LHO = Q, RHO = Kxx

 

At the point LHO wins the king you have eliminated case 3) AND you have also eliminated half of case 1) because in case 1) LHO had to pick one honour or the other. Thus the true situation that you are facing at the crucial moment is

 

Half of this case 1) LHO = KQ, RHO = xx

and all of this case 2) LHO = K, RHO = Qxx

 

Therefore a second finesse is nearly twice as likely to succeed as playing for the drop.

 

If that doesn't do it for you, look at this way - these SIX possibilities are all roughly equally likely

 

1a) LHO = KQ, RHO = xx, and LHO will choose the King

1b) LHO = KQ, RHO = xx, and LHO will choose the Queen

2a) LHO = K, RHO = Qxx, and LHO will play the King perforce

2b) LHO = K, RHO = Qxx, and LHO will play the King perforce

3a) LHO = Q, RHO = Kxx and LHO will play the Queen perforce

3b) LHO = Q, RHO = Kxx and LHO will play the Queen perforce

 

At the crucial moment you are left with cases 1a, 2a and 2b - and clearly the finesse is more likely.

 

As Han suggests, understanding this does not always make it obvious when to apply it at the table!!!

 

Nick