BBO Discussion Forums: The Theory of Restricted Choice - BBO Discussion Forums

Can the defence do anything to deprive the player of the advantage the theory gives him?

No

It’s like asking if there is anything we can do to stop 2+2 = 4.

Now, it’s important to understand when the principle arises but, when it does, it’s simply a matter of probabilities.

See above.

The only thing you can do is randomize the discards.

I dont know the math, but assume you have a 9 card fit, missing QJ,
you play a top honor, and they show you Q or J, restricted Choice
tells you it was a single with ??? % probability, i.e. you should go for
the finesse.

If defender always drop the lowest card, and the Q showes up, you know
the Q to be single with 100%. If you randomize, you are back to ???
probability.

Another thing that helps, if your bids have a broader range with regards
to points / shape, e.g. preempts.
This also reduces the probability, that certain lines are successful.

With kind regards
Marlowe

P_Marlowe, on 2023-November-09, 11:26, said:

This is not fully accurate. On average there is nothing you can do, including always playing the top card. It turns restricted choice (2:1 in favour after seeing an honour) into a 50% if you show the queen or 100% if you show the jack at a 2:1 ratio, for an average of 66.7%. A complete description of the defensive options hinges on the philosophical interpretation of what a probability means, in particular a Bayesian versus a Frequentist interpretation. Personally I find it really interesting, but also perhaps beyond the scope of the original question. But for all intents and purposes it is sufficient to explain that there is nothing the defenders can do to reduce the odds of declarer taking the maximum number of tricks in this situation (and on the bright side, there's also nothing you can do to increase them, short of voluntarily pitching an honour).

DavidKok, on 2023-November-09, 11:41, said:

Technically, you can be worse off non-randomising (if declarer is aware of your flaw) since it may reveal the distribution early enough to cause them to switch to a completely different line of play.

There was an interesting hand on BW recently where restricted choice came into play based on count and the spots declarer followed with, making one defensive line likely better than another (and definitely no worse). I wondered at the time how many declarers remember to randomize spot cards when following suit, and whether against most club players who may always follow low, the defensive choice was more of a 50/50 guess for that specific hand. Of course, in that case it didn't affect the choice, since one was no worse than 50/50, and one no better, but it may do in others..

While some bad players tend to always play the Jack from QJ….and others, thinking themselves a little more clever, always play the queen, the reality is that one usually won’t play enough boards against any one defender where one can reliably detect and remember their habits. So while we should all try to randomize which we play (and few humans can actually do this…we all have tendencies), in practice we can’t draw many inferences from the Q as opposed to the J….unless we play a lot against a relatively small number of players.

As for randomizing spot cards, that’s second nature for good players.

mikeh, on 2023-November-09, 13:28, said:

You're kidding right?
Does that mean good players only play spot cards systematically about half the time?

smerriman, on 2023-November-09, 12:41, said:

Nope, that's exactly my point above. While you may win or lose due to non-randomising on any particular layout, on average you will score the same as your non-randomising tendencies gain an equal amount on other layouts. You literally have no way to change the average, though as a defender you get to choose where you will be predictable. Analogously, on average it does not matter that declarer 'knows your habits'. That's exactly why I wrote my previous post, and the point that gets into more complicated zero-sum information games.

"We only signal what partner needs to know, when partner needs to know."

I have issues with that statement (primarily that they conveniently tend to forget to explain what their signalling method _is_ when they do signal; but also because "if you're not good enough to know what or when we would need to know, we feel no need to assist"), but that is its intent.

When the signal is important, they will signal, correctly (almost all the time). When it isn't, or when partner is expected to already have that information, and when the 7 or 8, say, is not going to be a relevant card to keep, they pitch small cards "randomly" from a suit. Frequently (especially in trump, when declarer), they hide the 2 (or even the 3). When they know they're going to have to pitch X cards, they "randomly" pick which of the X cards they know they're going to pitch, in particular not agonizing about the squeezed out card on the squeeze trick, telling declarer it worked.

One of the things that distinguishes experts from mere A players is knowing when cards are "randomable", and recognizing situations where they have to randomize their plays early enough to do so nonobviously.

Experts can often tell when signalling will help declarer more than partner. When I don't want to signal, I usually just play lowest cards consistently, rather than actively trying to randomize.

A useful rule of thumb is if the auction and sight of dummy has told you that partner is broke, you don't need to signal honestly, while the one with the weak hand should signal. The strong hand will be in control of the defense, so they need to be able to figure out partner's and declarer's shape, so count signals are important. On the other hand, the weak hand will probably never get the lead, so they don't need to know which suit you want them to lead, so you don't need to give attitude.

DavidKok, on 2023-November-09, 14:42, said:

You will score the same *in that suit in isolation* on average regardless of your habits, yes. Are you disagreeing with my point that it will affect the entire hand / declarer's plan? I'm positive there will be examples where failing to randomise in a restricted choice situation will reduce your scores in the long run, even if it doesn't affect the number of tricks in that suit in the long run. Will just need to come up with one..

Otherwise why does everyone say it's important to randomise in that situation?

In fact, it's not even true in the suit in isolation.

Take the classic example of AKTxxx in dummy opposite xxx in hand, and East drops an honor on the first round.

A priori, East holding QJ is 6.8%, Q is 6.2%, and J is 6.2%. Consider this in absolute terms of 1000 deals - we'll see 68, 62, 62 of each.

If East randomises, restricted choice tells us we'll only see the specific honor from QJ on 34 deals, so the finesse is a 62:34 favorite; a 64.6% chance of success.

If East always plays J from QJ, we have a guaranteed finesse on the 62 deals they have the Q; if we see the J, the drop is the better chance, allowing us to win on another 68 deals, for a grand total of 67.7% success rate.

Maybe that's what you were referring to in terms of Bayesian vs Frequentist; I wasn't sure what that meant. But whichever term you use, it definitely affects the probabilities in real life, which is why it's an improvement to randomise just to avoid the chance of being exploited.

(GIB doesn't randomise; it always plays the Q, and exploiting it works well.)

pilowsky, on 2023-November-09, 14:00, said:

No


I should have elaborated

As declarer one should avoid ‘honest’ carding routinely. Falsecarding is important, though how one falsecards varies from situation to situation

Also, as declarer, when deciding when and how to falsecard, one wants to know the signalling methods of the defenders.

A complete explanation would be lengthy.


As defenders, it’s a very different story.

Beginners and other non experts should usually try either not to signal at all or, when they do, be honest.

Experts in an expert partnership can and do falsecard or randomize when:

1. They have all the important cards so partner can’t ‘go wrong’ since he has nothing useful, or

2. They know that partner knows what’s going on, so they can ‘lie’ knowing that partner won’t be misled

The truth is that experts ‘know’ far more about most hands than do non-experts, strangely enough sometimes more so against good players than bad.

When I’m defending against a good declarer, I know how the bidding went (and it’s rare to distort one’s hand in a constructive auction) so that tells me something. Then dummy tells me more.

Then the play to trick one often tells me something.

Then, declarer’s line of play often gives rise to inferences. When declarer doesn’t make what seems, on the auction and dummy, to be the normal play, that’s a red flag. Not so much if declarer isn’t good enough to play ‘normally’. But against a good player, an unusual seeming line of play can be a clue.

So I suspect most non experts would be surprised to learn, mid way through many hands, just how much the defenders know…and they know that their partner also knows. In that situation both defenders are free to vary any way that want, trying to mislead declarer.

alphred, on 2023-November-09, 10:12, said:

More likely to give it away with body language

I find these endless debates very amusing

Back to cars and goats

I had never heard about it before I read the GiB system notes and thought seriously

I will be polite and well behaved - I have y own views about probaility theory in rare one-off situations

People will discuss such matters endlessly I imagine

Seriously if you don't play something the first time etc

alphred, on 2023-November-09, 10:12, said:

See "Nash Equilibrium"

alphred, on 2023-November-09, 10:12, said:

For sure, the defense will score a trick from QJ tight more often against the players who know the theory ;-}) There are also bidding strategies like Zia preempts where with a marginal preempt you quite often pass with a stiff and preempt more often with 5332/6322/7222 distribution.

When you have a singleton Q or J, you have to try to convince declarer that you have in fact QJ.

For example:
- open 1NT
- underbid. Declarer may think you would have bid more aggressively if you had a singleton
- fail to lead the suit against a suit contract
- give false count in another suit

Probably the cure is worse than the disease.

smerriman, on 2023-November-09, 18:55, said:

Actually, it should randomize. Here's the code comment:

/* What do you know about touching honors?  There are three cases:

1. Opening lead (?) or a non-honor.  Play randomly.

2. Declaring.  High if possibly winning and either leading or
following suit.  Low otherwise.

3. Defending.  Leading, play high.  Third play low if possibly
winning, high otherwise.  2nd/4th: If small (you have >= 3 cards) play
the same.  From a doubleton, play random because of restricted choice.  */

I'm aware GIB should randomize.

I'm aware there was a comment in the code about restricted choice based on a forum comment of yours years ago (yes, I remember everything) and that this is why you put this fact about restricted choice in the system notes.

(Though I wasn't aware of the exact comment; a new tidbit for the memory banks.)

I'm aware that GIB used to randomize at some point in the past.

I'm also aware that a claim was made on these forums a few years back that GIB always drops the Q from QJ in a 4th hand restricted choice situation, backed up by other responders. I was doubtful given your comment, so I tested this hypothesis on 2000 previously downloaded hands from MyHands, and there were only 8 cases where GIB held the appropriate QJ holding in 4th with declarer playing a high honor. But GIB played the Q 8/8 times.

I judged the fact GIB is broken to be a higher chance than the 0.39% chance this was a complete fluke. But I can repeat the process if you're unconvinced.

smerriman, on 2023-November-17, 12:09, said:

You can probably do a better experiment by generating hands with QJ only and forcing GIB to defend on some reasonably straight forward auctions like 1NT 3NT and 1♠ 3♠ 4♠ etc and observing what GIB does on a much bigger data set.