mixed strategy in the auction

[Mbodell]

I know there are certain situations where the line you take should be a mixed strategy. The obvious simplest example is playing J or Q from QJ under declarer's higher honor. If you always play one or the other you give away too much information some of the time, so a mixed strategy is optimal in a game theory sense.

 

BW had an interesting article a few months ago about non-symmetric MP lines where if the field is doing line A you want to do line B and if the field is doing line B you want to do line C and if the field is doing line C you want to do line A. Which again leads to a mixed strategy for optimal game theory outcome.

 

My question is can anyone think of a strategic reason and example of why you'd want to adopt a mixed strategy for bidding a given hand? That is given the exact same hand/vulnerability/scoring/state of the match/opponents/auction to date/etc. where you and your partner would regularly intentionally choose some bid some percent of the time and another bid some other percent of the time?

[Guest Jlall]

Fit jumps, game tries, lead directing bids in slam auctions.

 

I had a good example of the last one in the world pairs, the opps bid to 6S and our fit was hearts. I knew that 7H would be a good save, but thought they were cold for 7S. So, what to do? I hate to pass in such a situation, so I decided to bid 7D, my stiff, acting like I had a void there. The opps now were scared to bid 7S and doubled 7H.

 

It occured to me later that this psyche would always work at the point the game is at right now, so it should be psyched a lot. If it is psyched too much though the opps will disregard it, so there must be some equilibrium.

[hrothgar]

I know there are certain situations where the line you take should be a mixed strategy. The obvious simplest example is playing J or Q from QJ under declarer's higher honor. If you always play one or the other you give away too much information some of the time, so a mixed strategy is optimal in a game theory sense.

 

BW had an interesting article a few months ago about non-symmetric MP lines where if the field is doing line A you want to do line B and if the field is doing line B you want to do line C and if the field is doing line C you want to do line A. Which again leads to a mixed strategy for optimal game theory outcome.

 

My question is can anyone think of a strategic reason and example of why you'd want to adopt a mixed strategy for bidding a given hand? That is given the exact same hand/vulnerability/scoring/state of the match/opponents/auction to date/etc. where you and your partner would regularly intentionally choose some bid some percent of the time and another bid some other percent of the time?

Mixed Strategies as applied to Bridge

 

The academic discipline of game theory differentiates between

“pure” strategies and “mixed” strategies. Pure strategies are

deterministic. Players choosing a pure strategy follow a predictable

course of action. In contrast, mixed strategies deliberately

incorporate random action. The simplest example of a mixed strategy

equilibrium is the Penny Matching game. Two players simultaneous

display a penny. If the two coins “match” (both coins are heads or

both coins are tails) then Player 1 keeps the two pennies. If the two

coins don't match then Player 2 keeps both pennies. The only

equilibrium strategy to this game is mixed. Each player should

randomly determine whether to display Heads or Tails using a 50/50

weighting scheme.

The concept of a mixed strategy can be applied to a number of

areas within bridge. The simplest and best know examples come from

declarer play and defense. Many well understood problems like

restricted choice make use of mixed strategies. For example, declarer

leads a low Diamond into D QJ9 and plays the Queen after LHO plays

low. RHO holds both the Ace and the King and needs to determine which

card to cover with. Restricted choice analysis presumes that the

defender is applying a mixed strategy will randomly chose to cover

with the Ace or the King, once again applying a 50/50 weighing scheme.

Mixed strategies can also be applied to the design of bidding

systems. Players applying a “pure” bidding strategy will always chose

the same bid bid with a given hand. In contrast, players employing a

mixed bidding strategy allow deliberate randomization. Consider the

following example taken from Bridge My Way by Zia Mahmood. You hold

 

S AQJ3

H K5

D 873

C A653

 

The auction starts

 

1H – 1S

3S - ???

 

and you need to chose a rebid. Zia advocates a bidding style in which

players should randomize between 4C and 4D cuebids. Zia never goes so

far as to discuss probabilities, but hypothetically he might chose a

4C cuebid 80% of the time and a 4D cuebid 20% of the time.

Alternatively, consider the following example: White versus Red

partner opens 1H in first seat promising 5+ Hearts and 10-15 HCP. RHO

passes. You hold:

 

S 742

H AK762

D 9732

C 4

 

I advocate a hypothetical “mixed” strategy in which players bidders

 

4H: 60% of the time

3NT: 20% of the time

2NT: 10% of the time

2D: 5% of the time

1S: 5% of the time

 

Players who adopt mixed bidding strategies allow for the use of

multiple bids to describe a single hand. As a consequence, many

responses could show radically different hand types. For example,

players adopting Zia's Sting Cue bid style need to describe their 4C

cue bids as either “First round control of Clubs or [rarely] no

control of clubs”. In an equivalent fashion, my partners would need

to describe my 3NT raise of a Precision 1H openings as either a strong

balanced hand willing to declare 3NT OR [rarely] a preemptive raise of

Hearts.

In turn, this brings us to the last major area in which mixed

strategies and bridge overlap: Regulatory structures. Few if any

Zonal authorities incorporate mixed bidding strategies into their

regulatory structures. Instead, regulators attempt to sidestep the

issue using the concept of a psychic call. Regulators and players

pretend that psychic calls are “deliberate and gross misstatements of

honor strength or suit length”. In actuality, so-called psychic calls

are a subset of a more complex meta-agreement involving mixed bidding

strategies. I argue that neither players nor regulators are served by

this pretense. Complete disclosure can never be achieved unless the

regulatory structure matches the actual strategies employed by

players.

[Guest Jlall]

cuebidding was a good one Richard.

 

I disagree that mixed strategies are best when partner is still involved and you cannot control the auction though. (such as 1H p ).

[hrothgar]

cuebidding was a good one Richard.

 

I disagree that mixed strategies are best when partner is still involved and you cannot control the auction though. (such as 1H p ).

Please note that the example after the 1♥ response was in the context of a limited opening system like Precision.

 

Alternatively, consider numerous age old examples responding to a weak 2♠ opening.

[MFA]

My question is can anyone think of a strategic reason and example of why you'd want to adopt a mixed strategy for bidding a given hand?

Zia, for instance, uses tactical bids in various situations, but only occasionally. These bids might not win points by themselves, but they do give Zia a certain image.

So, on all the ordinary boards where he does completely ordinary things, he gains because the opponents simply cannot trust him in the usual way! They make strange leads, aggressive overcalls, etc. when they suspect a bluff, all sorts of mistakes, they'd never make against me. B)

 

jlall:

I had a good example of the last one in the world pairs, the opps bid to 6S and our fit was hearts. I knew that 7H would be a good save, but thought they were cold for 7S. So, what to do? I hate to pass in such a situation, so I decided to bid 7D, my stiff, acting like I had a void there. The opps now were scared to bid 7S and doubled 7H.

 

It occured to me later that this psyche would always work at the point the game is at right now, so it should be psyched a lot. If it is psyched too much though the opps will disregard it, so there must be some equilibrium.

 

Nice one.

 

As an ordinary (non-Zia) player, you are in a sense liable for the habbits of the field in these situations. What good does it do that you balance your plays perfectly, when nobody else does and your opponents are judging from their entire experience?

Sometimes, where in theory a mix-up of strategies is best, in practice one will simply be superior to the other.

 

Your example is such. So few find the 6♦ that the opponent is destined to go wrong. No need for you to balance the strategies here.

 

Another simple example:

You have KQ behind dummy's AJT. In general, against average players, if you win the king first, they are less likely to think that you have the other one too. It just works that way. Winning the king might trick partner, so even if this is rather obviously irrelevant on a given board, people tend to win the queen more often out of habbit.

You are inheriting the standards of the field.

[Guest Jlall]

Yes, obviously I don't believe that in my situation there will ever be a need to balance my bidding (except against people I play thousands of hands against). The only thing stopping me from making this psyche more than once other than the relative infrequency of the situation is the laws.

[MFA]

Yes, obviously I don't believe that in my situation there will ever be a need to balance my bidding (except against people I play thousands of hands against). The only thing stopping me from making this psyche more than once other than the relative infrequency of the situation is the laws.

I don't think the laws should deter you in any way.

 

Partner should explain 7♦ as "he wants a diamond lead against 7♠", and not say "he promises a diamond void". Because you don't!

 

Then it's up to the opponents to conclude. One reason for wanting a diamond lead is obviously to defeat 7♠ with a ruff. But your reason, to scare them out of bidding the grand in the first place, is also a completely valid bridge reason.

[jdonn]

Yes, obviously I don't believe that in my situation there will ever be a need to balance my bidding (except against people I play thousands of hands against). The only thing stopping me from making this psyche more than once other than the relative infrequency of the situation is the laws.

I don't think the laws should deter you in any way.

 

Partner should explain 7♦ as "he wants a diamond lead against 7♠", and not say "he promises a diamond void". Because you don't!

 

Then it's up to the opponents to conclude. One reason for wanting a diamond lead is obviously to defeat 7♠ with a ruff. But your reason, to scare them out of bidding the grand in the first place, is also a completely valid bridge reason.

So if I like to open 1♠ on a three card suit a lot simply to try and trick the opponents out of finding their spade fits, let me try your argument.

 

Partner should explain 1♠ as "he wants to show five spades", and not say "he promises five spades". Because you don't!

 

Then it's up to the opponents to conclude. One reason for wanting to show five spades is obviously to reach good spade contracts. But your reason, to trick the opponents out of playing in spades, is also a completely valid bridge reason.

 

Sure sounds ridiculous, doesn't it? Look, you have to explain what you are showing, and if you often don't have it you must alert that fact. You can't dance around the laws using ambiguous semantics in the way you describe. A 1♠ opening bid shows five spades, and his 7♦ bid shows a void. If Justin wants to bid it without one that's his business (damn good bid by the way!) but as he knows his partner must alert if it occurs too often. He can't just do it all the time and never clue the opponents in like you seem to be saying.

[MFA]

@ jdonn

 

Yes, it sounds ridiculous, but this is because your analogy doesn't hold!

 

Look, you have to explain what you are showing, and if you often don't have it you must alert that fact. You can't dance around the laws using ambiguous semantics in the way you describe. A 1♠ opening bid shows five spades, and his 7♦ bid shows a void.

 

No! This is the point. 7♦ doesn't show a void! It's perfectly OK to play that 7♦ doesn't show a void. It's a free world, you can play whatever you like!

Well, one spade that might not be a suit IS restricted.

 

Look, you have to explain what you are showing, and if you often don't have it you must alert that fact.

He can't just do it all the time and never clue the opponents in like you seem to be saying.

 

You are right, of course, you must declare your system. But I think you might have misunderstood me, because this is what I have every intention to do!

 

If this sequence comes up with my regular partner, I'd say as I stated ("He wants a diamond lead"). We don't have any special history about tricky bids, but our agreement in these situations is that partner wants a diamond lead, so this is what I'd say.

 

1. Perhaps he hates a heart lead

2. Perhaps he hates a trump lead

3. Perhaps he has a void or the ace of diamonds

4. Perhaps he wants to scare the opponents off the grand

 

How the **** should I know? I'd just lead a diamond and hope that p has his reasons.

 

It's clear, however, that if you establish a tendency for a specific tactical treatment, you must inform the opponents about it. Justin is perfectly entitled to bid 7♦ EVERY time in this position, but as this goes on, my phrasing (quickly) becomes inadequate. But for now, and for p & me so far, the wording is fine.

[MFA]

Just thought of a similar situation from my own partnership. :)

 

A long time ago, my partner doubled 4NT RKC. The opps asked, and I told them that I didn't have a clue - because I didn't! As it turned out, my partner had nothing. No surprise anywhere, no nothing. He just tried to be annoying, ... and it worked! Responder passed the double instead of showing the key cards, and they were completely asea. ;)

 

Not too long after that, he did it again! We hadn't discussed it in the meantime, so I said: "No agreements", but of course I also told them about what had happened the last time. And again, he had zip!

 

So now, our formal agreement is that this double shows ... nothing! We use it from time to time when we think that the opps are apt to [screw up - edit]. We have had no disasters so far but just about a handful of successes. :(

Edited November 4, 2007 by inquiry

[Guest Jlall]

Partner should explain 7♦ as "he wants a diamond lead against 7♠", and not say "he promises a diamond void". Because you don't!

If you really think this is the right explanation, you do not understand (or don't care about) the spirit of full disclosure. I won't even go into whether your definition is legally correct since I don't know, but I certainly feel like it would be dirty and against the spirit of full disclosure (which is the most important principle in bridge). The opponents certainly deserve to know what I might say I want a diamond lead with.

[ArtK78]

This discussion is descending into sillyness.

 

If you open 1♠ and your agreement is that it shows 5 spades, your partner is required to explain it as showing at least 5 spades. That is your agreement. He is not psychic (in a non-bridge manner), so he has no way of knowing that you have opened 1♠ on a 3-card suit. He has to explain your agreement. You are not under any obligation to follow your agreement.

 

As for the 7♦ bid, the meaning of that bid is not a matter of agreement. It is a matter of bridge logic. Of course it requests a diamond lead. And the only logical reason for requesting a diamond lead in the context of the auction is that partner can ruff a diamond lead. If he cannot ruff a diamond lead and made the bid for tactical reasons, that is his prerogative.

 

Note that all of these things are perfectly within the laws of bridge.

 

Now, if you make it a habit of psyching (in the bridge manner) 1♠ opening bids with this partner, your partner may have to add to his explanation of your bid that you have been known to psyche 1♠ opening bids. In fact, if you have psyched 1♠ opening bids often enough with this partner, he may even have to alert the opponents to that fact. But that does not change your agreement as to what the 1♠ opening bid shows.

[jdonn]

As for the 7♦ bid, the meaning of that bid is not a matter of agreement.

Why not? You are making the same wrong assumption MFA did. Justin even described the bid as a psych in his post, so obviously he has an agreement.

[3for3]

This discussion has veered from the mixed strategies, but getting back there for a minute:

 

One area that seems to need a mixed startegy approach is 'allowing' the opponents to accuratley judge the law of total tricks. Against some (most?) opponents you can take it to the bank that they have 8 trumps (or more) on certain auctions. Opponents bid and raise a suit to the 2 level, they certainly have 8. Overcall followed by a preemptive raise they have 9. Not only can you use their trumps to judge how high to compete, you can use them to deduce shortness in partner's hand. Against strict law abiders, the auction 2H-P-3H marks the opponents with 9 trumps. Well, perhaps we should be raising to 3 on some hands with 2 or 4 trumps to keep them off guard.

 

The problem, as Justin alluded to, is that unless you play literally 1000's of boards against these same opponents, you will not reap the benefit of their misjudgement as much as you might cost yourself from making the theoretically correct bid.

 

Danny

[MFA]

Partner should explain 7♦ as "he wants a diamond lead against 7♠", and not say "he promises a diamond void". Because you don't!

If you really think this is the right explanation, you do not understand (or don't care about) the spirit of full disclosure. I won't even go into whether your definition is legally correct since I don't know, but I certainly feel like it would be dirty and against the spirit of full disclosure (which is the most important principle in bridge). The opponents certainly deserve to know what I might say I want a diamond lead with.

Your answers are disappointing, since you don't seem to (be able to?) differentiate between partnership understandings/agreements and general knowledge about bridge.

 

You see, this "phonie void" thing has never come up in my 8years partnership, not even in a post mortem discussion or anything. (To the very best of my recollection). And our style is certainly not to go out of our ways to make inspired bids.

 

So, what do you want me to declare? That I once read a bridge book, in which this happened? That my partner could have read about similar things, since he is a good player? Well, I don't know anything about what he has read.

 

No. The point is that I know nothing more than had I played with Geir Helgemo for the first time ever. Namely that in this situation a good player might have other reasons than a void to make a lead directing bid. I thought of 4, but perhaps there are more.

 

"It's lead directing" is IMO a better way to handle it than "it shows a void ... ooops, he was bluffing". Because my bridge knowledge tells me that partner might not have a void for this bid - with a reasonable likelyhood. Not just that MY p might not, ANY good p might not.

Saying "void" implies that this is the extent of my bridge knowledge, and this is much less fair to the opponents, weak or strong, than the general "lead directing".

 

It's not that I in general want to wriggle out of giving proper explanations. Not at all. It just seems to me that you (and jdonn?) are grossly underestimating the readiness to make a non-void 7♦ in this situation, and thus are better off not just saying "void" to the opps.

2 questions to stress this point:

1) How many times have you actually made a legitimate bid with a void on the 7-level? Or even seen it been done? Then compare to the "bluffs"...

2) Why would you not just want to wait and DOUBLE 7♠ instead, if you had a void?

 

I don't want to drag this on forever, but your post was rather insulting about my ethical standards, so I had to answer. :D

(Also this whole situation about 7♦ void/not void is very much on-topic).

[jdonn]

You see, this "phonie void" thing has never come up in my 8years partnership, not even in a post mortem discussion or anything. (To the very best of my recollection). And our style is certainly not to go out of our ways to make inspired bids.

 

So, what do you want me to declare? That I once read a bridge book, in which this happened? That my partner could have read about similar things, since he is a good player? Well, I don't know anything about what he has read.

Uh, this wasn't talking about you, you told Justin what he should say! You were just making an assumption that he doesn't have an agreement. For one thing you don't know whether he does or not, and his post in fact suggested that he does. For another, general bridge knowledge can and often does constitute an agreement. If you were playing with a new partner how else do you know you're playing stayman? Sure this situation is more obscure but I guarantee two experts would have complete confidence playing together for the first time both in making that bid and knowing what it means.

 

Because my bridge knowledge tells me that partner might not have a void for this bid - with a reasonable likelyhood. Not just that MY p might not, ANY good p might not.

Your bridge knowledge is extraordinary then. This is the first time in my entire life I have heard of this bid being used as a "psych", and I assure you have I played and watched more hands of bridge than almost anyone.

 

2 questions to stress this point:

1) How many times have you actually made a legitimate bid with a void on the 7-level? Or even seen it been done? Then compare to the "bluffs"...

2) Why would you not just want to wait and DOUBLE 7♠ instead, if you had a void?

1) I would estimate I have in combination made it / seen it / read it in an article being done a total of about 20 times in my life. This was the first I have ever heard of it as a bluff.

2) Because partner might not be able to tell which of two suits he should lead if he has equal length.

[Guest Jlall]

1) How many times have you actually made a legitimate bid with a void on the 7-level? Or even seen it been done? Then compare to the "bluffs"...

Maybe half a dozen? I don't know. Enough that I was able to figure out that it may be good to do it at some point without a void.

 

2) Why would you not just want to wait and DOUBLE 7♠ instead, if you had a void?

 

This is a bit of a gamble as partner will have to guess a lead. He will have some information to go on, but I'd rather just make sure I get the right lead. Probably this should depend on the exact auction/hand, sometimes it might be clear for partner which lead to make, other times it will not be clear.

 

You are right that your partners are under no obligation to disclose anything if you make this bid if it has never come up for you. That wasn't really the point. I simply said that *I* do not feel comfortable doing this more than once because the fact that I have done it establishes an illicit agreement (yes, once is enough given the relative infrequency of the action). Obviously when I did this I did not feel unethical as I had never done it before and my partner had no idea. That partner now has seen me do it, and most of my other partners have heard about it, because, well, I like to brag lol. If you want my partners to still say "lead directing" without mentioning anything else, I would say that is not in the spirit of full disclosure. If you think the fact that this bid might be a bluff is general bridge knowledge, I would give that a hearty LOL.

[skjaeran]

1) How many times have you actually made a legitimate bid with a void on the 7-level? Or even seen it been done? Then compare to the "bluffs"...

Maybe half a dozen? I don't know. Enough that I was able to figure out that it may be good to do it at some point without a void.

 

2) Why would you not just want to wait and DOUBLE 7♠ instead, if you had a void?

 

This is a bit of a gamble as partner will have to guess a lead. He will have some information to go on, but I'd rather just make sure I get the right lead. Probably this should depend on the exact auction/hand, sometimes it might be clear for partner which lead to make, other times it will not be clear.

 

You are right that your partners are under no obligation to disclose anything if you make this bid if it has never come up for you. That wasn't really the point. I simply said that *I* do not feel comfortable doing this more than once because the fact that I have done it establishes an illicit agreement (yes, once is enough given the relative infrequency of the action). Obviously when I did this I did not feel unethical as I had never done it before and my partner had no idea. That partner now has seen me do it, and most of my other partners have heard about it, because, well, I like to brag lol. If you want my partners to still say "lead directing" without mentioning anything else, I would say that is not in the spirit of full disclosure. If you think the fact that this bid might be a bluff is general bridge knowledge, I would give that a hearty LOL.

I agree with Justin here. This bluff isn't part of "General bridge knowledge". You've got to have been there to think of this bluff or know a hand where someone pulled this one to be able to do such a thing.

 

I had a hand in a teams match a couple of years ago where I could have pulled this stunt. I had xx KQJTx Q AKxxx and opened 1♥. It went 1♠ 4♥ 6♠ and it was my turn. I knew RHO held good ♠ support and a long ♦ suit now. Misjudging the situation, I thought he was void in hearts and doubled for a ♣ lead, hoping partner would pick the right minor suit. He did, but alas RHO had the "obvious" hand with 4360 - inferring his partners ♥ void. They made an overtrick. At the other table the first round of bidding went the same, then my hand bid 7♣ and our teammates bid 7♠, earning us 8 IMPs. But afterwards I thought about the situation and realized that the winning bid with my hand would be 7♦. So I've never pulled this stunt, but I'm ready next time.

 

Since my partner know about my reasoning, if asked in such a situation later he should explain my bid as lead directing - psyche possible.

[MFA]

It IS (general) bridge knowledge, LOL if you wish. :) This doesn't mean that everybody knows about it. :unsure:

 

There are 3 categories in play here.

 

Agreements. Discussions and partnership experience.

Understandings. Jdonn's stayman falls under this. Things you know from analogies or from knowledge about your partner (perhaps you are from the same bridge community?).

(General) Bridge knowledge. All the individual stuff, you've read or just know. Common knowledge or not. Examples:

A 2♥ overcall could be much more frisky after 1♦-2♦ than after 1♠-2♦.

Voids, bad intermediates and side controls are flaws when you preempt.

What kind of tactical bids that might work and what kind that have virtually no chance at all.

 

Agreements and Understandings should be declared, Bridge knowledge shouldn't. Bridge knowledge could, however, "promote" to agreements through partnership practice.

 

skaren:

I agree with Justin here. This bluff isn't part of "General bridge knowledge". You've got to have been there to think of this bluff or know a hand where someone pulled this one to be able to do such a thing.

 

Well, this puts it in my first OR third category, doesn't it?

 

jlall:

That partner now has seen me do it, and most of my other partners have heard about it, because, well, I like to brag lol. If you want my partners to still say "lead directing" without mentioning anything else, I would say that is not in the spirit of full disclosure.

Of course, agree 100%. First or second category, depending on whom you are playing with.

 

jlall:

I simply said that *I* do not feel comfortable doing this more than once because the fact that I have done it establishes an illicit agreement...

It does - your system is now that 7♦ might not be a void. No problem, partner says so (and includes your history), and you can bid 7♦ as often as you like! (my primary point of the my post)

 

skaren:

Since my partner know about my reasoning, if asked in such a situation later he should explain my bid as lead directing - psyche possible.

 

It's not logical to explain something as a possible psych - they are per definition unexpectable. So what you really are doing is saying that your system is that 7♦ might not be a void.

 

This was my secondary point of my first post. 7♦ "lead directing" is the system, and "void" is the logical conclusion. But as we have learned from Justin's board, it's not the only logical conclusion.

So in a scenario with no partnership agreement/experience/understanding, might we not be better off sticking to "lead directing" and let all four players judge the likelyhood of a void, based on their individual, general bridge knowledge?

 

In a sense, my superior agenda is to avoid at all cost calling something "a bluff" if I in any way have seen it coming. Either through agreements, understandings OR general bridge knowledge.