[Benoit35]

I've read in regulation documents about bidding systems that call for random bids (addressing whether they are allowed or not). Can someone give me an sample case... when would it pay for partners to agree to somme random bidding?

[hrothgar]

The following is an article which I (regretfully) was unable to place in the Bridge World

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 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 weighting 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.

[kenrexford]

Benoit35, on Jan 21 2009, 01:38 PM, said:

I've read in regulation documents about bidding systems that call for random bids (addressing whether they are allowed or not). Can someone give me an sample case... when would it pay for partners to agree to somme random bidding?

Well, anyone who agrees to play with me expects some random calls, but we do well anyway. LOL

Actually, I'll give a reasoned answer of a tactical reason for a "random" call. Suppose that the auction is 2♥(weak)-X-2♠ and 2♠ is defined as "random," meaning that Responder could have anything. Actually, this would not be entirely "random," as Responder will typically have spades, or a heart fit, or both minors, or one long minor; in other words, a reason to keep the auction alive. The use of an all-purpose "random" bid leaves the opponents unable to establish the most effective tools to cater to the situation.

Another sort of example. 1NT-X(one-suited)-XX(penalty)-P-P-2♣. If 2♣ says, "I have a suit that might be clubs," this uses up no space but forces the opponents to know that Opener must double to find out the suit without an enabled pass. In other words, a lot of Responders will double clubs, allowing overcaller to simply bid until he reaches his suit, and then pass, where a penalty double might not be lucrative. Even if the opponents know how to compensate, they must forfeit something to cater to this predicament.

I call these bids "stepping stone" bids, because the opponents are essentially required to double to determine the meaning of the call.

[awm]

There are some pretty serious disclosure issues with random bids. Usually they are not really random, in the sense that they depend on things like state of the session/match, what the bidder thinks about the skill-level of the opponents, how the bidder feels that day, etc. These sorts of things are rarely if ever disclosed. It also depends a lot on the alternative actions, and what the follow-up agreements are. Even if the bid truly is just "random" usually the probability distribution is not very well-established, and people aren't good at generating random numbers anyway...

[jtfanclub]

Hw about the perfectly ordinary auction with a substitute partner on line...

1♠ 2♠
3♣

Where 3♣ might be a long suit, a help suit, or a short suit try...nobody knows, since you haven't discussed it with your substitute partner. It's just invitational while setting spades is trump. Did it really matter whether you picked 3♣ or 3♦?

[Benoit35]

Thanks. To clarify, my question was about randomly choosing between multiple calls for a given hand, and not about specific calls having multiple meanings.

[Ant590]

I guess someone might decide to randomize their 2/1 minor bids with 3=4=3=3 shape?

[shintaro]

it seems that there will always be those who play Bridge and those who wish to play 'Asylum Bridge'

[FrancesHinden]

The phrase "random bids" can be interpreted in more than one way:

1. The 'obvious' way for those of a mathematical background is the way hrothgar has described it: you choose between multiple possible calls for a given hand in a non-deterministic fashion. We've already had some examples, e.g. if the auction starts 1H x and I have a 2434 3-count then perhaps my real methods are to bid 1S 20% of the time and 3H 80% of the time.

2. There is a bridge usage, where (for example) a 1S overcall of a strong 1C opening that can be made on any hand is called a 'random overcall'. In the strict sense, it's the opposite, particularly if your method is to bid 1S literally on every hand.

Where there are regulations forbidding 'random' bids, they usually refer to the second meaning. The "1S shows 13 cards" defence to a strong club used to be illegal in the EBU, although it's now allowed, and I think is still illegal in the ACBL.

[Benoit35]

Very interesting stuff hrothgar; could you elaborate on the advantages of such a strategy? E.g. what would be gained by occasionally going 1♥ - 3NT on the hand you described?

Is this done solely to plant the seed of doubt into the opposition ("they might be in the wrong contract so we'll pass rather than double/compete and give them a chance to correct to 4♥"), or is there some other benefit?

[hrothgar]

Benoit35, on Jan 22 2009, 08:34 PM, said:

Very interesting stuff hrothgar; could you elaborate on the advantages of such a strategy?  E.g. what would be gained by occasionally going 1♥ - 3NT on the hand you described?

Is this done solely to plant the seed of doubt into the opposition ("they might be in the wrong contract so we'll pass rather than double/compete and give them a chance to correct to 4♥"), or is there some other benefit?

Lets assume that the auction starts

(1♥) - P - (4♥) Preemptive

You're sitting on decent hand with 6+ Spades and short hearts.

Bidding 4♠ looks pretty good (indeed, some of us jokingly call the 4♥ preemptive raise a transfer to Spades)

Conversely, let's assume that the auction starts

(1♥) - P - (3NT) (Values for game, tends to deny a Heart fit)

That 4♠ call suddenly looks a lot less attractive. The opponents aren't promising any kind of fit. They're both sitting on values. Yeah, they probably make game, but we could easily go for 500, 800, or more...

Do you see why a weak hand with long hearts and short Spades might have an incentive to bid as if he holds a GF without a fit? In general, you probably want to preempt to the max... However, ever once and a while, its nice to bid 3NT. Who knows, the next time the auction starts 1M - (P) - 4M, LHO might bid 4♠ with a marginal hand. With lucks, thats the time you have a balance 16 count with a stiff Heart and get to drop the axe.

More generally, there are all sorts of "Classic" situations where folks psyche:

1. I'm white on red and there are two passed to me
2. Partner opened a weak two, RHO passed, and I have a decent fit but only a few values.
3. Partner opened 1H, RHO doubles and I have short spades and 3-4 hearts.

The logic behind any of these "psyches" should be pretty apparant...

(If you make it easy on the opponents, they aren't going to make nearly enough mistakes. If they always know just what your bids mean, you're making it VERY easy for them)

Here's an example that happened during KO that Tim G and I played in a couple week's back. The pair that I was playing against was using some bizzarre home brew system where

A 1♣ opening denied 5+ cards in Clubs, Diamonds, or Hearts
A 1♦ response to 1♣ denies a 5 card major.

If the auction started 1♣ - (P) - 1♦ the opps had NO idea what kind of hand they held.

Last board of the match. Other than the fact that I started drinking heavily at half time, I had been playing down the straight and narrow. It's red on red, and I'm sitting on

KJxx
Kxx
KJxx
xx

LHO opens 1♣, partner passes, RHO bids 1♦ and I need to figure out what to do...

I could pass and give the opponents the chance to sort out their hands.
However, overcalling 1♥ seemed like a much better idea...

Sure enough, I got to buy the contract for 2♥...
Picked up something like 10 IMPs on that hand

Better yet, you should have heard the opponents when they had 4 top trump crash on each other... Makes your heart grow warm hearing language like that. I only wish it had happened at the start of the match.

[awm]

Hrothgar's post didn't seem to answer the question exactly, in that he explained why it would sometimes be a good idea to "psych" but not why you would pursue a mixed strategy rather than just always "psych" on those hand types.

I think the critical issue is that there is some circular dependence of methods and defenses.

For example, psyching a strong notrump can be pretty effective, especially NV and in third chair. However, it is much more effective if the opponents defense does not include a penalty double.

Now, assuming partner and I are ethical about disclosure, it is possible that partner should start alerting my third seat 1NT bids as something like "either 15-17 balanced, or 0-5 with any shape." But the problem is that if this is really my agreement, opponents will switch to a defense with a penalty double... at which point it will no longer be such a great idea to open 1nt on these 0-5 point hands.

Supposing we're going to disclose our methods fully, it makes sense that I should open 1nt occasionally with the 0-5 hands (since doing so generally gets me a good result assuming opponents don't play penalty double) but not with sufficient frequency that it becomes "obvious" that opponents should play that penalty double. Thus the mixed strategy. It also protects me if for whatever reason I decide not to open 1nt with a 0-5 point hand.

The problem is that it becomes very difficult to verify that our disclosure matches our agreements, since it is hard to distinguish a "secret agreement" about when to open what from simply "random selection."

[mycroft]

Richard, not exactly "homebrew" necessarily, it's almost as old as I am...
http://www.bridgeguy...trealRelay.html
I will admit I don't know the rest of your opponents' system; and you seem to have hit a great way to disrupt (occasionally) it.

[kenrexford]

Benoit35, on Jan 22 2009, 08:08 AM, said:

Thanks. To clarify, my question was about randomly choosing between multiple calls for a given hand, and not about specific calls having multiple meanings.

Well, any call can eventually be seen to have multiple "meanings."

Another example, I suppose, is minor openings. I think that opening 1♣ or 1♦ randomly when balanced at MP has some merit. Lead and takeouts are affected. However, I really do not randomize. What I do is to occasionally open 1♣ or 1♦ when that is the weaker and/or shorter minor because the hand looks right to dissuade that lead or to cause the opponents takeout problems.

So, "random" is never really random.

[hrothgar]

kenrexford, on Jan 23 2009, 04:37 PM, said:

Benoit35, on Jan 22 2009, 08:08 AM, said:

Thanks.  To clarify, my question was about randomly choosing between multiple calls for a given hand, and not about specific calls having multiple meanings.

Well, any call can eventually be seen to have multiple "meanings."

Another example, I suppose, is minor openings. I think that opening 1♣ or 1♦ randomly when balanced at MP has some merit. Lead and takeouts are affected. However, I really do not randomize. What I do is to occasionally open 1♣ or 1♦ when that is the weaker and/or shorter minor because the hand looks right to dissuade that lead or to cause the opponents takeout problems.

So, "random" is never really random.

The fact that you don't bid randomly doesn't mean that its impossible to bid randomly.

It's fairly easy to design structures by which you use the pips that you get dealt as a source of randomness.

[Benoit35]

Ah. I was wondering how to generate "true" randomness, and forgot that the cards themselves could provide it! For example, "Bid your normal 4H preempt unless you hold the 2 of clubs, in which case bid 3NT" will make you choose the alternate bid very close to 20% of the time (you hold 8 out of 39 non-♥ cards).

This in turn can raise a disclosure issue. You open 1H, partner raises to 3NT:

South: Alert!
East: Yes?
S: Partner probably wants to play 3NT, but may rarely have a hand for a 5-card 4H preempt.
E: How rarely?
S: He will bid 3NT rather than 4H about 20% of the time.
E: How does he generate this 20%?
S (must disclose the agreement): He does it if he has the two of clubs.
E (looking at own 2 of clubs): Thank you.

Therefore, each player should decide which rule they will use without telling their partner. Then, in the above conversation, you don't know, and therefore don't have to tell, anything more than "He decides this based on holding certain low cards in the side suits, but I don't know which ones. I don't tell him which cards I use to generate randomness either."

I would suppose that looking at the position of the running hand on one's watch, while providing good randomness, is unauthorised information.

[jdonn]

Benoit35, on Jan 23 2009, 11:30 AM, said:

Ah. I was wondering how to generate "true" randomness, and forgot that the cards themselves could provide it! For example, "Bid your normal 4H preempt unless you hold the 2 of clubs, in which case bid 3NT" will make you choose the alternate bid very close to 20% of the time (you hold 8 out of 39 non-♥ cards).

This in turn can raise a disclosure issue. You open 1H, partner raises to 3NT:

South: Alert!
East: Yes?
S: Partner probably wants to play 3NT, but may rarely have a hand for a 5-card 4H preempt.
E: How rarely?
S: He will bid 3NT rather than 4H about 20% of the time.
E: How does he generate this 20%?
S (must disclose the agreement): He does it if he has the two of clubs.
E (looking at own 2 of clubs): Thank you.

Therefore, each player should decide which rule they will use without telling their partner.

I would suppose that looking at the position of the running hand on one's watch, while providing good randomness, is unauthorised information.

You could avoid that problem by using a formula. Not that this is anything I would ever do, but say "if my non-heart cards (A = 1, K = 13, Q = 12, J = 11, else = card) add up to either 39, 47, 55, 63, or 71" etc etc. An opponent will then be unable to tell anything by looking at his hand.

[hrothgar]

Benoit35, on Jan 23 2009, 07:30 PM, said:

Ah. I was wondering how to generate "true" randomness, and forgot that the cards themselves could provide it! For example, "Bid your normal 4H preempt unless you hold the 2 of clubs, in which case bid 3NT" will make you choose the alternate bid very close to 20% of the time (you hold 8 out of 39 non-♥ cards).

This in turn can raise a disclosure issue. You open 1H, partner raises to 3NT:

South: Alert!
East: Yes?
S: Partner probably wants to play 3NT, but may rarely have a hand for a 5-card 4H preempt.
E: How rarely?
S: He will bid 3NT rather than 4H about 20% of the time.
E: How does he generate this 20%?
S (must disclose the agreement): He does it if he has the two of clubs.
E (looking at own 2 of clubs): Thank you.

Therefore, each player should decide which rule they will use without telling their partner. Then, in the above conversation, you don't know, and therefore don't have to tell more, than "He decides this based on holding certain low cards in the side suits, but I don't know which ones. I don't tell him which cards I use to generate randomness either."

I would suppose that looking at the position of the running hand on one's watch, while providing good randomness, is unauthorised information.

Here's how I think that (this subset of) disclosure should work

The existence of a mixed strategy should be disclosed
The PDF that governs the mixed strategy should be disclosed
The fact that card combinations are used to govern the mixed strategy should be dislosed

In all cases, this information should be made available to both the opponents and to partner.

The specific key (card combination) that governs the mixed strategy should not be shared with partner OR with the opponents.

A claim can be made that the specific key being used should be registered in advance w\with the TD so people validate that your actions match your agreements.

[jdonn]

hrothgar, on Jan 23 2009, 11:39 AM, said:

Here's how I think that (this subset of) disclosure should work

The existence of a mixed strategy should be disclosed
The PDF that governs the mixed strategy should be disclosed
The fact that card combinations are used to govern the mixed strategy should be dislosed

In all cases, this information should be made available to both the opponents and to partner.

The specific key (card combination) that governs the mixed strategy should not be shared with partner OR with the opponents.

A claim can be made that the specific key being used should be registered in advance w\with the TD so people validate that your actions match your agreements.

I might be very upset if my opponent did that. How do I know what he has or hasn't told his partner? Why not just do more like I suggested in my post and use a relatively simple formula that you can disclose to everyone, but that only gives them useless information?

[Benoit35]

Probably talking out of my rear end, but I'd only disagree with the last point:

Quote

A claim can be made that the specific key being used should be registered in advance w\with the TD so people validate that your actions match your agreements.

My partner may unwittingly discover a pattern in my random bidding (he always seems to have ♣43 when he does that baby psych), which he then would be required to disclose. I should be allowed to change keys every once in a while in order to make sure my randomness remains a "black box" to him.

That's a very hypothetical "I", because I'm nowhere near being able to play such a system...