"probabilistic" opening bids

[gombo121]

While discussing building a system with a friend I arrived to a curious question: suppose I'd like to introduce an two-way opening 2♥, which promise

1) 11-15, 6+♥

2) 5-8, 5+♠, 20%(!)

but with a twist - second variant is used not each time when a suitable hand presents itself, but in only, say, 20% cases chosen completely at random.

 

Is there any general regulations against such agreements (besides it is being obviously brown sticker)? I feel that probably there are some, but cannot come up with any concrete example.

 

The second, somewhat related question - is it legal to have two separate bids that describe the same (or, may be, overlapping) type of hands with choice between them being random?

[ArtK78]

I am sure it is not permitted, but I am not able to quote chapter and verse.

 

How would you insure that the 2♥ bid was made on 20% of the appropriate spade hands randomly? Would you roll a 5-sided die? Pull one of five perfectly equal balls (except that one was red, the others blue) out of a hat? In order to assure all involved that there was no UI being passed, would you use the selection method every time you open 2♥ whether or not the bid was being made based on hearts or spades? Even more - would you have to go through the selection process on every hand where you intend to pass so as to not convey UI? Clearly, the players cannot see the result of your method of making your random choice.

 

The concept is interesting in the abstract. If you think about how you would accomplish it in real life, it becomes comical.

[wyman]

The concept is interesting in the abstract. If you think about how you would accomplish it in real life, it becomes comical.

 

An idea that is often floated around the poker community is to use the position of the seconds hand of your watch as an RNG.

[G_R__E_G]

It's part of the GCC that opening bids above 2♣ must show at least one known suit. Therefore doing something of this nature wouldn't be legal for that reason alone (along with at least a few other reasons I'm sure).

 

Edit - it has been a while since I've read the GCC but I was sure this was there. I just went and looked at it and now I don't see it??? Has it changed when I wasn't looking?

[gwnn]

ArtK78: you could add together all the ranks of your cards and divide by 5. It would not be 20-20-20-20-20, but I'm sure it's not far either. furthermore, your disclosure would be immaculate. I'm not saying that it's workable or legal, just that it is theoretically possible. I'm sure hrothgar could come up with a much better approximation of 20% .

[ArtK78]

ArtK78: you could add together all the ranks of your cards and divide by 5. It would not be 20-20-20-20-20, but I'm sure it's not far either. furthermore, your disclosure would be immaculate. I'm not saying that it's workable or legal, just that it is theoretically possible. I'm sure hrothgar could come up with a much better approximation of 20% .

But the ranks of your cards is not independent from the requirements for the 2♥ opening.

[hrothgar]

I have long (and unsuccessfully) argued that psyches should be redefined in just such a manner...

 

FWIW, here's some content that I wrote a few years back

 

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.

[blackshoe]

It's part of the GCC that opening bids above 2♣ must show at least one known suit. Therefore doing something of this nature wouldn't be legal for that reason alone (along with at least a few other reasons I'm sure).

 

Edit - it has been a while since I've read the GCC but I was sure this was there. I just went and looked at it and now I don't see it??? Has it changed when I wasn't looking?

Possibly. I don't know. What I know is seven of the nine regulations about opening bids deal with the two level and above:

 

3. TWO CLUBS ARTIFICIAL OPENING BID indicating one of: a) a strong hand. b) a three-suiter with a minimum of 10 HCP.

4. STRENGTH SHOWING OPENING AT THE TWO LEVEL OR HIGHER that asks for aces, kings, queens, singletons, voids or trump quality and responses thereto.

5. TWO DIAMOND ARTIFICIAL OPENING BID indicating one of: a) a strong hand. b) a three-suiter with a minimum of 10 HCP.

6. OPENING BID AT THE TWO LEVEL OR HIGHER indicating two known suits, a minimum of 10 HCP and at least 5–4 distribution in the suits.

7. OPENING NOTRUMP BID AT THE TWO LEVEL OR HIGHER indicating at least 5-4 distribution in the minors.

8. OPENING THREE NOTRUMP BID indicating one of a) a solid suit or b) a minor one-suiter.

9. OPENING FOUR-LEVEL BID transferring to a known suit.

As you found, none of these require "at least one known suit".

 

All that said, the OP didn't indicate where he is. It's possible the GCC is irrelevant to him.

[semeai]

Let's start with an easier example. Maybe the bid is 2♠ showing 5-8 with 5+ spades but when you have that holding you only bid it 50% of the time and pass 50% of the time, choosing randomly. Other people may play 2♠ showing 5-8 with 5+ spades, only bidding it when they have that holding 50% of the time and passing 50% of the time, but deciding based on suit quality and other factors.

 

Surely when you have two bids that both describe your hand (here, pass and 2♠), you're free to decide on your own which to make as long as your disclosure of any partnership understandings is fine. This comes up all the time. Usually the answer isn't that you choose randomly, but if it is and you disclose properly, I don't see why that would be a problem. (Be warned, though, that I have no laws expertise.)

 

Often bids are just on a whim. If, say, my partner likes to upgrade unremarkable 14's to his 15-17 notrump "when he's feeling frisky" (and let's say that's 50% of the time), this is strikingly similar to him choosing randomly what to do with a 14. In fact, the former, even though much more common, is perhaps harder to properly disclose and not have UI from. I may be able to pick up on when my partner is feeling "frisky," whatever that means.

 

We are not simple automatons, and I'd argue that for even the most experienced, steady players (though for them would be less often), often enough the same hand in the same situation would be bid differently based on mood or lunch or the previous hand or whether a butterfly flapped through the neighboring room.

 

That all said, disclosure may be a problem. If you have a special method to choose pseudo-randomly, I suspect you should disclose it, and also make sure it's not one that your partner could crack. If you have no special method but it's "random, as decided by my gut sense of what's random", there's likely a problem with UI. Maybe you've recently had 5-8 with 5+ spades and you bid 2♠. Now it may be in your nature to make things "average out" and pass. This is a problem, as your partner has the past history, but your opponents do not. In other words, you'd better make sure your random variables for different instances of this bid are independent.

 

ArtK78: you could add together all the ranks of your cards and divide by 5. It would not be 20-20-20-20-20, but I'm sure it's not far either. furthermore, your disclosure would be immaculate. I'm not saying that it's workable or legal, just that it is theoretically possible. I'm sure hrothgar could come up with a much better approximation of 20% .

 

Awesome. This would make the play of the hand hilarious if there was any guessing to be done with few cards remaining.

 

Would this be considered "encrypted," though, and thus disallowed? Your partner doesn't have the key, of course.

 

But the ranks of your cards is not independent from the requirements for the 2♥ opening.

 

Gwnn didn't claim it was exact. In fact, he said "It would not be 20-20-20-20-20, but I'm sure it's not far either."

[bluejak]

While discussing building a system with a friend I arrived to a curious question: suppose I'd like to introduce an two-way opening 2♥, which promise

1) 11-15, 6+♥

2) 5-8, 5+♠, 20%(!)

but with a twist - second variant is used not each time when a suitable hand presents itself, but in only, say, 20% cases chosen completely at random.

 

Is there any general regulations against such agreements (besides it is being obviously brown sticker)? I feel that probably there are some, but cannot come up with any concrete example.

 

The second, somewhat related question - is it legal to have two separate bids that describe the same (or, may be, overlapping) type of hands with choice between them being random?

Are there general regulations? Presumably you mean Laws: no, there are not.

 

As for whether it is legal in a particular jurisdiction, there are lots of jurisdictions. Did you have anywhere in mind? Monaco? Thailand? Canada?

 

We ask that opening posts always say the jurisdiction [or "Online"] and quite a few discussions need to know that because of different regulations and different interpretations. This is one such question.

[aguahombre]

It's part of the GCC that opening bids above 2♣ must show at least one known suit. Therefore doing something of this nature wouldn't be legal for that reason alone (along with at least a few other reasons I'm sure).

 

Edit - it has been a while since I've read the GCC but I was sure this was there. I just went and looked at it and now I don't see it??? Has it changed when I wasn't looking?

Can't imagine it was ever true. gambling 3NT? Opening Blackwood? Roman?

 

The GCC conventions allowed over opponents' 1NT opening do require 2D and higher to have a known suit. Maybe that is what you were thinking about.

Edited September 1, 2011 by aguahombre

[wank]

as people seem to be ignoring the actual point of your post and quoting the regulations for baby level US tournaments, it would be perfectly legal to play as you suggest in a brown sticker event. of course opps might not believe you when you say you do it 20% of them time if they play against you a few times and you go on an unlikely run whereby each time you have the spade option, so it could lead to a little aggro.

 

and yes to play in the second way is legal. again people may start to believe it's not random and you'll get people whispering behind your back. i know a pair who say they played a random minor opening in a 5cM style and they're always slyly accused of being bent.

[Echognome]

I guess the esoteric, but related question, is whether it should be a public randomization device, which is disclosed (which would be relevant in Gwnn's example) or a private randomization device? I think a randomization device can be crafted if one thought hard enough, as a few examples were mentioned above.

[aguahombre]

I guess the esoteric, but related question, is whether it should be a public randomization device, which is disclosed (which would be relevant in Gwnn's example) or a private randomization device? I think a randomization device can be crafted if one thought hard enough, as a few examples were mentioned above.

back to whether 40c3a should be placed more prominently since it mentions technique as well as memory.

[gombo121]

I'm sorry I did not clarified the jurisdiction point. I understand that in a generally restrictive environment like GCC it does not stand a chance. But I'm not really going to try this concept in practice (at least, yet) and my actual jurisdiction (Russia) tends to be very permissive, so I'm interested in regulations (or, may be unwritten consensus) at international level concerning events that generally allow brown sticker conventions.

 

Concerning practical realization of the RNG, there is a very simple method - shuffle your hand before you look at it and then interpret red cards as zeros and black cards as ones - you get 13 bits of randomness, which should be enough for any practical purpose!

(OK, it won't work in online bridge, but then you probably can use RNG of your PC directly).

[helene_t]

The question is not if a BSC is a allowed under a particular regulation. OP acknowledged that it is a BSC and therefore disallowed under most regulations.

 

The question is if mixed strategies are allowed.

 

I haven't been able to find anything on google so I would expect they are. Also, when watching certain expert players on vugraph, they will open "psychic" 1NT in 3rd seat so often that it isn't a psyche and can only be explained as a mixed strategy. Other baby psyches, such as 1♥-(x)-1♠), are so frequent in some partnerships that they are not psyches.

[semeai]

Concerning practical realization of the RNG, there is a very simple method - shuffle your hand before you look at it and then interpret red cards as zeros and black cards as ones - you get 13 bits of randomness, which should be enough for any practical purpose!

 

This is great, as it sends no other signal about your hand and uses no (possibly illegal) outside aid.

 

In fact, it gives you one of 13 factorial possibilities, using any absolute ordering of the cards. That's more than 32 bits.

 

To get 50%, note two cards from your hand, shuffle your hand, and see which is first. To get 20%, note three cards from your hand, shuffle your hand, and if they appear in the order 123 shuffle again, and if they appear in the order 321, take your 20% action.

 

Added: Maybe you don't want to be seen shuffling your cards more than the one initial time. In that case, do it once, and look at the first two cards for 50% or the first three for 20%. If the first three are in the order 123, look at the next three for your "second shuffle", and so on (this doesn't give exacty 20% as you have only four chances not to get 123).

 

Added: To get exactly 20%, look at the first five cards and check whether the highest of them in your absolute order is first.

[gwnn]

That is a nice method, but I'm afraid it is not legal to base your system on such ideas. Your partner can not disclose this method in any satisfactory manner.

[semeai]

That is a nice method, but I'm afraid it is not legal to base your system on such ideas. Your partner can not disclose this method in any satisfactory manner.

 

Why? He just tells them exactly what you do. The result isn't knowable to your partner or opponents, but so what? Whether you're feeling frisky today is also perhaps not knowable, but it's allowed to base your actions on "whether I feel like taking a light action today."

[mgoetze]

Let's say someone were playing a method with several potentially overlapping opening bids, say

 

1NT: 15-17 balanced

1♠: 11-21, 5+ spades

1♥: 11-21, 5+ hearts

1♦: 11-21, 3+ diamonds

1♣: 11-21, 3+ clubs

 

Now he might open 2344 13-counts 1♦ 60% of the time and 1♣ 40% of the time. He might claim that there is some system behind this, or that he does it absolutely randomly. Well, does it matter? Can you tell the difference? (Cf. Rosenberg, M.: "Bridge, Zia ... and me", p. 43)

 

Or he might open a 3532 15-count sometimes 1NT and sometimes 1♥. Does it really matter if it is random, semirandom or completely deterministic which of these hands he chooses which opening bid with?

[bd71]

The possibility of "randomizing" penalty doubles -- say a double of a tentatively bid game when your hand is weak -- is briefly mentioned in an article ("Strategic Doubles") in the latest issue of Bridge World (September 2011).

[iviehoff]

Maybe OP can get away with this, or not far off, by removing reference to the randomisation. After all, plenty of people plenty of the time choose not to make a 3-level pre-empt with a hand that meets the formal minimal requirements they have defined on their card, which is probably something like 0+ points and 6+ cards. Or consider for example weak 2s, a lot of people put down 5+ card suit, but in practice there are plenty of players who would rarely use the bid with only 5 cards. Having a mixed meaning bid with strong meanings as well as the pre-empt, well that's just like the Multi-2D.

[barmar]

The spirit of full disclosure is that the opponents are entitled to any information you have about partner's hand. Since you don't know what random decision he's made, you don't know any more than the opponents.

 

What I find interesting about this particular example is that the disclusure isn't really needed when the 2♥ bid is made. When he makes that bid, you can definitively state that he has either an intermediate heart or weak spade hand, not much different from other multi bids. It's the PASSES that are really notable, since he might hold a weak spade hand that could have opened 2♥.

 

I'm not sure how you would describe that in any useful way, though. "He either has a normal non-opening hand, or he has 5-8 HCP 5+♠; 80% of the time when he has the latter hand he passes." Now, for someone to figure out the likelihood that he holds the weak spade hand, they need to know the frequency that non-opening hands fit that description, and then reduce that by 20%.

 

Another aspect of this is what it means when he passes, and then bids 1♠, either as a response or overcall. There's 20% less chance of him holding 5-8 and 5+ cards than there would be for most other players. So he's a little more likely to either have 9+ HCP or only 4 cards in the suit. So do you alert all these spade bids so you can disclose the small difference in probabilities?

[semeai]

What I find interesting about this particular example is that the disclusure isn't really needed when the 2♥ bid is made. When he makes that bid, you can definitively state that he has either an intermediate heart or weak spade hand, not much different from other multi bids. It's the PASSES that are really notable, since he might hold a weak spade hand that could have opened 2♥.

 

The 2♥ bid is affected as well. It changes the probability that he has a heart hand or a spade hand. Without the 20% it would be much more likely it was the spade hand, but with that it's probably close to even.

 

Using Bayes' Theorem:

 

prob(spade hand | 2♥) = prob(2♥ | spade hand) * prob(spade hand) / prob(2♥) = .2 * prob(spade hand) / prob(2♥)

prob(heart hand | 2♥) = prob(2♥ | heart hand) * prob(heart hand) / prob(2♥) = prob(heart hand) / prob(2♥)

 

So the ratio prob(spade hand | 2♥) : prob(heart hand | 2♥) is equal to .2 * prob(spade hand) : prob(heart hand) instead of the same expression without the .2 if the 20% provision weren't there.

 

Here spade hand = 5-8, 5+ spades, heart hand = 11-15, 6+ hearts.

 

Added: According to BBO's "deal source" widget, prob(spade hand) = 5.06%, and prob(heart hand) = 1.80 %. So without the 20% provision, it's more than twice as likely it's the spade hand. With it, it's almost twice as likely it's the heart hand.

[barmar]

So who's responsibility is it to perform these calculations? Is it reasonable to describe the hand as in the OP, and expect opponents to calculate the probabilities themselves at the table? Or should the pair playing this system figure this out, so that they can provide more useful disclosure?