Random bids?

[benlessard]

BTW, you're confusing the notion of a mixed strategy with that of a repeated game. It's very easy to demonstrate that mixed strategies are optimal without the need to introduce repeated games)

Nope, what im saying is that its mathematically knowned that in a "big ensemble" there is no need for mixed strategies.

 

Lets say that after a bidding sequence

 

1H – 1S

3S - ???

 

and now you are making a m cue.

 

The optimal strategy for the possible ensemble of hands is

90% you make the normal cue

10% you make the false cue.

 

This is NOT a mixed strategy.

Depending on your hand and whatever factor you like its possible to splits the ensemble of hands into 90%-10% and the ensemble is big anyway so you dont need to randomize. SO EVERY SINGLE HAND CAN BE BID EXACTLY THE SAME WAY OVER AND OVER WITHOUT SUFFERING ANY LOSSES because the opponent cannot predict your hand in fonction of your actions.

 

 

If your ensemble of hands is limited (like sometimes in poker) to

 

AA,KK,QQ,JJ,TT,99 (a pair is 6%)

AK,AQ,AJ,KQ, (non-pair is 16%)

 

assuming the optimal strategy is to raise 20% call 60% and fold 20% then youll need a mixed strategy because

 

1- you cannot split the hands 60-20-20%

2- playing the same way over and over make you predictable because your ensemble of hands after your decision will be very limited.

 

So here youll fold 16% of KQ, 4% of AJ

 

youll raise, AA,KK most of the times and sometimes raise with AKs and QQ.

 

So here youll need some mixed strat with AJ,AA,KK,QQ,AK.

 

Im trying to find a site where its neatly explained when ill get one ill post it.

[hrothgar]

BTW, you're confusing the notion of a mixed strategy with that of a repeated game. It's very easy to demonstrate that mixed strategies are optimal without the need to introduce repeated games)

Nope, what im saying is that its mathematically knowned that in a "big ensemble" there is no need for mixed strategies.

 

Lets say that after a bidding sequence

 

1H – 1S

3S - ???

 

and now you are making a m cue.

 

The optimal strategy for the possible ensemble of hands is

90% you make the normal cue

10% you make the false cue.

 

This is NOT a mixed strategy.

Depending on your hand and whatever factor you like its possible to splits the ensemble of hands into 90%-10% and the ensemble is big anyway so you dont need to randomize. SO EVERY SINGLE HAND CAN BE BID EXACTLY THE SAME WAY OVER AND OVER WITHOUT SUFFERING ANY LOSSES because the opponent cannot predict your hand in fonction of your actions.

Ben,

 

You appear to me making the following claim:

 

If you are dealing with a large enough set of hands, its possible to create a pure strategy that enjoys the same properties as a mixed strategy.

 

I don't dispute this. If you were paying attention, Josh and I already discussed this issues (though we did so in the context of a disclosure problem). A few posts back, I described the set of conditions that would be required to implement Josh's recommendation that both key and cipher to the opponents.

 

With this said and done: Lets assume that we could devise some cipher where in I could disclose BOTH the key and the cipher to both partner and opponents and none of them would be in a good position to infer my hand type based on the cards that they held...

 

This is the same set of conditions that would need to hold true to create a pure strategy that behaves as if it were a mixed strategy.

 

I suspect that there is one very important difference:

 

I have done any exhautive proof, however, I epxect that its much easier to implement a mixed strategy that behaves the way I want than to try and compute an ensemble of hands that mirror the mixed strategy.

 

Please note: I'm not claiming that solving for the mixed strategy is easier. I'm simply saying that the ensemble technique seems much more difficult.

 

I also suspect that the salient information that needs to be disclosed about the ensemble strategy is equivalent to the pdf for the mixed strategy.

[awm]

There is one major advantage to the ensemble strategy, which is disclosure.

 

Occasionally it is necessary to check that our disclosure actually matches our methods. With a deterministic method, it's not too hard to do this -- you look for hands where "what we disclosed" differs from "what we hold." If we never psych or used mixed strategies or misbid, then these should always be the same and obviously there is no issue.

 

But suppose I'm disclosing a mixed strategy. Since there are several possible actions on any hand, what we need to confirm is that:

 

(1) The frequency of various actions matches the probability distribution we disclosed.

(2) The choices made are actually random and not a function of some other information that might be available to partner.

 

This is way more difficult to handle. For the first, if you have a sufficient sample of identical decisions you might be able to do this, but this requires collecting a huge number of examples rather than just looking for a single "failure to disclose" as in the deterministic case. The second seems almost impossible, although I suppose we could look for instances when partner had to guess which random choice we made, and then see if the "success rate" is higher than ordinary chance would explain (although even then, this could be based on reads of the opponents or the like).

 

The ensemble strategy being deterministic is easy to check... we disclose: "I bid X if the sum of my spot cards is even, and Y if it's odd" and then it's a simple matter to check (after the hand of course) if my disclosure matched the action I took.

[bill1157]

There is a lot of myth around mixed strategies especially in poker. Most think that if you dont vary your play opps will sometimes deduced your play and get an edge. Most of the time this is false, only when the possibles holdings are severly limited youll need to used mixed strategy. There is no need whatsoever to use a mixed strategy in bridge bidding since your possible holdings are wide.

I think randomizing works terribly in poker (at least nl holdem) but probably works well in bridge (long team games and rubber bridge).

Having said that, what works for Zia may not work for the rest of us, or may not work except in a $1/pt rubber bridge game. He gets by with alot because people probably cave in when they play against him.

 

Bill