[sceptic]

Given the power of computers these days, would it not be possible to create a system that is the ultimate system

You could compare each opening bid against every combination of opener possible and each subsquent bid or pass etc etc and just work out against every concievable hand possible, for the best system

just working with the stats from hand types would be able to give you a system that should be workable

i.e. 5 spades and 11- 17 hcp 52,000 instances out of all total combinations
5 spades and 11 - 16 hcp 39,000 instances

If I have not made myself clear, someone else can elaborate for me LOL

[TylerE]

Well, since the number of hands is far, far (likes millions) of times less than the number of non-competitive auctions, it is possible for one hand to show the EXACT cards it's holding.

[ArtK78]

Matt Granovetter and Ron Rubin (and later Mike Becker) played a system some years back called the "Ultimate Club." It was a relay system, and they had a series of incredible scores in the Bridge World's Challenge the Champs competition. I tried learning it once some years ago - the amount of memorization required is enormous. There are few intuitive (i.e. "natural") sequences in the system.

Some variant on their system might, in fact, be the "Ultimate" system. However, once you leave the field of the laboratory and enter the field of play, the niceties of the system fall down. In other words, competitive auctions tend not to produce scientific accuracy. And all systems based on artificial bidding have problems in competitive auctions.

[helene_t]

TylerE, on Jan 9 2008, 09:28 PM, said:

Well, since the number of hands is far, far (likes millions) of times less than the number of non-competitive auctions, it is possible for one hand to show the EXACT cards it's holding.

Far from. In a relay sequence you can show some 0.7 bits per step. So you can show 10-11 bits without bypassing 3NT, equivalent to distinguishing between less than 2000 hand types.

The challenge is not so much to maximize the amount of information exchanged. Relay systems are practically optimal in that respect, although it gets more complex when mutual information exchange is considered. The real challenge is to find out what information partner needs (and doesn't help opps too much).

I suppose the question is if a computer program could find the optimal bidding system. In principle, this would require an optimal strategy for declarer play and defense also, since otherwise the computer would not know how information conveyed to opps influences the chance of making the contract etc. In principle an optimal strategy could be computed since bridge is a finite game.

With limited processing power, we are stuck with some heuristics that approximate the optimal strategy for declarer play and defense. As a simplest case, one could search for the optimal bidding system given that the hand will be played double dummy. One would have to optimize the opponents bidding strategies as well.

[jtfanclub]

There can be a possible best bidding system without competition.

I'm pretty sure there cannot be a best bidding system with competition. For example, the meaning of a 1 spade overcall over 1 club is not only going to vastly change the meaning of the continuations after 1 spade, but what you want to put in 1 club in the first place. That's an infinite series...you make your system, they make their defense, you change your system, they change their defense, etc. Even if you make the best possible system against the best possible defense, that won't make it the best possible system against some inferior defense.

"OK, so my partner opened 1 club. The next player overcalled one spade, which means that the sum of his spade length to the fourth power plus his heart length cubed plus his diamond length squared is either prime or an even number adjacent to a prime. The meaning of a 1NT call now is, um..."

[P_Marlowe]

jtfanclub, on Jan 9 2008, 03:28 PM, said:

<snip>
I'm pretty sure there cannot be a best bidding system with competition. For example, the meaning of a 1 spade overcall over 1 club is not only going to vastly change the meaning of the continuations after 1 spade, but what you want to put in 1 club in the first place. That's an infinite series...you make your system, they make their defense, you change your system, they change their defense, etc.
<snip>

Not an issue, according to the law
someone has to state, what he is
playing, and what his defence is,
there exists a lawrule, which makes
sure, there is no loop.

With kind regards
Marlowe

[jtfanclub]

P_Marlowe, on Jan 9 2008, 03:55 PM, said:

Not an issue, according to the law
someone has to state, what he is
playing, and what his defence is,
there exists a lawrule, which makes
sure, there is no loop.

So I'm playing a weekly team game against a computer with infinite processing power.

This week, I play the computer, and the computer plays The Best System In The Universe. It beats me.

Next week, I come in playing The Defense That Beats The Best System In The Universe. I win.

The following week, I come in playing the The Defense that Beats the Best System In The Universe, but the computer's changed to playing The System That Beats The Defense That Beats The Best System In The Universe. It beats me.

The week after that, I flip a coin before I go to our bridge game. If it's heads, I play The Defense That Beats The Best System In The Universe. If it's tails, I play The Defense That Beats the System That Beats The Defense That Beats The Best System In The Universe.

What should the computer play?

It really is an infinite loop...not during a match (when you can't change your system) but playing an infinite number of matches.

[helene_t]

It's not an infinite loop. Consider the paper-stone-scissors game. Bridge is sequential, so one player has to state his strategy first, and then the other adapts.

The computer says: if your 1♣ opening shows this, my overcall structure is that. If your 1st-seat opening "pass" shows this, my 2nd-seat opening structure will be that. Etc. Given all that information, you chose your 1st seat opening structure.

If N (or S) is dealer, there is, for each NS system, and optimal defence that EW should use. The best NS system is the one that works best, given that EW will always counter with the optimal defense.

It would be an infinite loop if the computer could counter your 1st-seat opening structure with a 0th-seat preempt structure, which you could counter by a minus-oneth-seat preempt structure and so on ad infinitum, But bridge is a finite game. So there can be no infinite loops.

[ArtK78]

Since when did we enter into Philosophy 101?

[P_Marlowe]

jtfanclub, on Jan 9 2008, 04:08 PM, said:

P_Marlowe, on Jan 9 2008, 03:55 PM, said:

Not an issue, according to the law
someone has to state, what he is
playing, and what his defence is,
there exists a lawrule,  which makes
sure, there is no loop.

So I'm playing a weekly team game against a computer with infinite processing power.

This week, I play the computer, and the computer plays The Best System In The Universe. It beats me.

Next week, I come in playing The Defense That Beats The Best System In The Universe. I win.

The following week, I come in playing the The Defense that Beats the Best System In The Universe, but the computer's changed to playing The System That Beats The Defense That Beats The Best System In The Universe. It beats me.

The week after that, I flip a coin before I go to our bridge game. If it's heads, I play The Defense That Beats The Best System In The Universe. If it's tails, I play The Defense That Beats the System That Beats The Defense That Beats The Best System In The Universe.

What should the computer play?

It really is an infinite loop...not during a match (when you can't change your system) but playing an infinite number of matches.

No, it is not.

What you describe is a standard game theory
problem, and it is possible to solve the issue.
The solution is a so called mixed strategy, i.e.
a certain amount of time you will play X, and
another time you will play Y, and that is your
system.

The main issue is to define the problem, the
constrains and what is meant by optimal system.

With kind regards
Marlowe

[jtfanclub]

helene_t, on Jan 9 2008, 04:30 PM, said:

If N (or S) is dealer, there is, for each NS system, and optimal defence that EW should use. The best NS system is the one that works best, given that EW will always counter with the optimal defense.

Ah, but that's a faulty assumption.

Suppose you have two computer teams playing in a Swiss match, along with a hundred human teams. Computer Team A plays the best possible opening system given that the opponents are playing an optimal defense. Computer Team B scouts the field, and plays the best possible opening system given the actual defense that the humans are using, which is decidedly suboptimal.

Which do you think is going to win?

Most forms of Bridge are drunk-punching contests: they determine the winner not by how well they do head to head, but by how well the best teams do against inferior teams. As with most similar games, the best strategy is dependent upon the quality of the drunks.

[helene_t]

OK, under your assumptions you are right, Matthew.

[jtfanclub]

Quote

The solution is a so called mixed strategy, i.e. a certain amount of time you will play X, and another time you will play Y, and that is your system.

Sorry, I don't accept that one. Playing, say, Precision 70% of the time and SAYC 30% of the time is not 'a system' by my definition, even if it turns out to be superior to playing Precision or SAYC all the time. It's a strategy, certainly, but I don't buy that it's a system.

[helene_t]

You could play a 2♣ opening as 70% chance that it's a Precision 2♣ and 30% chance that it's a SAYC 2♣. If partner doesn't know which one it is, obviously it's an inferior system. OTOH if p does know, opps must be told as well, and then it's not a mixed strategy anymore.

So the mixed strategy would be viable only under a zero-disclosure regimen. (Of course, mixed strategies could be viable is some other cases, for example whether or not to make a help suit trial, but basing the entire system on mixed strategies sounds silly).

[jtfanclub]

helene_t, on Jan 9 2008, 04:46 PM, said:

OK, under your assumptions you are right, Matthew.

Did you hear about the computer that solved chess? When it played as black, it always won. When it played as white, it always resigned before its opening move. You see, it assumed that the opponent would play optimally, and since the optimal play as black always won no matter what white did, what was the point in moving?

So there you have it...the best chess playing computer in the world, and it only wins half the time against rank beginners!

Edit- actually, that could come out pretty funny for bridge. Assume that whatever your opening bids mean, your opponents have the perfect defense to counter it, and that you can modify your defense to be the perfect one for their openings. I suspect the best solution would be to pass most hands!

[david_c]

Playing teams is what messes it all up. It's probably* true to say that for any given system, there exists an opposing system that beats it more than 50% of the time in a teams match.

If you play rubber bridge, on the other hand, an optimal system must exist for the reasons Helene gave. (That is, your long-term expectation is non-negative no matter what system the opponents are playing.)

*I say "probably" because, if you study game theory, games of this type tend to have this feature. But it's difficult to see how you could prove this without actually solving bridge completely.

[matmat]

jtfanclub, on Jan 9 2008, 05:11 PM, said:

helene_t, on Jan 9 2008, 04:46 PM, said:

OK, under your assumptions you are right, Matthew.

Did you hear about the computer that solved chess? When it played as black, it always won. When it played as white, it always resigned before its opening move. You see, it assumed that the opponent would play optimally, and since the optimal play as black always won no matter what white did, what was the point in moving?

So there you have it...the best chess playing computer in the world, and it only wins half the time against rank beginners!

Edit- actually, that could come out pretty funny for bridge. Assume that whatever your opening bids mean, your opponents have the perfect defense to counter it, and that you can modify your defense to be the perfect one for their openings. I suspect the best solution would be to pass most hands!

I am pretty sure you mean checkers. To my knowledge chess has not yet been solved.

[jtfanclub]

matmat, on Jan 9 2008, 06:08 PM, said:

I am pretty sure you mean checkers. To my knowledge chess has not yet been solved.

It was a joke. Oh well.

[barmar]

TylerE, on Jan 9 2008, 03:28 PM, said:

Well, since the number of hands is far, far (likes millions) of times less than the number of non-competitive auctions, it is possible for one hand to show the EXACT cards it's holding.

But an optimal bidding system doesn't just have to show the hands, it also has to find the best contract given the hands. When you're counting all those possible auctions, isn't it likely that many of them get you too high by the time both players have described their hands completely?

For instance, suppose one player has a strong NT and the other player has a Yarborough with long ♥, so you would like to end up in 2♥. There are only 8 bids available, and 128 possible auctions. But there are thousands of hands the two of them can hold.