[Antrax]

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it'd take a lot more effort than any of you probably think

What are you basing this on? Who said it seems easy or achievable with the current state of the art?

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Each system can be assigned a score based on its results in every possible hand, to come up with some sort of average.

Ignoring the play? Or are you considering playing the hand single-dummy a solved problem? What score does reaching a 99% slam receive for the set of hands where every break is bad and every finesse is wrong?

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Of course, if you faced opponents that used many different defenses you'd have to come up with different systems to deal with each of those, which is unbelievably many possibilities if you ever plan to actually play competitively using such a system. And the though of trying to show that all possible other systems would result in a worse value on average is just an absurd amount of work to try to get through, even in one little situation.

I really don't see the relevance. Given the opponent hands, some bidding system on earth has the "par final contract" bid that means "I am holding precisely these 13 cards" by the first opponent to bid. That system will beat the "best" system for that example. That's why you're not looking for some "always best" system.

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Long story short, I'm a math freak of nature and I can tell for sure that it is solvable, but it's hard for me to come up with a proof it.

I have no clue what your credentials are, but I hope you're being ironic.

[hrothgar]

Antrax, on 2013-July-01, 06:08, said:

>> Long story short, I'm a math freak of nature and I can tell for sure that it is solvable, but it's hard for me to come up with a proof it.

I have no clue what your credentials are, but I hope you're being ironic.

FWIW, I agree with the previous poster.

Bridge is clearly in the set of games that is (in theory) solvable.
(So is chess)

Off the top of my head, I'm not sure how to prove this. (I had forgotten that Zermelo's theorem requires perfect information).
However, I'm guessing if I poked around through my old textbook's something would pop up.

For anyone whose interested, the following page has some good information

http://en.wikipedia....sive-form_games

[helene_t]

hrothgar, on 2013-June-29, 17:21, said:

Acol > Regres
Regres > Roth Stone
Roth Stone > Acol

If this is the case it might just be because the optimal defense against a Regres 1st-seat pass is different from the optimal against a R-S 1st seat pass. There could be an optimal bidding system that defends differently against different 1st passes just like it defends differently against different 2♦ openings.

If we change the game so that it is played without disclosure then probably the optimal system would be a mixed strategy in which we chose a system randomly (from a menu of hundreds of systems) before each board without telling opps which one we chose. But that's quite different from bridge.

[FM75]

The perfect information objection to Zermelo's theorem is not applicable.

The set of all possibilities is clearly finite and enumerable.
6.35*10^11 deals * 4 positions for dealer * 4 vulnerability conditions * some number of scoring methods * a finite number of possible auctions.

So let's put number of scoring methods at about 5 for argument's sake, making the product of the middle three 80. Now we have:
5. * 10^13 times the number of auctions.

Anybody know off hand the number of possible auctions? There are 36 possible opening bids.
Starting with:
pppp
ppp1cppp
...
ppp1cppXppXXpp1d...7NppXppXX
...
7NppXppXX

This is a nice challenging problem. How many auctions?