[babalu1997]

is there such a thinh as the nash equilibrium for the game of bridge?

Sometimes rank beginners steal the score. I was playing with an 8 year old boy as a partber. At first he had a strong hand and he opened at the 3 level (more cards more open). After the hand was over i yold him, we open at the 3 level when we have no cards to scare the opps.

A couple of hands later he opened 3 Clubs. He had a complete yarborough with 4 cards in clubs and a 4-1 fit.
He played 3 clubs for a -250 score, undoubled, the opps had a slam, but had no idea how to defend, then accused the boy of psyching.

I say he just upset the bash equilibrium cart. Does that make sense?

[Antrax]

It has nothing to do with the Nash Equilibrium. The "par score" you can calculate given all four hands and double-dummy play is an example of a NE. In a way, weak bids demonstrate it. Playing randomly to screw with opponents has nothing to do with it, though.

[Lurpoa]

babalu1997, on 2011-June-06, 06:13, said:

is there such a thinh as the nash equilibrium for the game of bridge?

Sometimes rank beginners steal the score. I was playing with an 8 year old boy as a partber. At first he had a strong hand and he opened at the 3 level (more cards more open). After the hand was over i yold him, we open at the 3 level when we have no cards to scare the opps.

A couple of hands later he opened 3 Clubs. He had a complete yarborough with 4 cards in clubs and a 4-1 fit.
He played 3 clubs for a -250 score, undoubled, the opps had a slam, but had no idea how to defend, then accused the boy of psyching.

I say he just upset the bash equilibrium cart. Does that make sense?

♥

Yep, it is good to always question your methods.... and those of others...
Bidding is just a coded language, and most important is, that you speak the same language as your partner.

And almost as important, that you understand some of the language of your opponents...

[mgoetze]

babalu1997, on 2011-June-06, 06:13, said:

I was playing with an 8 year old boy as a partber. ... [The opponents] then accused the boy of psyching.

This belongs in the "bridge is dying?" thread.

[hrothgar]

It's been a long time since I spent any time working with existence proofs, however:

1. Bridge is a finite game
2. I'd better dollars to donuts that a Nash equilbirum exists
3. The existence of said equilbrium says nothing about the ability to describe said equilbrium

With this said and done: It sounds like your partner was randomly flailing rather than making an informed decision about expectation maximization. I'd be hesitant to trot out game theory constructs...

[jogs]

hrothgar, on 2011-June-06, 08:45, said:

It's been a long time since I spent any time working with existence proofs, however:

1. Bridge is a finite game
2. I'd better dollars to donuts that a Nash equilbirum exists
3. The existence of said equilbrium says nothing about the ability to describe said equilbrium

Bridge is a probabilistic game. Chess is deterministic. Does Nash equilibriums even exists for probabilistic games? Is there a Nash equilibrium for hold'em? The two person game has been 'solved' and the favorite still loses quite often.

[Antrax]

jogs, on 2011-June-06, 12:29, said:

Bridge is a probabilistic game. Chess is deterministic. Does Nash equilibriums even exists for probabilistic games? Is there a Nash equilibrium for hold'em? The two person game has been 'solved' and the favorite still loses quite often.

Yes, it exists. For instance, the NE for rock, paper, scissors is playing each with 1/3 probability.
Nash equilibria (is that a word?) for Texas Hold'Em certainly is relevant, mostly in the area of (semi-)bluffing frequency and most adjustments you make for stack size in tournament play. Informally, a strategy that is NE for such games has the characteristic that if I tell you what I'm doing, you won't be able to use the knowledge to beat me. So if I tell you "I am going to bet 2/7th of the time I raise preflop and the flop is ace rag rag and I don't have the ace, and 100% of the time when I have the ace" (just random numbers, don't use this strategy), and you work out the math and figure out that you get even expectation between calling me, raising me and folding, then you've been Nash Equilibrium-ed.

[Vampyr]

babalu1997, on 2011-June-06, 06:13, said:

then accused the boy of psyching.

What does "accused the boy of psyching" mean? Did they suggest that, if he did psych, he should not have done?

[blackshoe]

Antrax, on 2011-June-06, 12:39, said:

Yes, it exists. For instance, the NE for rock, paper, scissors is playing each with 1/3 probability.
Nash equilibria (is that a word?)

Equilibria is the plural of equilibrium.

[jogs]

babalu1997, on 2011-June-06, 06:13, said:

... accused the boy of psyching.

It's still legal to psych, isn't it? What difference does it make, whether he psyched or not?

[benlessard]

Everytime you can get an edge by knowing what the other people are doing there is a Nash Equilibrium.

Probabilistic, deterministic, finite, infite , cooperative or competitive it doesnt really matter. What really matter is the possibility or gaining or giving information away and that information is useful for designing strategies.

In chess game for example knowing your opponent opening repertoire will help you prepare for the game but he too will know that you have acces to the information and he will have the choice of throwing you a "curveball" or sticking to his usuall fastball. On the road the tendencies of the other drivers will influence your driving strategies wich will influence the other drivers and at the end there is some sort of possible maxima
equilibrium.

[Antrax]

benlessard, that's not entirely true. For instance, let's play the "open interval" game, where we both pick a number smaller than 1 and whoever picks the greater number wins. Clearly if I know your strategy I can win. What's the NE for this game?
The examples you give are also not NE. Again, informally, a NE is a sort of a stable state (hence the name "equilibrium"), where if all the players in a game know what the other guys are going to be doing, they still don't want to change their choice of strategy.

Thanks blackshoe. It's what I thought except sometimes that plural form is incorrect (like "fora" not being the plural of "forums")

[1eyedjack]

jogs, on 2011-June-06, 17:21, said:

It's still legal to psych, isn't it?

Not on most BBO tourneys it isn't (not that the OP was playing in a BBO tourney, I suspect).

[benlessard]

I dont really understand the open interval game. If its a number theory game or deal with infinites than maybe there exceptions.


From what i understand. In a symmetric game Player A show his matchplan to B.


A = a%, B =b%, C=c% etc

B has an optimal strategy to counter A plan. Player B matrix payoff will yield a profit because of B ability to know player A plan. But in such game, its possible for A to randomize the decision in a way that even if player B know the matchplan he wont be able to get a +EV result and that is a NE.

If its impossible to compute the best strategy because of raw complexity or because the other player play poorly, than i admit NE is going to be impossible to reach but its still there in theory.

[Antrax]

Okay, that's a lot more accurate. I probably misunderstood your previous post.
Playing poorly is no defense. It's possible the NE strategy for player B will benefit less against poor player A than some other strategy B can adopt (this is what usually happens with poker - if you want to gain the most from people's poor play, you should make strategic adaptations that overall make you play poorer too), but the NE will not show negative EV (assuming zero-sum game). In the example in the opening post, if those opponents would keep playing that pair, on the long run they would gain from his random 3♣ bids. They could design a bidding system meant to deal with random 3♣ interference that says nothing and gain even more, but just playing good bridge should suffice.

[benlessard]

For the op the way that i see it is

Pair A, never psych

Pair B psych X% amount

pair C psych twice as often as pair B.

Pair D (Us)

If pair D play against ABC but dont know them and dont play long enough to learn their tendency. We (Pair D) will keep the same strategies against all of them but we are going to have a different payoff matrix against each of them. Our strategy will deal against their psyching habit a certain way. Those payoff matrix have nothing to do wiht NE. Its possible pair C just psych too much and get bad results agaisnt us even if we have dont have any method to deal with psych.

2nd case we get to know ABC and devise a strategies against them knowing their psych habits. (for example against the pair who never psych i use some double that are normally penalty and played them takeout.)etc

Now if we can get better results with 1 specific strategy against each of them, its because this new information (their psyching ratio) give me an edge. If that is the case than there is a NE somewhere. There is a psych % amount that even if it know it i will not be able to devise a counter strategy that will yield profit. This is a NE. Any deviation of this % ratio of psych can be exploited if we know the deviation.

[blackshoe]

Antrax, on 2011-June-06, 22:15, said:

Thanks blackshoe. It's what I thought except sometimes that plural form is incorrect (like "fora" not being the plural of "forums")

Interesting. My dictionary app has three definitions for "forum", for the first two of which the plural is specified to be "forums". The third sense is

Quote

( pl. fora |ˈfôrə|) (in an ancient Roman city) a public square or marketplace used for judicial and other purposes.

[nige1]

Antrax, on 2011-June-06, 06:45, said:

It has nothing to do with the Nash Equilibrium. The "par score" you can calculate given all four hands and double-dummy play is an example of a NE. In a way, weak bids demonstrate it. Playing randomly to screw with opponents has nothing to do with it, though.

Vampyr, on 2011-June-06, 12:39, said:

What does "accused the boy of psyching" mean?

The boy's opponents accused him of playing Bridge. Optimal Bridge strategy mandates the occasional psych.

[cherdano]

hrothgar, on 2011-June-06, 08:45, said:

It's been a long time since I spent any time working with existence proofs, however:

1. Bridge is a finite game
2. I'd better dollars to donuts that a Nash equilbirum exists
3. The existence of said equilbrium says nothing about the ability to describe said equilbrium

With this said and done: It sounds like your partner was randomly flailing rather than making an informed decision about expectation maximization. I'd be hesitant to trot out game theory constructs...

Quote

"Matchpoints is a multi-player game and hence does not have a Nash equilibrium." - Bob Hamman

Oh, that's not quite how the quote goes? I am sure that's what he meant though!

[Echognome]

jogs, on 2011-June-06, 12:29, said:

Bridge is a probabilistic game. Chess is deterministic. Does Nash equilibriums even exists for probabilistic games? Is there a Nash equilibrium for hold'em? The two person game has been 'solved' and the favorite still loses quite often.

Moreover, the existence of a Nash Equilibrium is dependent on the ability to employ "mixed strategies". See, for example, the Matching Pennies game.

http://en.wikipedia....atching_pennies

There are other types of equilibrium depending on whether the game has incomplete information or imperfect information; whether the game is static or dynamic; and whether the game is deterministic or stochastic. Search the following terms:

Subgame Perfect Equilibrium
Bayesian-Nash Equilibrium
Perfect Bayesian Equilibrium
Sequential Equilibrium
Stochastic Game

You can (obviously) spend a lot of time learning these concepts, but I will say that most of them have been studied extensively before!