Is bridge a fair game: references/heuristics?
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Though not knowledgeable on card games or game theory, I've just learnt the rules of bridge, and I'm starting to wonder whether it can be proven that bridge is a fair game.
Of course, to give an answer, one must specify a scoring system, or else simplify the game (e.g. determining the trump by a die toss and aiming to win as many tricks as possible, instead of the messy business of bidding). And of course I ignore the 'trivial' symmetry which randomly determines who sits where and who leads - one wants to know whether bridge is fair after all that.
But if anyone could provide me references or heuristics in relation to the fairness of bridge, I would be grateful!
probability recreational-mathematics game-theory card-games
asked Aug 16 at 7:49
Chris Sanders
1,148216
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up vote
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Though not knowledgeable on card games or game theory, I've just learnt the rules of bridge, and I'm starting to wonder whether it can be proven that bridge is a fair game.
Of course, to give an answer, one must specify a scoring system, or else simplify the game (e.g. determining the trump by a die toss and aiming to win as many tricks as possible, instead of the messy business of bidding). And of course I ignore the 'trivial' symmetry which randomly determines who sits where and who leads - one wants to know whether bridge is fair after all that.
But if anyone could provide me references or heuristics in relation to the fairness of bridge, I would be grateful!
probability recreational-mathematics game-theory card-games
asked Aug 16 at 7:49
Chris Sanders
1,148216
1
There should be no reason to think Bridge should be fair between the pair bidding first and the other pair, or in your simplified version (Whist?) the pair leading first and the other pair. But a random allocation of position (plus rotation of position in successive hands) makes it fair by what you call the trivial symmetry
– Henry
Aug 16 at 8:08
It depends on how do you define fair. Say two teams are in the final of a team event, boards are duplicate along two tables so the board/location factor is evened out. The remaining factor affecting the result are the choice of bidding system / method by each team, the bidding judgement at the table, the first lead, the subsequent play, and last but not least some accident. Do you mean If all things being equal then it should be a perfect draw?
– BGM
Aug 16 at 10:42
@BGM yes that's what I had in mind
– Chris Sanders
Aug 16 at 11:00
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Though not knowledgeable on card games or game theory, I've just learnt the rules of bridge, and I'm starting to wonder whether it can be proven that bridge is a fair game.
Of course, to give an answer, one must specify a scoring system, or else simplify the game (e.g. determining the trump by a die toss and aiming to win as many tricks as possible, instead of the messy business of bidding). And of course I ignore the 'trivial' symmetry which randomly determines who sits where and who leads - one wants to know whether bridge is fair after all that.
But if anyone could provide me references or heuristics in relation to the fairness of bridge, I would be grateful!
probability recreational-mathematics game-theory card-games
asked Aug 16 at 7:49
Chris Sanders
1,148216
Though not knowledgeable on card games or game theory, I've just learnt the rules of bridge, and I'm starting to wonder whether it can be proven that bridge is a fair game.
Of course, to give an answer, one must specify a scoring system, or else simplify the game (e.g. determining the trump by a die toss and aiming to win as many tricks as possible, instead of the messy business of bidding). And of course I ignore the 'trivial' symmetry which randomly determines who sits where and who leads - one wants to know whether bridge is fair after all that.
But if anyone could provide me references or heuristics in relation to the fairness of bridge, I would be grateful!
probability recreational-mathematics game-theory card-games
asked Aug 16 at 7:49
Chris Sanders
1,148216
edited Aug 16 at 7:55
asked Aug 16 at 7:49
Chris Sanders
1,148216
asked Aug 16 at 7:49
Chris Sanders
1,148216
asked Aug 16 at 7:49
Chris Sanders
1,148216
1,148216
1
There should be no reason to think Bridge should be fair between the pair bidding first and the other pair, or in your simplified version (Whist?) the pair leading first and the other pair. But a random allocation of position (plus rotation of position in successive hands) makes it fair by what you call the trivial symmetry
– Henry
Aug 16 at 8:08
It depends on how do you define fair. Say two teams are in the final of a team event, boards are duplicate along two tables so the board/location factor is evened out. The remaining factor affecting the result are the choice of bidding system / method by each team, the bidding judgement at the table, the first lead, the subsequent play, and last but not least some accident. Do you mean If all things being equal then it should be a perfect draw?
– BGM
Aug 16 at 10:42
@BGM yes that's what I had in mind
– Chris Sanders
Aug 16 at 11:00
add a comment |Â
1
There should be no reason to think Bridge should be fair between the pair bidding first and the other pair, or in your simplified version (Whist?) the pair leading first and the other pair. But a random allocation of position (plus rotation of position in successive hands) makes it fair by what you call the trivial symmetry
– Henry
Aug 16 at 8:08
It depends on how do you define fair. Say two teams are in the final of a team event, boards are duplicate along two tables so the board/location factor is evened out. The remaining factor affecting the result are the choice of bidding system / method by each team, the bidding judgement at the table, the first lead, the subsequent play, and last but not least some accident. Do you mean If all things being equal then it should be a perfect draw?
– BGM
Aug 16 at 10:42
@BGM yes that's what I had in mind
– Chris Sanders
Aug 16 at 11:00
1
1
There should be no reason to think Bridge should be fair between the pair bidding first and the other pair, or in your simplified version (Whist?) the pair leading first and the other pair. But a random allocation of position (plus rotation of position in successive hands) makes it fair by what you call the trivial symmetry
– Henry
Aug 16 at 8:08
There should be no reason to think Bridge should be fair between the pair bidding first and the other pair, or in your simplified version (Whist?) the pair leading first and the other pair. But a random allocation of position (plus rotation of position in successive hands) makes it fair by what you call the trivial symmetry
– Henry
Aug 16 at 8:08
It depends on how do you define fair. Say two teams are in the final of a team event, boards are duplicate along two tables so the board/location factor is evened out. The remaining factor affecting the result are the choice of bidding system / method by each team, the bidding judgement at the table, the first lead, the subsequent play, and last but not least some accident. Do you mean If all things being equal then it should be a perfect draw?
– BGM
Aug 16 at 10:42
It depends on how do you define fair. Say two teams are in the final of a team event, boards are duplicate along two tables so the board/location factor is evened out. The remaining factor affecting the result are the choice of bidding system / method by each team, the bidding judgement at the table, the first lead, the subsequent play, and last but not least some accident. Do you mean If all things being equal then it should be a perfect draw?
– BGM
Aug 16 at 10:42
@BGM yes that's what I had in mind
– Chris Sanders
Aug 16 at 11:00
@BGM yes that's what I had in mind
– Chris Sanders
Aug 16 at 11:00
add a comment |Â
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1
There should be no reason to think Bridge should be fair between the pair bidding first and the other pair, or in your simplified version (Whist?) the pair leading first and the other pair. But a random allocation of position (plus rotation of position in successive hands) makes it fair by what you call the trivial symmetry
– Henry
Aug 16 at 8:08
It depends on how do you define fair. Say two teams are in the final of a team event, boards are duplicate along two tables so the board/location factor is evened out. The remaining factor affecting the result are the choice of bidding system / method by each team, the bidding judgement at the table, the first lead, the subsequent play, and last but not least some accident. Do you mean If all things being equal then it should be a perfect draw?
– BGM
Aug 16 at 10:42
@BGM yes that's what I had in mind
– Chris Sanders
Aug 16 at 11:00