msk
01-01-2003, 05:15 PM
I was talking to my friend Harold, the math professor, about David's Theory of Collusion problem, and he pointed out a bug in my simulation programs. Based on rerunning the programs, with the bug fixed, here is better (I hope) results to some questions David asked, and to some others:
- Two player game, each antes 1 unit, gets a number less than 100. Result shows that player A should fold only about
a quarter of the time, player B should fold a bit less than 50% when A bets. Player B wins about .25 units per hand.
- Three player game, each antes 1 unit, but Players A and B are playing best hand (or folding). (This is David's second question). The team of A and B, playing the same strategy as above, will *lose* .10 unit per hand.
So when does collusion pay:
- Four player game, first 3 are colluding, but player D goes last every time. A and B and C play their best hand (only one of them) using the same strategy as above. The colluders now win .15 unit per hand.
Three player non-collusion (David's question #1) is a more difficult problem, I will pass on programming the 'minimax' solution to it for now. And my simple programs probably still have bugs anyway, need to check my work. /forums/images/icons/cool.gif
Mark
- Two player game, each antes 1 unit, gets a number less than 100. Result shows that player A should fold only about
a quarter of the time, player B should fold a bit less than 50% when A bets. Player B wins about .25 units per hand.
- Three player game, each antes 1 unit, but Players A and B are playing best hand (or folding). (This is David's second question). The team of A and B, playing the same strategy as above, will *lose* .10 unit per hand.
So when does collusion pay:
- Four player game, first 3 are colluding, but player D goes last every time. A and B and C play their best hand (only one of them) using the same strategy as above. The colluders now win .15 unit per hand.
Three player non-collusion (David's question #1) is a more difficult problem, I will pass on programming the 'minimax' solution to it for now. And my simple programs probably still have bugs anyway, need to check my work. /forums/images/icons/cool.gif
Mark