ddubois
06-17-2005, 08:05 PM
I'm writing some AI for a poker game that's going to include, amount other things, a single-player mode with SNG play against 5 computer opponents. Currently, I'm working specifically on the aspect of the SNG play when you are in "push mode", ala less than ~10x BB. I believe estimating fold equity for an open push from any given position includes estimating the likelihood of calls from the players left to act, which can be estimated by multiplying the likelihood of individual folds.
For instance, consider the following scenario (ignore the possibility of multiple callers, for ease):
Blinds are 100/200 (let's say level just started), and these stack sizes are after posting:
UTG (t2010)
CO (t500)
BUT (t2890)
SB (t1360)
BB (t940)
If you have time, please answer with a % for each of these:
1) If UTG pushes, how often does a) CO call? b) BUT call (when folded to)? c) SB call? d) BB call?
2) If CO pushes, how often does e) BUT call? f) SB call? g) BB call?
3) If BUT pushes, how often does h) SB call? i) BB call?
4) If SB pushes, how often does j) BB call?
Thank you. Ok, now that we have some data, let's see if we can make a formula that gets anywhere near that data.
Probably the "best case" scenario for any push for any position is to assume that no one ever calls unless they have a top5% hand, Thus, the high estimate of fold probability would be (1 - call_percent) ^ num_players_to_act, where call_percent is 0.05. Obviously, this is WAY unrealistically optimistic from the pusher's perspective. As the stack size of the pusher goes down, the calling frequency of any player behind goes up. As the relative stack size of the potential caller goes up, the frequency of calls go up. And as the potential caller's pot odds go up (due to blinds), his calling frequency goes up.
I don't need to create a truly realistic formula - even something very rough should give the human player a sense that the computer is "thinking" about things. Let me toss out my first-pass example algorithm:
// factor 1, default case, everyone plays top5% TT+,AQ+
call_percent = 0.05 +
// factor 2, bigger stack, more call; i.e. when I have half the chips at the table, I'll call 10% more often
(0.20 * my_chips/total_chips) +
// factor 3, when you are desperate, I'll call 10% more often
(0.10 * (pushers_chips < bb_amount * 6) +
// factor 4, as the pot approaches laying 2:1, I'll call up to 50% more often, when pot is 1:1, factor 4 has no impact
(0.50 * (pot/to_call - 1)^2 +
// factor 5, remaining players discourage me from calling
(-0.02 * num_players_to_act)
Do you think the direction I am taking with this is a good one? How do you like my factors? My coefficients?
For instance, consider the following scenario (ignore the possibility of multiple callers, for ease):
Blinds are 100/200 (let's say level just started), and these stack sizes are after posting:
UTG (t2010)
CO (t500)
BUT (t2890)
SB (t1360)
BB (t940)
If you have time, please answer with a % for each of these:
1) If UTG pushes, how often does a) CO call? b) BUT call (when folded to)? c) SB call? d) BB call?
2) If CO pushes, how often does e) BUT call? f) SB call? g) BB call?
3) If BUT pushes, how often does h) SB call? i) BB call?
4) If SB pushes, how often does j) BB call?
Thank you. Ok, now that we have some data, let's see if we can make a formula that gets anywhere near that data.
Probably the "best case" scenario for any push for any position is to assume that no one ever calls unless they have a top5% hand, Thus, the high estimate of fold probability would be (1 - call_percent) ^ num_players_to_act, where call_percent is 0.05. Obviously, this is WAY unrealistically optimistic from the pusher's perspective. As the stack size of the pusher goes down, the calling frequency of any player behind goes up. As the relative stack size of the potential caller goes up, the frequency of calls go up. And as the potential caller's pot odds go up (due to blinds), his calling frequency goes up.
I don't need to create a truly realistic formula - even something very rough should give the human player a sense that the computer is "thinking" about things. Let me toss out my first-pass example algorithm:
// factor 1, default case, everyone plays top5% TT+,AQ+
call_percent = 0.05 +
// factor 2, bigger stack, more call; i.e. when I have half the chips at the table, I'll call 10% more often
(0.20 * my_chips/total_chips) +
// factor 3, when you are desperate, I'll call 10% more often
(0.10 * (pushers_chips < bb_amount * 6) +
// factor 4, as the pot approaches laying 2:1, I'll call up to 50% more often, when pot is 1:1, factor 4 has no impact
(0.50 * (pot/to_call - 1)^2 +
// factor 5, remaining players discourage me from calling
(-0.02 * num_players_to_act)
Do you think the direction I am taking with this is a good one? How do you like my factors? My coefficients?