gaming_mouse
04-29-2005, 03:52 PM
We want to estimate the % of HU turn raise bluffs in the game we play based on hand histories. For convenience, "showdown" means that the oppo who raised the turn ended up showing his hand down, and "bluff/r" means "bluff raise."
P(showdown & bluff/r) = P(bluff/r | showdown)*P(showdown)
Both quantities on the right can be estimated. That is, if need be, we can manually look at all showndown hands in which there was a turn/r and decide if the raiser was bluffing or not, enabling calculation of P(bluff/r | showdown). P(showdown) is just the % of HU hands where the turn raiser shows down.
So we now have an estimate of P(showdown & bluff/r) which will converge to the true value.
Note that:
P(showdown | bluff/r) = P(showdown & bluff/r)*P(bluff/r)
Which means that we can estimate the value we are ultimately interested in -- P(bluff/r) -- as:
P(showdown | bluff/r)/P(showdown & bluff/r)
The problem now is that we have no airtight way of estimating P(showdown | bluff/r). There are some possibilities for crude estimates, however:
1. We could assume that bluff raises are exactly as likely to be called down (and hence shown down) as raises in general (real and bluff combined), and estimate P(showdown | bluff/r) using P(showdown). This seems like a bad idea, as I'd guess bluff raises are, in general, more likely to be called down, though I have no idea HOW much more likely.
2. We could use information about how often OUR OWN bluff raises (or those of other players whose hand histories we have access to) are called down, and use that to estimate overall population stat. This seems like a better option than 1., but is still flawed, since I'd guess that the bluff raises of TAGs are less likely to be called down than the bluff raises of players in general. Intuitively, however, this bias (at least to me) seems like a less egregious error than the bias in 1. In addition, we could estimate the magnitude of the error if we had access to histories for playes with higher VPIPs.
I'm curious if anyone else has other ideas about how to solve these problems, and would like to hear thoughts on the above ideas as well.
TIA,
gm
P(showdown & bluff/r) = P(bluff/r | showdown)*P(showdown)
Both quantities on the right can be estimated. That is, if need be, we can manually look at all showndown hands in which there was a turn/r and decide if the raiser was bluffing or not, enabling calculation of P(bluff/r | showdown). P(showdown) is just the % of HU hands where the turn raiser shows down.
So we now have an estimate of P(showdown & bluff/r) which will converge to the true value.
Note that:
P(showdown | bluff/r) = P(showdown & bluff/r)*P(bluff/r)
Which means that we can estimate the value we are ultimately interested in -- P(bluff/r) -- as:
P(showdown | bluff/r)/P(showdown & bluff/r)
The problem now is that we have no airtight way of estimating P(showdown | bluff/r). There are some possibilities for crude estimates, however:
1. We could assume that bluff raises are exactly as likely to be called down (and hence shown down) as raises in general (real and bluff combined), and estimate P(showdown | bluff/r) using P(showdown). This seems like a bad idea, as I'd guess bluff raises are, in general, more likely to be called down, though I have no idea HOW much more likely.
2. We could use information about how often OUR OWN bluff raises (or those of other players whose hand histories we have access to) are called down, and use that to estimate overall population stat. This seems like a better option than 1., but is still flawed, since I'd guess that the bluff raises of TAGs are less likely to be called down than the bluff raises of players in general. Intuitively, however, this bias (at least to me) seems like a less egregious error than the bias in 1. In addition, we could estimate the magnitude of the error if we had access to histories for playes with higher VPIPs.
I'm curious if anyone else has other ideas about how to solve these problems, and would like to hear thoughts on the above ideas as well.
TIA,
gm