Kelly criterion for poker
Join Date: Aug 2010
Posts: 2,334
Suppose we have a win rate of W BB/hour, and a std dev of S BB / hour... We want to buy-in to a game for N BB. How can we estimate the probability of doubling up vs losing our N BB? Can we use those probabilities and apply the Kelly Criterion to decide what our minimum bankroll should be for those stakes?
Like say we win 10 BB / hour, have a std dev of 100 BB / hour, and want to buy-in to a game for 200 BBs. Then we would find that buy-in is a Kelly optimum for a bankroll of size X BBs. What is X?
Join Date: Aug 2010
Posts: 2,334
Oops... Guess google is my friend... I think I found that:
edge = win rate / std dev
And BR = buyin / edge
So in the example I posted,
edge = 10 / 100 = 0.1
BR = 200 BB / 0.1 = 2000 BBs
Something seems a little off here, but I think at least this seems to be a decent way to get a ballpark idea.
Join Date: Jan 2009
Posts: 4,987
As a comparison, for win rate = 10 and sd = 100, a bankroll of 2000bb will result is a risk of ruin (ROR) of 1.8%.
Join Date: Jan 2005
Posts: 4,822
No surprise that Kelly would bring 2000 BB to a poker table.
What about individual hands of poker?
Deep stack NLHE has some polar spots where you are WAWB, with the chance to be a 75 percent favorite (thinking about second set against a flush draw board).
Is there a way to estimate the amount of bankroll we bring to the table for such a hand of poker, regardless of BB.
Just X percent of total poker bankroll, is what I am wondering.
If we choose to be relative to Kelly for the amount of bankroll we risk, we would need to estimate the likelihood of getting all in and called with the current nuts versus a draw.
Join Date: Jan 2005
Posts: 4,822
Just found and read all the great stuff from Mason Malmuth and others concerning winrates and variance and sessions of poker (at the time it was fixed limit, and players wanted to stay at that limit indefinitely).
So that much is solved, quite a while ago.
My only further interest is that bankroll is optimally considered fungible in that you can sit in or sit out at any stake you like with any portion of bankroll that is optimal. So, in reality, sessions of poker do not exist and we should be free to bring a standard portion of bankroll to any no-limit Hold’em table where our portion is above minimum buyin and below maximum buyin.
