[Seb86]

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This is for cash games . I've also answered the question pertaining to sng's in another post below .

For a player following the Kelly criterion , you may use the following approach :

B=-(standard deviation)^2/(2*win-rate)*lnr where r is your risk of ruin .

A player following an aggressive bankroll plan will typically use half-kelly which is equivalent to -lnr/2=2 and so r~ e^-4 or
1.83% .

For the heads up player , it is common for your standard deviation to be higher than 100 big blinds per 100 hands . Your win-rate may vary and it could be anywhere from 10 big blinds to 20 big blinds per 100 hands . If it is the former , then your bankroll requirements for half-kelly would be :

B=2*100^2/10
B=2000 big blinds or the equivalent of 20 maximum buy-ins .

If your standard deviation is 120 big blinds per 100 hands and you win-rate is 10 big blinds , then you would require :

B= 2*120^2/10
B= 2880 big blinds or the equivalent of about 28 buy-ins .

If you're prone to tilt , then you should be willing to add a few more buy-ins to your mathematical total for B since we're working under the assumption that each hand is independent .

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clever enough to make nerdz math but not enough to read OP.