Limit Poker Parameters

♠♣ the parameters of limit poker ♥
β=bank roll
R=win rate
σ = standard deviation = √variance
T = time (hours)
τ = sample size
99.5% of the population is within 3 standard deviations = 3 σ
σ = √τ

β = R T - 3 σ √T
So, 0 = R T - 3 σ √T hours necessary to ensure a profit
(if you know your win rate)
dβ = R d(T - 3 σ √T )
0 = R dT – 3σ dT¹∕²
0 = R (1) – 3σ ½ (1/√T)
T = |3σ/2R|²