Bankroll
Risk of Ruin Calculator
Explore an infinite-horizon risk of ruin approximation from an entered bankroll, expected profit and standard deviation per equal independent step.
Your result
0.00453999%
Infinite-horizon diffusion ruin approximation
- Variance per step
- 100
- Bankroll for target probability
- 460.5170186
Copy was unavailable. Select and copy the result below.
Continuous approximation, fixed positive drift and stationary independent variance; not a session simulator.
Risk of ruin for a constant-drift model
For positive mean μ, variance σ² and bankroll B, the continuous diffusion approximation gives ruin probability exp(−2μB/σ²). With B = 1000, μ = 0.5 and σ = 10, that is exp(−10), about 0.00454%. The corresponding bankroll for target risk r is −σ² ln(r)/(2μ).
This is an infinite-horizon approximation with a zero-bankroll absorbing boundary, fixed units and independent stationary steps. It is not an exact discrete blackjack or poker simulator. Negative or zero drift with positive variance gives eventual ruin probability one under this model.
Blackjack bankroll and poker risk of ruin units
For blackjack, use a per-hand mean and standard deviation in currency or base-bet units, with bankroll in the same units. For poker, per-100-hand inputs work when both the mean and deviation describe that same block. Do not mix per-hand mean with per-100-hand deviation.
Changing bet sizes, finite sessions, table limits and uncertain advantage alter risk. Use blackjack outcome analysis or poker variance to explore input assumptions. The output is not a personal bankroll recommendation.