Bankroll & Kelly Calculator
Stake sizing and risk of ruin
Bankroll management does not beat the house edge, but it decides how long you last and how bumpy the ride is. The Kelly criterion gives the mathematically optimal stake when you genuinely have an edge, and the risk-of-ruin formula tells you how likely a bankroll is to be wiped out.
Enter your bankroll, win chance and payout to see the recommended stake, the fractional-Kelly alternatives and the number of units you need to survive normal variance.
Total return including the stake.
Kelly stake
0
No edge — optimal stake is zero
Half Kelly
0
The usual practical compromise
Your stake as % of bankroll
1.00%
100 units of bankroll
Expected value per bet
-0.10
Edge 1.00%
This bet has a negative expected value, which is normal for casino games. Kelly returns zero: there is no stake size that grows the bankroll long-term. Set a session budget instead — at 100 units you can absorb roughly that many losses before the bankroll is gone.
Kelly assumes an accurately known edge; overestimating it makes full Kelly ruinous. Risk of ruin assumes flat stakes over an unlimited number of bets.
How to read the results
- Kelly is only positive when the bet has positive expected value — on casino games it will read zero or negative.
- Most professionals stake a quarter or a half of Kelly to cut drawdowns at a small cost in growth.
- Risk of ruin assumes flat stakes; progressions make it far worse.
- As a practical rule, keep a single bet below 1-2% of your bankroll on any negative-edge game.
Frequently asked questions
What is the Kelly criterion?
The stake fraction that maximises long-run bankroll growth: (probability x payout - 1) divided by (payout - 1). Bets with negative expected value return a negative Kelly, meaning the optimal stake is zero.
How big should my casino bankroll be?
For a low-variance game, 100 to 200 units of your base bet is a reasonable session bankroll. High-variance play at 100x targets can require thousands of units to survive normal dry spells.
What is risk of ruin?
The probability of losing your entire bankroll before reaching a target. On a negative-edge game played long enough it converges to 100%, which is why session limits matter more than stake sizing.
Related calculators
These tools are informational. They describe the mathematics of casino games; they do not predict outcomes and no calculator can overcome a house edge. Gambling involves real financial risk — 18+ only, and seek help if it stops being entertainment.