Bankroll & Risk of Ruin: 9 Calculators

How to read EV, variance and risk of ruin

Bankroll size cannot be judged from average edge alone. Two games with the same EV can require very different capital when one produces much wider swings. The calculators therefore keep two quantities separate: the expected mean result and the standard deviation. The first describes the long-run direction of the process; the second measures how far actual results can move away from that mean.

From 100 rounds to the actual horizon

When EV and standard deviation are expressed per 100 rounds, a useful first reading is: expected result = EV₁₀₀ × (N/100). With comparable and approximately independent blocks, dispersion grows with the square root of time: SD ≈ SD₁₀₀ × √(N/100). This is why a small positive edge can coexist with large drawdowns for a long time.

Example. With an EV of +0.50 units and a standard deviation of 12 units per 100 rounds, 10,000 rounds have an expected mean of +50 units while total standard deviation is about 120 units. A negative result over that sample does not contradict the positive EV; it can still be part of the process variance. The purpose of the calculator is to quantify this gap between theoretical edge and financial risk.

Risk of ruin and goal probability answer different questions

Risk of ruin asks whether capital can hit the loss boundary before the process has enough time to express its EV. Goal probability instead asks whether a positive target can be reached before a negative barrier. Adding a time limit changes the problem again: a planned 5,000-round sample does not have the same risk profile as a theoretically unlimited horizon.

What to enter

• use the same unit for EV, standard deviation and bankroll;
• estimate EV and SD over the same 100-round block;
• recalculate both when rules, bet spread or operating conditions change;
• use the finite-horizon model for a planned session or fixed sample;
• compare several scenarios: sensitivity analysis is usually more informative than one isolated output.

The model becomes less informative when EV or variance is poorly estimated, wager sizes change in a way not represented by the inputs, observations are strongly dependent, or game conditions change during the sample. In those cases the calculation may be mathematically precise for the numbers entered while still describing the real situation poorly.