Bankroll calculator

The rule that decides how long a bad run you survive

A unit is a percentage of the bankroll, not an amount, and the difference only shows up when things go wrong. Stake a fixed 40 forever and a bankroll that has fallen to 1,000 is betting 4% instead of 2%: the rule tightens exactly when it should loosen. Recalculate the unit against the current balance and every loss makes the next stake smaller, which is what stops a bad run from finishing the job. The asymmetry underneath is the whole reason to care — losing 20% needs +25.00% to recover, losing 50% needs +100.00%, and losing 80% needs +400.00%. Nothing in the second half of those pairs is symmetric with the first, and no edge is big enough to make a 400.00% recovery a plan rather than a hope. A 2,000 bankroll at 2% stakes 40 a bet, absorbs ten straight losses for 400.00, and comes out down 20.00% — having used ten of the 50 consecutive losses that stake could survive.

A run of ten losses at prices around 2.00 is ordinary, not bad luck, and this is the number that makes the point. At even money any single sequence of ten has a probability of 0.098% — one in 1,024 — which reads like never until you count how many sequences a season contains. Across 1,000 bets the chance of meeting at least one losing run of ten or longer is 38.54%; at 2.10, where a bettor with no edge wins 47.62% of the time, it is 52.31% — better than a coin flip. Over 500 bets the same two figures are 21.45% and 30.73%, and the longest run to expect in 1,000 even-money bets is about ten, because it grows with the base-two logarithm of the number of bets. The run is not the tail of the distribution, it is the middle of it, so a unit above 5% is a bet on not meeting the ordinary case: at 5% those ten losses take half the bankroll, at 10% they take all of it. When the edge is measured rather than assumed, the Kelly criterion calculator sizes the unit from the edge itself — read what it gives you as a ceiling, and this page as the floor beneath it.