Streak Probability Calculator

Even with a 55% win rate, the probability of hitting a 5-bet losing streak in 200 bets is 88.0%. Streaks are not a sign of bad luck, they are a guaranteed feature of random variance. The longer you play, the longer your worst streak will be. A 50% bettor playing 1,000 bets hits a 10-loss streak 38.5% of the time, and needs about 2,000 bets before that becomes more likely than not.

After 7 losses in a row, many bettors feel they’re “due” for a win. This is false. Each bet is independent, and the coin has no memory. The probability of losing the 8th bet is exactly the same as the 1st. Streaks feel like patterns, but they are just clusters of randomness. Never increase bet size because you think a streak “must end.”

Do not size your bankroll off your longest expected streak. It is the intuitive move and it is roughly half the answer. A break-even bettor over 1,000 flat bets has a worst expected losing streak of about 9, but 30 units still goes broke 34% of the time, because losses accumulate through ordinary choppy stretches rather than in one unbroken run. Holding to a 5% risk of ruin over those 1,000 bets takes about 62 units. Streak length grows like a logarithm of the number of bets, so it barely moves. The bankroll you need grows like a square root, so it keeps climbing. Read the risk-of-ruin table above, not the streak table.

The longest expected streak grows logarithmically with sample size. For a break-even bettor: about 6 in 100 bets, about 9 in 1,000, about 13 in 10,000. Ten times the bets buys you roughly three more consecutive losses. So the more you play the worse your worst streak gets, but it grows slowly, and slowly enough that sizing a bankroll off it will leave you short. Use this calculator to plan for the right sample size and avoid being shocked when variance hits.