Streaks

How often do winning and losing streaks occur?

In a game where the odds are roughly even, the probability of a streak of wins or losses occurring are roughly:

2345678910
25.00%12.50%6.25%3.13%1.56%0.78%0.39%0.20%0.10%

Their frequency will depend on the length of the series you are considering. For example, if you toss a coin 100 times, you are likely to encounter two runs of six consecutive heads or tails (100 * 1.56% = 1.56). A run of ten consecutive heads or tails is bound to occur at least once per every thousand tosses(1000 * 0.10% = 1).

Two important notes:

  • These figures do not suggest that a run is more or less likely to occur given a certain pattern of past results—only the likelihood of the back-to-back occurrence of heads or tails in a random pattern.
  • Also, mathematical probability does not guarantee that a run of ten heads or tails will not occur on the first ten throws, only that the possibility is remote (10 * 0.10% = 0.01, which is a 1 in 100 chance).

Also, the figures above are based on a 50-50 odds, which is not accurate forblackjack. Although a basic strategy player can trim the house’s edge to less than half a percent and have roughly a 50:50 chance of winning or losing money over the course of many hands, this not the same as the odds of winning or losing each individual hand. The strategic player gains edge by doubling and splitting hands, increasing the money won or lost rather than the number of individual hands won. The actualwin:lose ratio of individual hands is actually around 60:40, so the probability of a streak in blackjack would be:

WINNING STREAK
2345678910
16.00%6.40%2.56%1.02%0.41%0.16%0.07%0.03%0.01%
LOSING STREAK
2345678910
36.00%21.60%12.96%7.78%4.67%2.80%1.68%1.01%0.60%

In most cases, this information is merely trivia. It’s only practical toknow if you’re planning your bankroll in order to use a wagering system. For example, if you plan to use Martingale (doubling after a loss) for an session of 200 hands, at least one run of ten consecutive wins or losses is likely to occur (200 * 0.60% = 1.2), so you’ll need to bring a bankroll of at least 512 times you base wager in order to survive the streak should it be a losing one.