How often do casino gambling winning streaks occur?

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

2 3 4 5 6 7 8 9 10
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:

  1. 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.
  2. 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).

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

2 3 4 5 6 7 8 9 10
16.00% 6.40% 2.56% 1.02% 0.41% 0.16% 0.07% 0.03% 0.01%
2 3 4 5 6 7 8 9 10
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 to know if you’re planning your bankroll to use a wagering system. For example, if you plan to use Martingale (doubling after a loss) for a session of 200 hands, at least one run of ten consecutive wins or losses are 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.

Are winning and losing streaks predictable?

In a word: no.

Winning or losing “streaks” are observations of a run of wins or losses that have already occurred. If a coin toss comes up heads three times in a row, the odds for the fourth toss coming up heads (continuing the streak) or tails(ending it) are still 50:50—so you can confidently declare that there has been a “streak” of heads, you could not have predicted it beforehand.

Mathematics can demonstrate that runs of wins or losses can occur (explored in detail elsewhere), but there is no method for predicting when they will happen, how long a single streak will last, or when it will end.

That said, there are a few techniques, discussed in detail in advanced strategy, that can predict the bias in the cards that remain to be dealt. For example, a card counter can detect whether the preference is with or against him by considering the tickets that have already been removed and a shuffle tracker can know that an ace will show in the next round after a key card has been dealt.

However, this is not the same as predicting a “streak,” as the high-value cards may well be clumped on the far side of the cut card, and the next few hands may turn out poorly— and the ace that’s certain to show can just as well end up in the dealer’s hand.