Nothing convinces a player that a game is rigged like a streak. Six reds in a row. Eight blackjack hands without a win. A coin pusher that swallows twenty coins and gives nothing back. The instinct is that a fair game would not do that. The instinct is wrong, and the numbers show by how much.

The rule of thumb

For a bet you lose slightly more than half the time, the longest losing streak you should expect in a session of n bets is roughly the number of times you can halve n before reaching one. That is:

  • In 100 bets: a longest run of about 6 or 7 losses.
  • In 1,000 bets: about 10.
  • In 10,000 bets: about 13 or 14.

These are not worst cases. They are the typical longest run. Half of all sessions of that length will contain a run at least that long. A session of a hundred hands without a six-loss streak is the unusual one.

Why it has to be this way

Each bet is independent. The chance of losing seven in a row from any given starting point is about one in a hundred and thirty on a near-even bet. But in a hundred bets there are nearly a hundred starting points, and every one of them gets a try. Something that is a one-in-a-hundred-and-thirty shot, attempted a hundred times, comes up more often than not. Long streaks are not evidence against randomness; they are what randomness produces when you give it enough attempts.

Winning streaks too

The same arithmetic applies in the other direction, which is why hot runs happen and why they are equally meaningless. A run of six wins in a hundred hands is about as likely as a run of six losses. The house edge does not stop you winning six in a row; it makes the losing runs very slightly longer and very slightly more frequent than the winning ones, and over thousands of hands that slight difference is the whole of its income. The mechanism is in variance versus house edge.

What a streak does not tell you

It does not tell you the next bet is more likely to win. Seven losses do not make the eighth bet “due”; the wheel, the deck and the dice have no memory, and the error of believing otherwise has a name — the gambler's fallacy. It also does not tell you the game is broken. A genuinely rigged game would look different: streaks far longer than the rule of thumb, or results that cluster around particular bets. Six reds is not that. Sixty would be.

What to do when one arrives

Nothing different. That is the honest answer and the hard one. The bet that was correct before the streak is correct after it. What a streak should change is nothing about your play and everything about your patience: the player who doubles up to recover, or plays faster to get through it, is the one the streak actually hurts — see why chasing losses makes things worse. Expect the streak. Budget for it in your limit. And when it comes, recognise it as the ordinary thing it is.