Winning 20 Spins in a Row at 3x
The chance of 20 winning spins in a row at 3x on the Wheel is 3.49 × 10-9%, or 1 in 28.68 billion. At 3x a single spin wins 30% of the time.
The odds of 20 wins in a row
| Measure | Value |
|---|---|
| Chance of one win at 3x | 30% |
| Chance of 20 wins in a row, starting from a given spin | 3.49 × 10-9% |
| Odds | 1 in 28.68 billion |
| Spins to wait for it, on average | 40.97 billion |
| Chance it happens at least once in 100 spins | 1.99 × 10-7% |
| Chance it happens at least once in 500 spins | 1.18 × 10-6% |
| Chance it happens at least once in 1,000 spins | 2.4 × 10-6% |
| Chance it happens at least once in 10,000 spins | 2.44 × 10-5% |
| Profit across the streak at 1 per spin | 40 |
| Returned if the streak had been compounded (each win staked again) | 3.49 billionx the first stake |
The average wait counts spins until the first run of 20 wins is completed. It is an average over many players, and any individual can see it on their first 20 spins or never. The "at least once" figures are exact: they account for a run starting on any spin, not just the first.
What it means
A streak of 20 wins has a probability of 30% to the power of 20, which is 3.49 × 10-9%. Any one run of 20 spins is unlikely to do it, but over 500 spins the chance it shows up at least once is 1.18 × 10-6%.
A hot streak does not make the next spin likelier to win. After 20 wins the chance of another is still exactly 30%. Each spin gets its own provably fair roll, so there is no momentum to ride and no balance to correct. The belief that a winner is due to lose, or keeps winning, is the gambler's fallacy and the hot-hand fallacy: two sides of the same mistake.
A streak is a good moment to stop, not to raise the stake. The expected return is 90 per 100 staked whatever just happened, so winnings at risk on the next spin are expected to shrink on average. Deciding in advance when you will cash out is the only part of this you control.
Related
- 15 wins in a row at 3x
- Every winning streak at 3x
- The 3x multiplier in full
- 20 wins in a row at 1.5x
- 20 wins in a row at 1.75x
- 20 wins in a row at 2x
- 20 wins in a row at 2.5x
- 20 wins in a row at 3.5x