What this tests
The gambler’s fallacy says that after a run of one result, the opposite result is due. This lab counts every time the last few results were identical and checks what came next. If results are independent, the next result matches the run with the ordinary probability: 50% for a fair coin, and 18/37, about 48.65%, for red or for black on a European wheel.
How to use it
- Choose the coin or the wheel, and the length of run to watch for.
- Use the spin buttons or Auto-run (it keeps spinning until you press it again) to produce a few thousand results.
- Compare the observed share with the expected one. With only a few runs the observed share wanders widely, which shows why small samples are unreliable.
What to notice
- Long runs do appear. The longest run grows slowly as results accumulate.
- The share of runs followed by the same result stays close to the expected value once there are many runs. The run changes nothing about the next result.
- On the wheel, a zero ends a run of reds or blacks and counts as neither.
The arithmetic behind a run is in the gambler’s fallacy, explained. Everything here is simulated with your browser’s random number generator; no money is involved.
If gambling stops feeling under control, see signs it is time to stop gambling.
Frequently asked questions
Why is the observed share not exactly 50%?
Because it is an average over a limited number of runs. It gets closer to the expected value as the number of runs grows; the typical gap shrinks in proportion to 1 divided by the square root of that number.
Does the run length matter?
No. For independent results every run length gives the same expected share. A longer run only appears less often, so you need more spins to collect enough of them.
