Gambler's fallacy in roulette
Seven blacks in a row. At many tables that is the moment the red chips come out, on the theory that red is now "due". The wheel has no memory, and the theory has a name: the gambler's fallacy.
On a fair single-zero wheel each spin is an independent event. Red has 18 chances in 37 on every spin, whether the previous result was red, black, zero or a run of twenty blacks. Streaks are not a sign of anything being out of balance; a fair random sequence produces them constantly.
Price follows probability, not history. A red bet pays 1 to 1 and loses in full on zero, so its expected result is −1/37 of the stake, about −2.70%, before a streak and after it. Doubling the stake after each loss changes how much money is exposed per spin, but each spin is still priced at 2.70% of whatever sits on the table. The bet-by-bet figures at [https://casinohouseedge.com/roulette-house-edge/ https://casinohouseedge.com/roulette-house-edge/] make the point another way: none of them carries a condition about prior outcomes.
The marquee board listing the last twenty numbers describes the sample. Accurate as a record, useless as a forecast. A table with 24 reds in the last 40 spins is not "hot", and one with 15 is not "cold"; both sequences come up on fair wheels all the time.
Could a real wheel be biased? Possibly. Worn frets or a tilted rotor can favour a sector. But bias is shown by recording thousands of spins and comparing sector frequencies with chance, including the sessions where the suspected sector failed. One evening's streak is not that evidence, since streaks appear on perfectly fair wheels too.