Fallacy of the maturity of chances is the belief that a departure from a long-term average must self-correct in the very short-term.
Obviously, however, for each new spin of the wheel, black and red numbers on the roulette wheel are equally likely to appear on each spin.
If we assume only two possible results on the wheel, red or black numbers, the probability of each appearing is 50%, just like a coin flip.
From any given coin flip, probability tells us that we would expect heads or tails to occur the next 26 consecutive times is an astronomically small 0.0000015% of the time or about once every 67,100,000 times.
What people fail to realize is that the probability of each incremental coin flip is still 50%.
In other words, even after 26 straight black rolls, the probability of black coming up on the 27th roll was still 50%.
From a logical perspective, remember that the operator was not changing how he rolled the ball and that the wheel was standard.
Nonetheless, casinos continue to exploit this fallacy to their advantage, with every modern roulette wheel equipped with a sign showing the past 20 spins, an addition that makes it incredibly easy for guests to yield to their natural temptation to bet against streaks.