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Chances of a gambler are always lower than chances of a casino in the case ofan ideal, mathematically perfect roulette, if the capital of the gambler islimited and the minimum and maximum allowed bets are limited by the casino.However, a realistic roulette is not ideal: the probabilities of realisation ofdifferent numbers slightly deviate. Describing this deviation by a statisticaldistribution with a width {\delta} we find a critical {\delta} that equalizeschances of gambler and casino in the case of a simple strategy of the game: thegambler always puts equal bets to the last N numbers. For up-critical {\delta}the expected return of the roulette becomes positive. We show that the dramaticincrease of gambler's chances is a manifestation of bunching of numbers in anon-ideal roulette. We also estimate the critical starting capital needed toensure the low risk game for an indefinite time.

Bunching of numbers in a non-ideal roulette: the key to winning strategies