TY - JOUR

T1 - Bunching of Numbers in a Non-Ideal Roulette: The Key to Winning Strategies

AU - Кавокин, Алексей Витальевич

AU - Шеремет, Александра

AU - Петров, Михаил Юрьевич

N1 - References 1. Bass TA (1990) The Newtonian Casino, London: Penguin. 2. Small M, Tse CK (2012) Predicting the outcome of roulette, Chaos 22, 033150. 3. Thorp EO (1969) Optimal gambling systems for favorable games, Review of the International Statistical Institute 37: 273. 4. Rubinstein RY, Kroese DP (2008) Simulation and the Monte Carlo Method, (2nd edn). New-York: Wiley. 5. Reference Manual for Intel(R) Math Kernel Library Ver. 11.1.

PY - 2018/9/21

Y1 - 2018/9/21

N2 - Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a realistic roulette is not ideal: the probabilities of realisation of different numbers slightly deviate. Describing this deviation by a statistical distribution with a width δ we find a critical δ that equalizes chances of gambler and casino in the case of a simple strategy of the game: the gambler always puts equal bets to the last N numbers. For up-critical δ the expected return of the roulette becomes positive. We show that the dramatic increase of gambler’s chances is a manifestation of bunching of numbers in a non-ideal roulette. We also estimate the critical starting capital needed to ensure the low risk game for an indefinite time.

AB - Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a realistic roulette is not ideal: the probabilities of realisation of different numbers slightly deviate. Describing this deviation by a statistical distribution with a width δ we find a critical δ that equalizes chances of gambler and casino in the case of a simple strategy of the game: the gambler always puts equal bets to the last N numbers. For up-critical δ the expected return of the roulette becomes positive. We show that the dramatic increase of gambler’s chances is a manifestation of bunching of numbers in a non-ideal roulette. We also estimate the critical starting capital needed to ensure the low risk game for an indefinite time.

M3 - Article

VL - 1

SP - 1

JO - Journal of Mathematical and Statistical Analysis

JF - Journal of Mathematical and Statistical Analysis

IS - 1

ER -