Nonrandom Shuffling with Applications to the Game of Faro

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Abstract
De Moivre, Euler, and Montmort analyzed a predecessor of Faro. We consider the modern game first under the assumption of random shuffling, then with nonrandom shuffling. With random shuffling we find the house edge can be less than 0.0006 percent, but it is at least 0.526 percent if the player is limited to negative expectation bets. Human shuffling is nonrandom and a simple model for it indicates that, in principle, the player can achieve significant positive expectation. The ideas used to apply nonrandom shuffling to Faro also extend to other games. We illustrate with casino Blackjack. An appendix discusses previous work on modern Faro.

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