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Analyzing The Shuffle

So far the statistics given with regard to the player's expectation have been calculated on the basis that the shuffle is entirely random, that is, every card has an exactly equal chance of finishing in any position in the deck. In fact, this is a virtually impossible feat for even the most proficient croupier. Richard Epstein likened a random shuffle to a drunken inebriate scattering the cards in the air and retrieving them while blindfolded. At this point, Professor Edward Thorp reenters the story. In a little known paper in the Journal of the Royal Statistical Society entitled "Nonrandom Shuffling With Application to the games of Faro," he wrote:

Card games have been played for centuries, and today hundreds are well-known. There is an extensive literature of the heuristic, and to a lesser extent, of the mathematical analyses of these games. Virtually without exception, these treatments tacitly or explicitly assume random shuffling.... It is surprising, because the play of many games is altered by the no randomness of human shuffling. In particular, this nonrandom ness yields simple winning strategies at online blackjack games, Online Baccarat Games, and faro.

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Razz is low-only Seven-Card Stud. This game can be a lot of fun. The interesting thing about it is that no one can start with a particularly strong hand, because everyone is on a draw to a good 5card low. In fact, one-card draws to a good low hand are statistical favorites over worse low hands that are made on Fifth Street. Bluffing based on your up cards becomes much more prevalent. Since this is low only, there is no 8-or-Better rule. Also, the player with the highest card showing makes the bring-iii bet, and thereafter, the lowest hand showing is first to act. Hellmuth's book includes an excellent little write-up on Razz,
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