In a true random memoryless game any betting strategy (like Martingale) can't improve the expected winnings. The odds of winning are entirely governed by the expected calculation of house edge. Classic casino games such as European Roulette has an expected loss of 19/37 for each play, American roulette is 20/38, Pass line bet in craps is 251/459, and the Don't pass Line is 1031/1980. Slot machines also have an expectation but it is legally permitted to be kept secret from the player. The acronym for the table that shows the probability for different outcomes for a given machine is its PARS, which is an acronym for Paytable and Reel Strips.

Card counting has a superficial resemblance to betting strategies because the initial wager is increased and decreased. However a deck of cards is not a random memoryless game. The strategy is based on the reality that a deck with many Aces and 10 value cards remaining is very likely to produce a blackjack (or natural). The blackjack is just as likely to go to the dealer as the player. However, the player gets paid a bonus for getting a blackjack (traditionally 50%) while the dealer only wins the original stake. If the player uses a strategy to estimate that the remaining cards in the deck are rich in 10's and Aces he increases his bet to take advantage of the increased possibility of a blackjack. The traditional game previous to 1960 used a single deck of cards and was dealt nearly to the bottom of the deck. It was possible to invent strategies that could easily be taught to make good estimates of the number of Aces and 10's remaining in the deck. Card counting is not cheating because the player does not use subterfuge to know the outcome, he merely knows that the probabilities have changed to be more in his favor. So an effective card counter must have an extremely large bankroll to cover the times when his initial bet is large, but the dealer still wins. Casinos have implemented multiple rule changes that make this estimation much more difficult. The easiest one is that the pit boss does not permit a wide range of initial wagers and invites the player to change to a different game if he insists on maintaining this behaviour.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.