Many gamblers want to believe there are ways to beat the house. Without relying on luck or the occult. With methods that win consistently. If not every game or session, then at least in a manner that ensures more earnings than losses over reasonable time periods. Such a desirable effect is, indeed, possible. Understanding how, which isn't the same as doing it, requires appreciating the mechanism by which casinos earn their money.
The $5 Place bet on the nine at craps exemplifies how this works. Bettors recover the $5 and win $7 four ways, on 3-6, 4-5, 5-4, or 6-3; the house gets $5 six ways, on 1-6, 2-5, 3-4, 4-3, 5-2, or 6-1. So, on the average, for every 10 coups, solid citizens bet 10 x $5 = $50, win 4 x $7 = $28, and lose 6 x $5 = $30 $2 loss for $50 at risk. And $2 is 4 percent of $50. Anything can happen in 10 particular cycles. But, over many trials, casinos can bank on earning roughly 4 percent of the gross wagered on the nine.
Multiple simultaneous or sequential bets can't alter the basic math. However, occasions exist to invert the margin with bets whose payoff ratio is greater, not less, than the odds against success. This, because situations may arise in which chances of winning exceed the nominal values while payoffs stay constant.
For instance, probabilities in blackjack depend on the make-up of the shoe from which cards are drawn. Each rank from ace through king has the same one out of 13 chance right after the shuffle. The probability varies as cards are removed from the shoe and not replaced, such that proportions of remaining ranks change.
The likelihood of an ace at the top of a shuffled shoe, for instance, is that one out of 13 (7.6923 percent). If the first three cards drawn are aces, the chance the fourth card will be an ace is one out of 49 (2.04 percent) with one deck or, say, 21 out of 309 (6.80 percent) with six decks. Dealers follow rigid rules no matter what's been removed. Card counters who size bets and make decisions based on current probabilities can get an edge.
Also in card games, shuffling doesn't randomize perfectly. And, dealers vary in the degree of mixing they achieve. Players can acquire the skill to identify the shuffling characteristics of dealers and track the positions of critical individual or groups of cards from the discard pile to the shoe being dealt. One way they use this information is to memorize sequences of cards preceding their targets, to anticipate what's likely to come next out of the shoe, and make hit or stand decisions accordingly.
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