[dottrap]

Look up Edward Thorp, the famous mathematician who was the first to use probability theory to beat blackjack and write a book about it (Beat the Dealer). Basically, as a deck uses up cards, the remaining in the deck may present a positive expected value. By counting cards and knowing expected values, you can adjust your bets to capitalize.

Since Thorp, Casinos have made it harder to beat them (e.g. larger decks), but they still tease the possibility you can beat them to entice people to try (and lose).

Edward Thorp later went on to write Beat the Market, where he tried to apply similar probability principles to the stock market. He independently invented the options formula, before Black-Scholes (which the latter won a Nobel Prize).