Beat the Dealer

Edward O. Thorp

3 ideas

1. Card removal shifts the edge between player and house

   Blackjack differs from dice or roulette because the deck has memory: dealt cards stay out until the shuffle, so the composition of the remaining deck changes from hand to hand. When the remaining cards are rich in tens and aces, the player gains a positive expected value, and when they are rich in small cards the house edge grows. The game's odds are therefore not fixed but fluctuate in a way the player can measure by tracking which cards have gone.

2. Bet small by default, bigger when favored

   The player bets small when the count shows the house has the edge and raises the bet when the count shows a player advantage, so that more money is wagered in the favorable situations. Thorp pairs this with bankroll management, sizing bets relative to capital so that the risk of ruin from a losing streak is reduced, though not eliminated.

3. Basic strategy computed from probability analysis

   Using computer-aided probability calculations under simplifying assumptions, the book works out a table of hit, stand, double and split decisions for player totals against dealer upcards. Applied consistently, this basic strategy brings the house edge close to even before any counting, and it departs from common intuitions such as copying the dealer's rules.

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