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Beat the Dealer: A Winning Strategy for the Game of Twenty-One; Edward O. Thorp

“When a lamb goes to the slaughter, the lamb might kill the butcher. But we always bet on the butcher.”

Calculations show that in a typical casino the player who uses the correct basic strategy has an edge of 0.12 per cent over the house. In some casinos the player actually has a narrow advantage of as much as 0.6 per cent. In casinos with the most adverse rules the player has a disadvantage of less than 1 per cent. Against some of the automatic blackjack machines, the basic-strategy player should theoretically have an advantage of 1.6 per cent and be able to win consistently.

The fewer the number of players at a table, the better it is for the player.

The principal ones are whether to split a pair, if he has one; whether to double down or not; and whether to stand or draw.

Drawing or Standing with Hard Hands.
Drawing or Standing with Soft Hands.

Never double down, never split pairs, and never insure. How will you do? Surprisingly enough, the casino edge will be only about 2 per cent. Your game is already close to even.

Once you have mastered the strategy for hard doubling, you further cut the casino’s edge to less than 1 per cent.

The average gain after one thousand $1 bets is $1.

mathematicians call “independent trials processes.” (Craps and roulette are such games. * 1 ) What this means is that each play of the game is uninfluenced by past outcomes and, in turn, has no influence on future outcomes. the cards do have a memory!

a shortage of cards having values 2 through 8 might give the player an advantage, while a relative excess of such cards might hurt the player. Conversely, a shortage of Nines, Tens, and Aces ought to hurt the player. removing the Fives gives an advantage of 3.6 per cent to the player.

When the deck is poor in high cards ( 10,A ), Table 4.1 of Chapter 4 indicates that the casino has the advantage. When the deck is poor in low cards ( 2,3,4,5,6 ), Table 4.1 indicates that the player has the advantage. Sevens, Eights, and Nines are not counted.

the large bets should be no more than three or four times the size of the smaller bets.

Counting Tens: this strategy finds for the player generally range from 1 to 10 per cent.four Tens added to the deck give the player an advantage of 1.89 per cent, whereas four Fives removed from the deck give an advantage of 3.58 per cent. the ratio “others/tens”