# blackjack

Blackjack, also known as **twenty-one**, is the most popular
casino game in the world and the only such game with a *fluctuating* probability: the odds of winning change with the makeup of the deck. The
cards two to nine have a numerical value equal to the number printed on
the card. Tens and all face cards (jack, queen and king) have the value
of 10. Aces may be counted as either 11 or one. A dealer plays against one
to seven players. Every player and the dealer receive initially two cards
each, dealt by the dealer. Each player's hand is played against the dealer's
hand only. If a player's hand has a value closer to 21 (without going over)
than the dealer's hand, the player wins.

The best possible hand is known as a *blackjack* (21 in the first two
cards) and consists of an ace and a ten-valued card (10, J, Q, K). The payout
for a blackjack is 3-to-2: the player is paid three chips for every two
chips bet. When both the player and the dealer have blackjacks, it is a
normal *tie* (*push*) situation and the player retains the initial
bet. The player has several choices after receiving the first two cards.
(1) *Hit* or *draw*: take one or more cards to add-up to a better
hand. (2) *Stand*: stop taking more cards. (3) *Double down*:
double the initial amount (in cases considered more favorable). (4) *Split
pairs*: if the two cards are equal in value they may be played in two
separate hands. The dealer must draw until his hand adds up to 17 or more.
Both the player and the dealer can go over 21, a situation known as *bust*.
The player loses the bet immediately. The dealer plays his hand last, after
all the players at the table. This rule creates the so called *house edge*.
John Scarne^{1} was the first to calculate the house advantage at
blackjack: 5.9%. However, the house edge can be cut to around 1% if the
player follows certain rules. The set of rules known as *basic strategy* make blackjack one of the fairest games of any kind, almost as fair as coin
tossing.

In 1962, Edward O. Thorp, an IBM computer scientist, published *Beat the
Dealer*,^{2} which introduced a winning method called *card
counting*. This method considered the ten-valued cards and the aces as
positive, and the cards 2 to 6 as negative. If the net value of the remaining
deck was positive, the player must increase the bet accordingly. The method
had visible results when only one deck was used and very few cards remained
in the deck. Casinos responded by changing the rules dramatically. The *penetration* was introduced: not all the cards in the deck are played. Shuffling is done
unexpectedly. Also, most casinos introduced the *multiple deck blackjack*.

## References

1. Scarne, John. *Scarne's New Complete Guide to Gambling*. New
York: Simon and Schuster, 1986.

2. Thorpe, Edward O. *Beat the Dealer*, rev. ed. New York: Random
House, 1966.