Blackjack, also known as 21, seems like one of the easiest card games to play at a casino. But it’s not so simple when you consider that the odds are against the player. In this article we’ll look at some of the mathematics involved in blackjack that can help turn the tables on the casino and give you an edge in this popular game.

In blackjack the objective is to beat the dealer by getting a hand value closer to 21 than theirs without going over. Players bet against the dealer and can make a bet called insurance or surrender their hand. Players can also choose to double their bet or split their cards and receive another card for each of them. If a player’s hand totals more than 21 they will bust and lose their wager.

The dealer’s face up card is usually a ten and the dealers’s hole card can be an ace, eight or any other face card. The dealer will check their hole card using a special viewing window before players begin official play. If the dealer has a ten underneath their ace they will have a blackjack and will take all of the players’ insurance bets. They will also pay out anyone with a blackjack at 3 to 2. If the dealer does not have a blackjack they will push any insurance or blackjack bets and the hand will continue.

Before the dealer begins to deal a blackjack, players may buy insurance or surrender their hand. Insurance is a side bet that pays 2 to 1 on any dealer’s blackjack and is generally considered a bad bet for players because it gives the dealer an advantage. Surrendering is a more conservative move and is recommended for those who believe they will bust their hand.

As the cards are dealt, a basic strategy chart is used to determine what action to take (hit, stand, split or double down) depending on the dealers’ up card and the player’s hand total. This chart is based on millions of hands played and provides the best chances for winning by a player in a particular situation. However, as the deck is used up the chart is no longer accurate and this is where a card counting system can help.

Keeping track of the cards that have been played and the cards remaining in the deck allows the player to make larger bets when the chance for a win is high. A card counting system can help the player identify these opportunities by analyzing the ratio of good cards to bad. Various systems exist, some of which require the player to remember each card that has been played while others only need the player to keep track of a simple point count.

There are a number of legal methods that can be used to gain an advantage at blackjack including shuffle tracking, the use of a shoe with a different index than the standard one and the use of a special viewer to see the dealer’s hole card. Arnold Snyder’s articles in Blackjack Forum magazine and his book, The Shuffle Tracker’s Cookbook were the first to bring shuffle tracking to the public’s attention.