# How crunching numbers found blackjack’s hole

The origins of the game of blackjack or “21” are unclear. Gaming historians can trace an early version, called trente un, to the late 16th century. The brilliant Spanish novelist Miguel de Cervantes references cheating at the game in A Comical History of Rinconete and Cortadillo, published in 1570. In the centuries since, at least one thing has remained essentially unchanged: people are still trying to figure out ways to beat the game.

The modern game is fairly simple. The object is to beat the dealer by getting a total as close to 21 as possible without going over. In the standard version, the dealer deals two cards to each player as well as themselves. Players’ cards can be dealt either face up or face down but the dealer always takes one exposed “up card” and one hidden “hole card”. The players make their decisions based on both the value of their own hands and the dealer’s up card. These include whether to “hit” (draw additional cards) and when to “stand” (take no more cards).

The value of the dealer’s hole card is hidden through this play. If the players knew its value they would have a significant advantage.

In the late 1980s a team of Las Vegas-based players managed to develop a hidden, wearable blackjack computer called Captain Crunch able to determine the dealer’s hole card. The algorithm built into the computer took advantage of a decades-old procedure from an old card trick. Its result was then signalled to another player at the table. The method was nothing short of ingenious.

Captain Crunch could determine the hole card roughly 65% of the time.

Take a deck of cards and remove an entire suit. Hearts will work nicely. Put all of the hearts into numerical sequence, beginning with the Ace and ending with the King. Next remove the entire suit of clubs and place them in order. Now take these two suits and execute a casino-style ‘riffle shuffle’ to shuffle them together. A casual hand shuffle will not work – the method depends on a casino shuffle to function properly. Only perform a single shuffle. Once you’ve shuffled the two suits together, turn the combined packet face up and spread the cards out on the table, being careful not to disturb their position.

Examine the sequence you see. You’ll notice that although you’ve shuffled the two suits together, their individual sequences are still present in the spread. You’ll either have the AH or AC as the top card, followed by the rest of the cards with either the KH or KC as your bottom card. The 2H will come after the AH and, depending on your shuffle, these two cards may have some of the clubs shuffled in between them. Regardless, you should be able to see the sequences of hearts and clubs clearly.

What does this mean? It means a single shuffle does a poor job of mixing playing cards. Performing two shuffles isn’t much better. Captain Crunch took advantage of this by calculating, from the cards dealt, any “missing” cards. Here’s how:

Pick up your shuffled packet and cut the cards anywhere you like. Complete the cut. Place the top card aside without looking at it; this will represent the dealer’s hole card. Now cut the combined packet again.

Begin turning over the cards from the top of the packet one at a time. Place them aside as you do so. Depending on where you’ve cut the packet, a typical sequence may look something like this: 5H, 6H, 5C, 6C, 7C, 7H, 8C, 9H, 9C, 10H. Notice anything strange? Though it’s only a small portion of the cards, you can already tell the sequence is missing the 8H. Where is it? It is the card you set aside earlier.

Using virtually this exact procedure, Captain Crunch was able to positively determine the dealer’s hole card roughly 65% of the time. The player wearing the computer had to input every card’s suit and value into the computer using hidden toe switches. The algorithm depended on weak shuffling procedures using only a few riffle shuffles. Shuffling procedures are more secure now, but using only a small number of shuffles was common in the 1980s. As the hands were dealt and played, Crunch was told what cards were in the players’ hands and what the hit cards were. Within a few cards, the computer was usually able to determine the hole card. The player wearing the computer then secretly signalled to the last player at the table. This player would bet large sums and typically be the only player to benefit from the hole card information. The other players, including the one operating Captain Crunch, bet the table minimum.

While we determined our missing card by examining two different suits, Crunch was able to work with any cards, regardless of suit or value, by grouping them in threes. The method won an absolute fortune for the developers and was never discovered by the casinos. Eventually, though, stronger shuffling procedures brought an end to its success.