Is it possible to beat the dealer? In a nutshell.

Further and deeper exploration of paradoxes and challenges of intuition and logic can be found in my recently published book, Probability, Choice and Reason.

It is said that on returning from a day at the races, a certain Lord Falmouth was asked by a friend how he had fared.  “I’m quits on the day”, came the triumphant reply.  “You mean by that,” asked the friend, “that you are glad when you are quits?”   When Falmouth replied that indeed he was, his companion suggested that there was a far easier way of breaking even, and without the trouble or annoyance. “By not betting at all!”  The noble lord said that he had never looked at it like that and, according to legend, gave up betting from that very moment.

While this may well serve as a very instructive tale for many, Ed Thorpe, writing in 1962, took a rather different view. He had devised a strategy, based on probability theory, for consistently beating the house at Blackjack (or ‘21’). In his book, ‘Beat the Dealer: A Winning Strategy for the Game of Twenty – One’, Thorp presents the system. On the inside cover of the dust jacket he claims that “the player can gain and keep a decided advantage over the house by relying on the strategy”.

The basic rules of blackjack are simple. To win a round, the player has to draw cards to beat the dealer’s total and not exceed a total of 21. Because players have choices to make, most obviously as to whether to take another card or not, there is an optimal strategy for playing the game. The precise strategy depends on the house rules, but generally speaking it pays, for example, to hit (take another card) when the total of your cards is 14 and the dealer’s face-up card is 7 or higher. If the dealer’s face-up card is a 6 or lower, on the other hand, you should stand (decline another card). This is known as ‘basic strategy.’

While basic strategy will reduce the house edge, it is not enough to turn the edge in the player’s favour. That requires exploitation of the additional factor inherent in the tradition that the used cards are put to one side and not shuffled back into the deck. This means that by counting which cards have been removed from the deck, we can re-evaluate the probabilities of particular cards or card sizes being dealt moving forward. For example, a disproportionate number of high cards in the deck is good for the player, not least because in those situations where the rules dictate that the house is obliged to take a card, a plethora of remaining high cards increases the dealer’s probability of going bust (exceeding a total of 21).

Thorp’s genius was in devising a method of reducing this strategy to a few simple rules which could be understood, memorized and made operational by the average player in real time. As the book blurb puts it, “The presentation of the system lends itself readily to the rapid play normally encountered in the casinos.” Essentially, all that is needed is to attach a tag to specific cards (such as +1 or -1) and then add or subtract the tags as the cards are dealt.Depending on the net score in relation to the cards dealt, it is easy to see whether the edge iswith the house or the player. This system is called keeping a ‘running count.’

There are variations on this theme, but the core strategy and original insights hold. The problem simply changed to one familiar to many successful horse players, i.e. how to get your money on before being closed down.

References and Links

Card counting. Wikipedia. https://en.wikipedia.org/wiki/Card_counting

https://wizardofodds.com/games/blackjack/card-counting/introduction/

https://wizardofodds.com/games/blackjack/card-counting/high-low/

4-Deck to 8-Deck Blackjack Strategy. https://wizardofodds.com/games/blackjack/strategy/4-decks/

The Ace-Five Count. https://wizardofodds.com/games/blackjack/appendix/17/