Blog Archives

Basic Instinct 2: Counting the cost of blackjack (again)

In a previous blog I looked at the psychology of following ‘basic’ strategy and card counting based on the seminal work by Ed Thorp. Compared with other forms of gambling, there has been very little psychological research into blackjack – about one or two studies per decade by my reckoning. In the 1970s, Dr. Nicholas Bond (who at the time was at the California State University at Sacramento, USA) did some research asking blackjack players some simple questions like ‘When do you take insurance?’ and ‘What do you do when you have 7-7 and the dealer has 6 up?’ Bond’s results showed that most players did not know when to spilt pairs and had the wrong idea about the value of insurance. For instance, players often said that insurance should be taken “when the cards are running right” suggesting that players can predict the run of the cards and when the dealer will turn over blackjack. Although this research revealed strategy errors it didn’t give any insight into why such errors are made.

Dutch psychologists Dr Gideon Keren and Professor Willem Wagenaar went one stage further than Bond and examined in great detail the strategies and beliefs of regular blackjack players. They observed 112 players in the natural environment of a casino and then interviewed 149 players. They found that lots of blackjack players have many erroneous beliefs particularly if they claim they are following basic strategy. The most interesting findings were that players believed (i) a bad player could spoil a game for everyone, (ii) they felt worse if they lost on 20 than if they did with 13, (iii) they only knew if their decisions were correct after the round was over, and (iv) that if they were very unlucky on a particular day they should quit playing. While some of these beliefs may be understandable (and I’ll explain why below), if blackjack players follow basic strategy, none of these beliefs should exist. In short, the findings suggest that players believe in luck and conservatism as a legitimate strategic approach rather than the principles of basic strategy.

It is clear from players’ feelings about “bad” players that they are displaying what we psychologists call a ‘self-serving bias’. Put more simply, when good players win they attribute the outcome as something that was deserved whether or not it came about through other players’ incorrect play. However, when another player plays badly by asking for too many cards, the game may be spoiled for the other (better) players. It will be spoiled when a good player loses because a poor player has taken one card too many. Such players ignore the role of the bad player when the “wrong” cards they receive lead to a win.

These findings also shown that regular blackjack players have the illusion that they can control luck by playing when their luck is in and quitting when their luck is out (although such a finding is not unique to blackjack and can be found among gamblers more generally). What is interesting is that blackjack players appear to conceptualise ‘luck’ as a personal characteristic that can come and go like emotional mood states. It is therefore little surprise if players believe bad players can spoil the game for others – they believe bad players can change the run of good luck for others simply by taking too many cards.

According to the late Australian psychologist, Dr Michael Walker (University of Sydney, Australia), another interesting implication of Keren and Wagenaar’s research is that players are clearly unconcerned about the long-term correctness of decisions but see each hand as a contest with the dealer that may be won or lost depending on the decision made by the player. Take the case of a player who has a hand of 13. Players in such a position will make a judgement concerning the likelihood that the next card will be a 10. Most players will not hit 13 against a dealer’s 7 or 8 if there has been a run of small value cards, but will hit 13 if they are convinced that the next card is not a 10. In such situations, players find out the accuracy of their decisions once the round is over. Most players (including myself) dislike holding on 13 – it is too far from 21 to be psychologically comfortable but there is still the possibility of busting if a 9 or 10 is drawn. If we are dealt 20, there is an elated state because we feel the dealer is unlikely to beat our hand. If the 20 is beaten, we feel psychologically cheated whereas on 13, players can blame themselves for not hitting.

A study by Albert Chau (University of Hong Kong) and colleagues at Monash University (Australia) carried out a blackjack study on a small number of university students. They wanted to investigate whether departures from rational play in blackjack reflected ignorance and/or fatigue. The students were taught basic strategy in blackjack and then asked to play a simplified version of blackjack on computer. Initially the students followed basic strategy but this was eventually discarded for much higher risk strategies. Irrational play didn’t affect ignorance or fatigue (and the student players didn’t perceive basic strategy to be effective). Chau and colleagues argued that “because basic strategy is not a personalized strategy, it seems less likely to be maintained in the face of losses – players were more optimistic that they might win when utilizing their personalized strategies”.

In summary, blackjack is clearly a game that the player can win if basic strategy is used as a starting point. The strategy can be modified as the deck composition changes and good card counters are able to extract an edge over the casino. However, psychological research has shown quite clearly that regular players deviate significantly from basic strategy and make sub-optimal decisions because they perceive themselves as being engaged in a hand-by-hand contest with the dealer. Dr. Walker makes the point that since the characteristics of good play can be specified, blackjack is a good example of the extent to which players can bring about their own losses through the false beliefs that they hold. These false beliefs are held tenaciously, and despite playing countless hands, the beliefs that bring about gambling losses are maintained in the face of failure.

Dr Mark Griffiths, Professor of Gambling Studies, International Gaming Research Unit, Nottingham Trent University, Nottingham, UK

Further reading

Bond, N.A. (1974). Basic strategy and expectation in casino Blackjack. Organizational Behavior and Human Performance, 12, 413-428.

Chau, A.W.L., Phillips, J.G. & Von Baggo, K.L. (2000). Departures from sensible play in computer blackjack. Journal of General Psychology: Experimental, Physiological, and Comparative Psychology,127, 426-438.

Keren, G.B. & Wagenaar, W.A. (1985). On the psychology of playing blackjack: Normative and descriptive considerations with implications for decision theory. Journal of Experimental Psychology: General, 114, 133-158.

Thorp, E.O. (1966). Beat the Dealer: A Winning Strategy for the Game of Twenty-One. New York: Random House.

Wagenaar, W. (1988) Paradoxes of gambling behaviour. London: Erlbaum.


Basic instinct: Counting the cost of blackjack

Playing blackjack is relatively straightforward. Most of us played variations like ‘21’ and ‘pontoon’ as children. In the casino, all a player has to do is make a bet before a card is dealt and decide whether to ‘hit’ or ‘stand’ on the total. Simple. However, as with the psychology of all great games, the rules are easy enough for almost anyone to play but can take a lifetime to master.

One of the main reasons that blackjack attracts regular gamblers is that it is a game that the skilful player can expect a profit in the long run. It is the only game that casinos offer where the chances of winning favour the gambler. A gambler’s playing strategy is dictated by how they can influence the outcome simply by taking or avoiding extra cards. Research into the psychological strategies of blackjack playing have shown that gamblers fall into one of three main types. Firstly, there is the ultra-conservative “never bust” approach where the gambler sticks on any hand that could go bust on the next card (i.e., any hand of 12 and over). Since the dealer must draw until they reach 16, this approach will certainly pay off some of the time. A second popular strategy is ‘mimic the dealer’ where gamblers sit on 17 or more but draw to 16 or less. The psychology here is that if it’s good for the dealer it must be good for the gambler. However, very few regular players will follow either of these simplistic strategies.

Most gamblers adopt optimum “basic” strategies in which the decision to hit or stand depends on the ‘up-card’ held by the dealer. The player knows that as the game progresses, the number of cards left in the shoe is limited. If a player keeps count of the ratio of 10 value cards to non-10 value cards they can place minimum bets when the deck is favourable to the gambler and maximum bets when the ratio is favourable. The smaller the ratio, the richer the deck is with 10 value cards and the greater the advantage to the gambler. This well known card counting method was first laid out over 40 years ago by the mathematician Ed Thorp in his classic 1966 book Beat The Dealer.

Some people have said that the book stands in relation to gambling as Einstein’s theory of relativity does to physics – it changed perception of reality! More elaborate counting methods are available based on awarding points to low, medium and high cards and by keeping a running count of unseen cards. Over the years, many people have used elaborate systems in order to keep count.

The reaction of the casinos to card counting has been predictable. Many in the gaming industry view card counting as cheating and will ask players to leave the casino. Many casinos use up to eight packs of cards in the shoe to make counting hard. In casinos where only one or two decks are used, the cards are constantly reshuffled. Some casinos even teach the dealers how to card count so that they will only reshuffle when the odds are favouring the gambler. What’s more, the casinos find card counters easy to spot. They will make minimum bets on most hands and then occasionally make very large bets to take advantage of favourable decks. Therefore, really good counters must also be able to ‘camouflage’ their counting methods by being more variable in their betting strategy.

The good news for card counters is that most casinos prefer smaller decks so that more games can be played per hour (which means more money for the casino). Most casinos know that card counting gamblers may lose count or patience. Furthermore, some gamblers are competent in the short term but may crack under pressure with the long hours needed to make a consistent profit. It is estimated that one out of 20,000 players is a genuine counter and of these only one in twenty is a winner.

Research has been carried out into the most common errors that blackjack players make while gambling. One of the most well known was a study carried out in Holland by the psychologists Dr Gideon Keren and Professor Willem Wagenaar on 112 regular blackjack players. Wagennar showed that 44% of playing errors involved not taking an extra card when they should have and that 16% of errors involved taking an extra card when they shouldn’t have. They also found that the error rates were related to the value of the dealer’s up-card. When the players should have stood they were less likely to do so when the dealer’s up-card had a low value. Where they should have taken an extra card, they were also less likely to do so if the dealer’s up-card had a low value. Keren and Wagennaar also showed that players exhibited poor insurance strategies when the dealer’s up-card was an ace. These findings clearly show that most gamblers play conservatively in an attempt to stay in the game. They stand when extra cards should be taken, do not double up when they should do, and take out insurance unnecessarily.

Dr Mark Griffiths, Professor of Gambling Studies, International Gaming Research Unit, Nottingham Trent University, Nottingham, UK

Further reading

Nicholas A. Bond (1974). Basic strategy and expectation in casino Blackjack. Organizational Behavior and Human Performance, 12, 413-428.

Keren, G.B. & Wagenaar, W.A. (1985). On the psychology of playing blackjack: Normative and descriptive considerations with implications for decision theory. Journal of Experimental Psychology: General, 114, 133-158.

Thorp, E.O. (1966). Beat the Dealer: A Winning Strategy for the Game of Twenty-One. New York: Random House.

Wagenaar, W. (1988) Paradoxes of Gambling Behaviour. London: Erlbaum.