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Getting Lucky at Blackjack

By Eliot Jacobson, Ph.D.

If a non-advantage player beats the house for an extended period of time there are usually two significant consequences, especially if the player is a high-roller. First, the player will most likely believe he has a system to beat the house. Second, the casino may expend significant resources investigating the player. In either case, the illusion of skill is created by a lack of understanding of statistical inevitability and the so-called “long run.”

So just how long can an average blackjack player beat the house purely by luck? The answer depends on the meaning of “average” and the rules of the game he’s playing. In this article, I’m going to answer this question for one of the most common types of players playing one of the most common games.

Consider a player who is giving up a 1% house edge and is playing a typical double deck game. Surely you recognize this player – he plays in your casino day after day, making only a few common strategy mistakes. Here are some results:

  • After 100 hands, about 45% of these players will be beating the house.
  • After 10,000 hands, the percentage still beating the house drops to about 19%. At a game pace of 100 hands per hour, nearly one-in-five average skill players will be beating the house after 100 hours of play.
  • The striking result, however, is that even after 100,000 hands, about 1,000 hours of play, one average player out of 335 will still be beating the house just by luck.

There is nothing the casino can do about these lucky players. They must exist, purely by chance. In a large casino there are going to be quite a few players whose luck appears to persist beyond reason. If one of these players happens to be a high-roller then things can get ugly. Often, valuable resources are expended investigating the player. Sometimes, the casino just kicks the player out for no good reason, saying something like “we can’t beat this guy.” There may be no logical argument that is effective with management when they face such a player. They view the player’s future results as likely to be similar to the player’s past results — in other words, they expect this player to continue winning. This is nonsense, pure and simple.

Conversely, I often hear stories of some relative, friend or colleague who is a “professional” and always beats the house. I’ve stopped doubting these people; they are right, of course. Their associate has been beating the house over the course of hundreds of hours. The annoying consequence, however, is that these players write books, post on social media and brag in public about their knowledge and skills. They often have flimsy arguments about how they achieved their success and will defend their position with mockery and double-talk. There is no argument that can convince such a player that he is just one of the lucky guys who must exist by virtue of the statistics for the game. The problem is that some in casino management believe the nonsense these guys say; that there are hidden systems that exploit patterns, timing, progressions, etc. Management stops relying on experts and science. It’s a sign of the times.

To get another view of the “long run,” we can ask for the number of hands it takes to achieve a certain confidence of beating a player. In statistics, this is called computing “confidence intervals.” Unlike the previous backward-looking percentages, this is a forward looking measurement.

For example, it requires about 21,500 hands before the casino has a 90% chance of beating an average player. Put another way, 10% of all average players who walk through the casino door will still be beating the house after 21,500 hands.

After 125,000 hands, the casino will have a 99.9% chance of beating the average player. In other words, one player in 1,000 will still be beating the house after playing 125,000 hands, purely by chance. If that player happens to be a high-roller, he will surely pose a significant managerial and game protection problem for the casino.

Now consider the perfect basic strategy player – he isn’t playing a 1% game, he’s playing exactly at the house edge. In this case, the number of hands required to achieve various levels of confidence increase dramatically. It now requires 145,000 hands to have 90% confidence in beating such a player. It requires a stunning 475,000 hands to have 99% confidence. Put another way, after 475,000 hands, one perfect basic strategy player in 100 will still be beating the house! This is more than a lifetime of blackjack hands for most players.

In simple terms, if a player is using perfect basic strategy, there can be no reasonable long-term expectation of beating the player. There is nothing the casino can do about the variety of results players have. Looking at the history of a player’s results in a casino may trigger various investigations for cheating or advantage play, but such results are not conclusive by themselves. Kicking out winning players just because they are winning is a profit-losing proposition for the casino. There is no such thing as “fake math.”

The goal of a casino is not to beat every player. That’s an absurdity that is unfortunately part of the vernacular of the misinformed in the casino industry. The goal of a casino is to get players to wager as much as possible on games that have as high a house edge as possible as often as possible. Wise casino management lets the math take care of the rest. The lesson is easy: let honest players play and forget about the long run.