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Negative Expectation

What is ‘Negative Expectation’?

A game with negative expectation is a casino game in which the house has a mathematical advantage over the player. This advantage guarantees the house a percentage return over time and, therefore, guarantees a loss for the player.While a player may win in the short term, if the game has negative expectation, the player will always end up losing money in the long run. Negative expectation can also be described as the house edge.Most casino games have negative expectation including, blackjack, baccarat, roulette, craps and keno. However, standard poker games do not have negative expectation; in poker games, the house makes its money from the rake (a percentage of the pot).

‘Negative Expectation’ Explained

On a European roulette wheel there are 36 numbers and a single zero. When the croupier spins the wheel the ball can land on any of the numbers plus the zero giving 37 possible outcomes.The mathematical odds of winning the bet are, therefore, 1 in 37; however, the house only pays out at 35 to 1 giving them a 2.7% advantage over time. No amount of perceived skill on the player's part can make up for the fact that, over time, the casino will win 2.7% more games than it loses.Some players argue that betting on red/black is a safer strategy because it is a 50/50 bet, so over the long term you won’t lose any money. This information is false, a red/black bet is not exactly even because the zero is neither red nor black. In this case, your odds are 18/37 or 48.7%, not 50%, so even if you bet on red/black, the game still has negative expectation.On an American roulette wheel the odds are even worse because they have double zeros and the payout is the same. This gives the casino a 5.3% advantage over the player.Negative expectation does not mean the player will always walk away from the table empty-handed. The house advantage works out over time and it usually takes around 100,000 games before the odds revert to the mean.
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