Expected Value, Variance & Volatility of Casino Games

Casino Games

If you've been doing any reading on improving the profitability of your casino game play you will probably have come across the terms Expected Value (EV), Variance and Volatility. In order to better understand just how casino games operate and how to gain advantages in your favourite ones you'll need to understand these terms.

For the purpose of this article we will look at the basics of these terms without getting into in-depth mathematical explanations and equations so that you are able to gain a general understanding of these terms and how to apply them when playing at casinos.

Expected Value or EV is the average amount that you stand to win or lose when placing a bet at a casino over the long term. To give an explanation of how to apply expected value, if you flip a coin for $1 you stand a 50/50 chance of either winning or losing $1. The calculation is as follows:

0.5 (for the 50%)*1 + 0.5*(-1) = 0

This shows that the Expected Value (EV) over time for this type of game is 0 as you will neither win nor lose money in the long term.

If however you play a casino game with a 3% house edge and make a $100 wager your EV will be a loss of 3% of $100, which is $3. When playing popular casino games like European Roulette online every single bet that you make of the same value will have the same EV.

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While the Expected value may remain the same for bets of the same size in some casino games, the variance or volatility of these games can be very different.

Variance and volatility are very similar and for the purpose of this discussion will be treated as the same thing. These terms refer to how volatile a casino game is or how often it swings from profitability with big payouts to unprofitability caused by losses. If we look at the roulette example and the straight-up wager valued at $10 will have the same value as a wager on red for $10, the straight-up wager will still have a larger variance (and volatility) that the bet on red.

The terms volatility and variance refer to the size of the reward to risk ratios with a low volatility meaning that both the risk and reward are low and a high volatility meaning that the risk and reward are high. Low volatility slots will offer a balanced paytable with opportunities to win at every level of the game so you will experience fewer big swings between huge wins and losses. Some video poker games on the other hand have a high volatility with huge jackpot prizes but no small to medium payouts throughout the game, which really means that it's all or nothing.