Understanding Variance in Casino Games

Understanding Variance in Casino Games

June 2, 2011.

Most gamblers are familiar with the concept of the house edge. While they may not understand all the complex arithmetic behind gaming math, it's a well-known fact that the casinos use math to create games that will, in the end, make them the winners. This concept explains that everyone will eventually lose.

However, many players do not know that there is a mathematical explanation for why some people are lucky. Lady Luck is not actually an invisible woman showering a select number of people with good fortune. Rather, she's a number called "variance". Variance explains, in mathematical terms, how likely you are to deviate from the expected house edge. Let's take a look at the numbers behind variance, and how you can use this knowledge to pick what Casino Games to play.

What, exactly, does variance mean?

In order to illustrate how variance works in casino games, here's a simple example. Suppose that there is a casino game where you flip a coin: heads wins; tails loses. In this game, you can expect to win exactly half the time in the long run. These regular wins mean that variance will be low. If heads won 1:1 with a 5% commission, the variance for this coin toss game would be a low .95.

Contrast this game with the lottery. In a lottery, gamblers select a set of numbers that they think will be drawn from a pool of possible numbers. These often feature multi-million jackpots. If you have a 1 in 70 million chance of getting a $60 million jackpot, and no chance of winning anything else, the variance would be over 50 million.

With these examples, you can see that variance indicates the likelihood of expected outcomes. In a low variance game, players can expect to hover closely to the expected return. As variance increases, players become more likely to end up with amounts farther away from the expected return. This, of course, goes in both the positive and negative direction. As variance increases, so does your likelihood of busting out more quickly.

How can I use this to choose what to play?

Knowing the variance of various casino games can help you choose which one to play. If you want the chance at big jackpots, but are willing to lose more often, you'll want to select a game with high variance. Conversely, if you want the chance at modest wins and extended play time, pick games with low variance.

High variance games

The highest variance games in online casinos are also the most popular: the Slots. The odds of hitting a win are low, but when it does hit, it's usually for huge amounts of money. It's this variance that makes the slots so fun and exciting. Traditional one-line, three-reel slots have the highest variance. Multi-line video slots have lower variance since you are essentially spreading your bet around. Check a video slot's paytable to get an estimate for its variance. As feature prizes increase and line payouts decrease, variance increases.

Typically, the second-highest variance is found in video poker. Video poker lovers know that the winnings can be massive, and its house edge is almost always much lower than that of the slots, assuming proper strategy is in use. If you want the greatest chance at getting a big win, play single-hand video poker. If you play multi-hand video poker, the variance decreases as you add more hands.

Other high variance wagers for the jackpot-seeking adrenaline junkies include Keno, bingo, proposition bets in craps, straight-up bets in Roulette, and high-paying bets in sic bo.

Low variance games

If you're looking for low variance games, you'll want to stick to the Table Games. Every table game has a relatively low variance, with some lower than others. The casino game with the lowest variance is pai gow poker. Assuming the player uses optimal strategy, it's essentially a coin toss between the player and the dealer. The frequent amount of pushes make pai gow poker's variance so low.

Other low variance games include baccarat, craps, casino war, blackjack, and even money bets in roulette or sic bo. Other casino pokers, red dog, and let it ride, while still relatively low in variance, are slightly more volatile.