Casino odds, house edge & pay-out percentage

Learn the mathematics behind casino gambling – understand the odds and optimise your play.

Casino odds can be a tricky business. While for some games they are fixed and there is nothing players can do to affect them, other games allow room for optimisation.

Casino odds

Casino odds have two main components: pay-out percentage and the house edge. Individual bets have different odds attached to them, but it all eventually boils down to these two figures.

payout

Pay-out percentage

The ‘pay-out percentage’ is the percentage of bet cash returned to players. Incredibly, the pay-out percentage for online slots games is usually no less than 95 percent. For certain games (played with an optimal betting strategy) the pay-out can be above 100 percent.

Taking European roulette as an example, the pay-out percentage is approximately 97.3 percent. Therefore, if £10,000 was wagered on European roulette in one night at a casino, the house would expect to return £9,730 to its customers, resulting in a £270 profit.

houseedge

House edge

In the example above, the casino’s profit is equal to 2.7 percent of total bets. This figure represents the ‘house edge’, meaning the proportional profit that the casino can expect to make from European roulette.

The nature of roulette means that this edge will be consistent irrespective of how players bet and how much they wager. Whether they’ve got bankrolls of hundreds or millions, whether they make even or straight bets, in the long term they will give approximately 2.7 percent of their money to the casino.

Calculating expected value

The amount of money a player can expect to win or lose in the long term is referred to as the player’s expectation or expected value (EV). This is the EV calculation for betting on a single number on European (single zero) roulette.

EV = (1 * (18 / 37)) + ((−1) * (19 / 37)) = - 0.027

The expected value of a casino game is always a value between -1 and 1.

To derive the house edge, you just multiply by 100 to get a percentage. This gives European roulette a house edge of 2.7 percent.

Most casino games come with negative expectation, with the exception of blackjack, craps and video poker in certain conditions. For skilled practitioners, poker and sports betting can come with positive expectation.

Betting optimisation

There are certain bets that are mathematically superior in certain circumstances, producing better odds. Whereas roulette is a fixed-odds game (meaning the house edge never changes), it is possible to affect the house edge in other games through betting optimisation.

Blackjack

When playing 8-deck blackjack, it is possible to reduce the house edge (in ideal circumstances) to 0.45 percent by playing according to basic strategy. Click here to learn more.

There are also a number of ‘silly bets’ which should be avoided due to their extremely unfavourable odds. For instance, never accept insurance bets when the dealer’s visible card is an ace, because the house edge is extremely high in this instance.

Craps

The house edge in craps is determined on the basis of individual bets, ranging from 16.67 percent to zero - this means that optimal betting in craps can massively impact your expected pay-out percentage.

For further information about optimal betting in craps, click here.

Video poker

By adhering to perfect play, it is actually possible to beat the house edge – one of the few casino games that can offer the player an advantage. Even when played imperfectly, the house edge in video poker is extremely low, making it a popular choice among advantage gamblers.

For more information about video poker systems, click here.

Published pay-out percentages

Many casinos and software developers will publish the pay-out percentages attached to its games. You need to find out if these figures are based on independent audits or internal assessments. If it’s the latter, they probably aren’t trustworthy.