Casino Maths: The House Edge Explained

Casino Maths: The House Edge Explained

Knowing the house edge of casino games is vital to deciding what games to play, and understanding how it works is central to any statistical strategy.

Definition

If you're new to casino betting, or you've decided to take a more mathematical approach, the chances are you've encountered discussions about the 'house edge' or 'house advantage'. But what exactly does it mean?

The house edge shows the advantage held by the casino (or gaming website) in any given game. It is a statistical calculation, expressed as a percentage, based on the discrepancy between the odds of something happening (you win) and the odds of it not happening (house win). It is therefore a representation of the statistical advantage that any game gives to the house. Another way of viewing the house edge is the average percentage profit the house should statistically make from bets over a prolonged period of time; or the average losses you would make if you played with large sums, over a long period of time with no strategy.

An Example

To see how a house edge is calculated, let's take one of the simplest bets in the game: red/black bets in Roulette. A common misconception is that you have a 50% chance of winning, because there's two outcomes and the casino pays evens. But on a US Roulette table, the two zeroes change the odds by pushing the total possible outcomes to three (red, black or neither), with 38 individual variations (being numbers 1-36, plus 0 and 00). Because only 18 of those 38 numbers result in a win, your chances are calculated as:

18/38 = 47.37%

Because the house also wins on 0 and 00, 20 numbers deliver a win and so the odds are:

20/38 = 52.63%

The house edge is the difference between those figures:

52.63 - 47.63 = 5.26%

And the more permutations a game has, the more complex the calculations become.

How to Use It

House edge calculations are easily found for most popular games, making it simple to identify games that are good for beginners: those which will average out to a small cost for a lot of fun, or where a little luck can leave you up for the night. On a slightly higher level the house edge tells you how much you're risking if you push a lucky streak, and helps promote rational behaviour and fight gambler's fallacy with cold hard stats. But the most important use for the house edge is as a tool to dissect the mechanics of a game. By understanding where the odds are more or less against you, you can start to analyse the outcomes that push the payouts one way or the other, and try to turn the tide more in your favour.


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Statistical Strategies

Blackjack is a prime example of where the house edge can help develop your strategy. In blackjack, the source of the house edge (generally 0.28%, but rule variations can complicate things) is the player bust - since the dealer automatically wins. So reducing the edge is about calculating when to hit and when to stick, based on the likelihood of going bust vs. losing on value.

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