House edge: the maths behind casino games

Why the operator expects to come out ahead over time, how to work out the cost, and why no betting system changes it.

House edge is the average share of each bet that a game keeps over the long run. It is the price of the game, and on a simple bet you can work it out yourself.

Working it out on a roulette wheel

A European wheel has 37 pockets, and a bet on one number pays 35 to 1. Imagine betting RM1 on one number 37 times, with each pocket coming up exactly once. You win once (+RM35) and lose 36 times (−RM36). You have staked RM37 and lost RM1, which is 1 ÷ 37, or 2.70%.

An American wheel has 38 pockets and the same payout. You win RM35 and lose RM37, so you lose RM2 per RM38 staked, which is 5.26%. One extra pocket nearly doubles the cost.

House edge and RTP are two sides of one number

Return to player is simply 100% minus the house edge. A 2.70% edge is a 97.30% RTP. A slot with 96% RTP has an edge of 4%. Our slots guide goes further into how that plays out across a session.

The cost depends on the total staked

The useful formula is: expected cost = total staked × house edge. Here is what 100 rounds at RM10 (RM1,000 staked) costs on average:

Game and betHouse edgeAverage cost of RM1,000 staked
Baccarat, Banker1.06%RM10.60
Roulette, European2.70%RM27.00
Slot with 96% RTP4.00%RM40.00
Roulette, American5.26%RM52.60
Baccarat, Tie14.36%RM143.60

These are long-run averages, not a forecast of any one session. They do show why a fast game costs more than it seems to: more rounds means more staked, even when your stake per round stays the same.

Why betting systems do not beat it

The Martingale system doubles the stake after each loss, hoping one win recovers everything. Start at RM10 on an even-money bet. After seven straight losses (10, 20, 40, 80, 160, 320, 640) you are down RM1,270, and the next bet needs RM1,280 just to end RM10 ahead.

On a European wheel that losing run happens about once in every 106 attempts, so it is not rare. Table limits or your budget stop the system at exactly that point. Each bet still carries the same edge, so changing the size of your bets does not change the average.

The same goes for reading patterns. A run of red does not make black more likely, because the wheel has no memory. Believing otherwise is known as the gambler’s fallacy.

You cannot beat a fixed house edge by changing when or how much you bet. You can only change how much you stake in total.

A bonus has a cost as well

Bonuses usually come with wagering requirements, meaning you must stake a multiple of the bonus before you can withdraw it. Take a RM50 bonus with a 30 times requirement. That is RM1,500 to stake. At a 4% edge, the expected cost of doing so is RM60, which is more than the bonus is worth.

Always work out the sum before you treat a bonus as free money.

What to do with the number

  • Treat the expected cost as the price of entertainment, and never as an investment.
  • Know which bets carry the highest edge. In baccarat, the Tie costs over ten times as much as Banker.
  • Slow down. Fewer rounds means less staked and a lower expected cost.
  • Set your limits before you start. See responsible gaming.

Sources

About the author

Mhelie Sy is an iGaming content specialist and the official content author at BCB88. She focuses on casino guides, slot games and responsible gaming. Read her profile.

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