Le coeur perdu – Paris

The Mathematics Behind Casino House Edge

Every single game on a casino floor is meticulously designed with a built-in mathematical advantage for the operator.

This mathematical advantage is universally known as the ‘house edge,’ and it is the secret to their massive profits.

How the House Edge is Calculated

Casinos make their money by paying out slightly less than the true mathematical probability of a win.

Take European Roulette: there are 37 numbers on the wheel, meaning your true odds of hitting a single number are 1 in 37.

  • This slight discrepancy in payouts guarantees that the casino retains a small percentage of all money wagered
  • A 2% house edge means the casino expects to keep two dollars out of every one hundred dollars bet
  • Over millions of spins, this tiny percentage translates into billions of dollars in guaranteed revenue

RTP: The Player’s Perspective

RTP and house edge are two sides of the exact same mathematical coin.

If a slot machine has an RTP of 96%, it means the house edge is exactly 4%.

Game Average House Edge Average RTP
European Roulette 2.70% 97.30%
American Roulette 5.26% 94.74%

While you can absolutely win in the short term due to variance, the math is inescapable over the long run.

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