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How to Calculate Expected Loss for Casino Games

As many people know, when it comes to gambling, the house always wins. It is because almost all casino games have set up a statistical advantage against the players. So of course, the big question is, which game will cost you the most.

Firstly, it is important to clarify what is an expected loss:

The average financial loss or impact that can be anticipated for a particular loss event or risk. It is calculated based on experience and past information. It is normally given as the average loss amount over a specified period of time.”

Because of the nature of practically all casino games, we do not have to determine expected loss based on experience or past information. The average loss can be easily calculated. Every casino game has defined the House Edge, which tells us average casino profit over time. The house edge of the game is defined by its rules naturally, not by the software provider or .

Expected Loss on Roulette

Let us take a look at the example with the probably the most famous casino game – roulette.

House edge for American roulette is 5.26%. Therefore, for every $ 5 wagered, the casino will keep an average of $ 0.26. Then your “expected loss” of a $ 5 bet on roulette is $ 0.26.

But if you you can’t just lose exactly $ 0.26. If you bet on black or red, you can either win $ 5 or lose the entire bet. So you can’t expect to lose $ 0.26. This is just an average loss of a $ 5 bet in the long run.

So why are we even talking about the expected loss, when we can’t lose exactly this amount in one game? Because the longer you play, the closer you get to the expected loss. Suppose you play 1000 spins on roulette, the bet is $ 1 per game, and you still bet only on red.

Because of the house edge, you can expect to be € 52.6 (1*0.0526*1000) poorer after 1000 spins on roulette. The reality may, and probably will, differ. However, the expected loss is a good indicator when comparing games in terms of risk. The expected loss depends on three factors:

  • How much you bet (amount per game)
  • Game speed (number of games per hour)
  • House edge (average casino profit per bet)

And the formula is as follows:

Bet * House Edge * Number of Games = Expected Loss

Comparison of Casino Games

The following table shows the expected loss after 16 hours of play using regular and regular bets.

Table html

As you can see, the house edge indicator is useful, but there are other factors like frequency, which considerably influence the costs of the game. That is why it is crucial to know expected loss for particular casino games before you start playing.

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