Explaining Expected Value (EV) and what it means

[Enzo]

What is Expected Value for casino games

Expected Value is the long-run average value of repetitions of the experiment it represents. This we usually call simply as “Expectation” and doesn’t tell us if and how much we can win or lose by a specific bet in a gambling game.

In gambling, by Expected Value or Average Expectation, we mean the calculation of how much money we will win or lose in the long run based on the odds and payouts of the game. Some clarifications are needed:

1. The amount of money we should expect to win or lose is usually given as a percentage of the money wagered.
2. By long run we mean after many thousands of trials. The more trials the closer we will get to the expected value prediction.
3. This is a relatively accurate theoretical prediction of the long run result of our play, but still, actual results can vary.

The House Edge of casino games

Naturally, all casino games have a negative expected value. All players are expected to lose in the long run. The games are designed in favor of the casino. Actually, the expected value of any casino games is equal (in a negative way) to the house edge – they are the same thing. 

How to calculate the expected value of any game and any bet

Sometimes there can be special rules or maybe the is no fixed house edge. You can always calculate the probability and the expected value (negative house edge) of any bet by using the following equation:

If we have multiple bets at the same time: We multiply the probability of our bets to win with their respective profits in case of win and we add them together. Then we deduct the probability to lose multiplied by the loss (which is our bet amount). Then we divide the sum to the amount of our bet.

With the equation presented in this short topic you can calculate the advantage or disadvantage of any random or lucky bet, if you know the probability of winning.

 

Let me know if you have any questions

[CntryBoy]

Very informative post sir.  I have studied this countless times and am very familiar with it, since I enjoy playing poker in my spare time.  EV is extremely important when determining possible outcomes in poker.

[Enzo]

On 7/12/2019 at 8:38 PM, CntryBoy said:

Very informative post sir.  I have studied this countless times and am very familiar with it, since I enjoy playing poker in my spare time.  EV is extremely important when determining possible outcomes in poker.

Thanks for the kind words! And you're extremely right, EV comes in play in poker a LOT. That's one of the reasons I'd like to see some sort of Texas Hold'Em worked into Stake. Would add a PVP aspect that this site doesn't yet have.

[williamshennie9]

Great post! It goes to show that if you take the house edge into account, the casino will always win in the long run. I am quite a fan of statistics and probabilities, so I enjoyed reading this post.

[htetaungxx]

i found that what i want to know about House Edge and probability fair. thank enzo really helpful to me.