How to Calculate Your Expected Value

Understanding Probability and Odds

When it comes to calculating the expected value of a game, many gamblers are unaware that they need to first understand the basic concepts of probability and odds. These two terms may seem interchangeable, but they have distinct meanings.

Probability refers to the likelihood of an event occurring in a given situation. For example, when rolling a six-sided die, the probability of rolling a 6 is 1/6, as there are six possible outcomes and only one favorable outcome (rolling a 6).

Odds, on the other hand, refer to the ratio https://wanteddeadorawildgame.com/ of favorable outcomes to unfavorable outcomes. In the case of rolling a 6, the odds are 5:1 against rolling a 6, or in favor of not rolling a 6.

Understanding Expected Value

Expected value is the average return you can expect from a game over time. To calculate expected value, you need to multiply each outcome by its probability and then sum up all the products.

Let’s use an example: suppose we have two possible outcomes for a slot machine spin – winning 5 dollars with a 10% chance or losing 1 dollar with an 80% chance.

The calculation of expected value is as follows:

Expected Value = (Outcome A x Probability of Outcome A) + (Outcome B x Probability of Outcome B) = ($5 x 0.10) + (-$1 x 0.80) = $0.50 – $0.80 = -$0.30

Using the Kelly Criterion

The Kelly criterion is a formula that can be used to determine the optimal bet size for a given expected value. The formula is as follows:

f = (bp – q)/b

Where:

• f: the optimal fraction of bankroll to wager each time
• b: the odds in favor (how many times more likely you are to win than lose)
• p: the probability of winning
• q: the probability of losing