It is important to look into how the expected value in roulette works. This refers to the potential for making money on the game but also how one might end up losing money over a period of time.
Expected values are typically analyzed to see how well one might earn a good deal of money. In particular, it focuses on how a roulette wheel includes several evenly-sized spaces.
The expected value especially gives you an idea of what the overall house edge might be. The house always has the edge on a spin but the intensity of that particular value will vary based on what you do with the game. You have to watch for this to get a good idea of what to expect as you play the game. Be aware of this when figuring out what you can utilize with a bet.
Probability Points
The expected value on a roulette game is based on the particular types of wins that can occur. A typical American roulette game entails 38 spaces on the wheel. Therefore, the probability of a ball landing on a certain number is always 1/38. The odds of a ball landing on a red or black number is 18/38. The potential for one color to not occur is 20/38.
These probabilities suggest that certain numbers have better expected values. The green numbers clearly are not worth as much because they are not as likely to occur on a spin.
A Random Variable Is Important
The random variable refers to the winnings that come about on a spin. For instance, if you bet a dollar on the ball landing on red, you will win a dollar if the bet is successful. Meanwhile, you will lose that dollar if the ball lands on black or green.
The random variable for a winning spin in this example is 1. The variable on the losing spin is -1.
The random variable is important to analyze when planning an expected value. This helps you to see how you could win or lose a certain total based on what you plan on betting.
How to Calculate
To calculate the expected value, you must use a few rules:
1. Take the probability of one result and multiple it by the value of the random variable.
2. Calculate the probability of the opposite result and multiply that by the random variable on that one.
3. Add the two together to get the expected value.
For instance, you might place a bet on an even number. This would entail an 18/38 change to win one dollar. The product of that would still be 18/38.
Then, you would calculate what may happen if you land on 0, 00 or an odd number. This would have a 20/38 probability with a random variable of -1.
By taking 18/38 and adding -20/38 to it, you will get -2/38 or -0.053. This means that the house has an overall advantage.
In short, you must watch for how the expected value in roulette works. This is to give you a sensible idea of what value might come with a particular bet and to see if it is a worthwhile one to get into.