Mathematical Method For The Calculation Of The Expected Value In The Roulette - AN INTERESTING EXPOSURE THAT EXPLAINS THE MATHEMATICAL METHOD WITH WHICH THE CHANCE OF THE WINNINGS OF THE AMERICAN ROULETTE IN CASINO IS CALCULATED
The proposed method explains in a simple but technically correct way how to calculate the expected value ("expected value") of the game of roulette in the American version, available both in traditional American casinos and in all online casinos, even if not widely practiced because of unfavorable odds with respect to the European counterpart.
HOW TO CALCULATE THE VALUE EXPECTED AT THE ROULETTE?
A Roulette has 38 numbers, 18 are red, 18 are black and two represent zeros (green).
For the record, I'm describing an American roulette. European roulette has only 1 zero.
The simplest aspect of roulette is being able to bet on one color, say red. Point 1 dollar on red. It is an odd probability bet, which means that if you bet 1 dollar, you can win 1 dollar or lose a dollar, based on the color of the number coming out.
Let's try. Red! 27, I won! Now, what are the odds of winning? We have 38 numbers, each of which has the same probability of being issued and 18 of these are red. So the probability of winning is 18/38 = 0.473 = 47.3%.
Clearly you are disadvantaged in this game (compared to the bank, ed). We can quantify this disadvantage using the important concept of "Expected Value", ie the weighted average of how much can be won or lost.
When you bet a dollar on red, you have a chance of winning equal to 18/38 or a chance of losing 20/38, or winning a "negative" dollar. The expected value is 1 * (18/38) + (-1) * (20/38) = -0.526. This means that on average you lose 5.26 cents ($ 0.0526) for every dollar wagered.
In roulette you can also bet on other things besides color. For example you can bet on a number between 1 and 12 (first dozen, ed.). We bet a dollar on the first dozen. The casino pays 2 to 1 this bet, which means that by betting 1 dollar in case of winning the casino pays 2 dollars. We calculate the expected value: the probability of winning 2 dollars is 12/38, that of losing 1 dollar of 26/38. The expected value for this bet is 2 * (12/38) + (-1) * (26/38) = -0.526, the same value as the previous bet!
