# Casino Math

- happyswan831
- Jun, 22, 2018
- Math
- No Comments

Some questions about the probability of winning and income gambling. How casino math is arranged and how casinos make money

1. The probability of winning

2. Return percentage

3. Distribution of results when gambling

If you decide to play or play in a casino, and perhaps you want to become the owner of a gambling establishment, then it is useful to know a little theory. There are many questions: What is the probability of winning (losing), what can you expect when playing in a casino, what income does a gambling establishment receive, can you increase the chances of winning, is it really possible to win at a casino?

These questions began to worry people a long time ago. Many processes in gambling are explained by probability theory. Actually, the probability theory itself was created in the study of gaming systems. For an example of gameplay, consider a simple game:

Plays a player and institution. The usual dice with 6 faces is thrown. The player puts 1 dollar on the fact that one of the numbers from 1 to 6 falls out. In case he guesses, the player gets a 1: 5 win. That is, he gets $ 5 winnings and back his bet. If any other number drops out, the institution takes the bet – the player loses.

Consider the concepts of this game: Dice

– Bid size 1 $

– Payout 1: 5

The probability of dropping any face of the cube is the same. There are six possible variants of events. Favorable for the player 1 event – unfavorable 5. The probability of winning a player in one game is equal to:

B = Number of winning combinations / Total number of combinations

B = 1/6 = 16.66%

Expected Player Win (G):

OB = Rate x B x Payout = $ 1 x 1/6 x 6 = 1 $

As you can see, on average, out of 6 shots, the player will win in one and lose in five. When playing one or more games, both the player and the institution can win. However, for exаmple, if we play the game 10,000 times, then the law of large numbers will work, which says that with a large number of tests, the numbеr of events will tend to the number of tests multiplied by the probability. The merit of this discovery belongs to Jacob Bernoulli (1654 … 1705).

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