Does Probability Theory Work In Games Of Chance?

A branch of mathematics that studies the regularities of random phenomena is called probability theory. The definition of “probability” is the degree of possibility of occurrence of any event.

As has been shown many times, with the help of mathematical formulas the probability of occurrence of a certain card can be calculated, and the chances of a player winning in games such as roulette , craps, blackjack , poker can be calculated , the lottery, etc. Now we will see in more detail how you can apply the science of mathematics to games of chance.

How do dependent or independent events affect the outcome of the game?

Independent events are those cases in which the occurrence of event A does not change the probability of event B. A simple example: if you toss a coin twice, the result of the second toss will not depend on the first. This means that the two actions (events) that occurred do not affect each other in any way. So in this case you can calculate the probability that the head of the coin will land on the next flip. This can be done using the following formula: (1/2) × 2 = ¼ or 25%.

If, in addition to the random factors, the probability also depends on the occurrence or not of another event, such events are called dependent events. Let’s use a simple example to find the probability that when 3 cards are drawn at random from a deck, each card turns out to be an Ace.

The standard deck, or also called “French deck” contains 52 cards, of which there are 4 Aces. This means that the probability that an Ace will appear in the first draw is from 4 to 52. Now let’s analyze: If the first card drawn is an Ace, it means that after that there will only be 51 cards in the deck, among which there will be 3 aces remaining. So the probability of the next Ace will be 3 to 51. If the second card drawn is also an Ace, then the probability of the third Ace of the same value will be 2 to 50.

However, it is important to understand that in the case of dependent events, each new result affects the result of the next action. That is, in the case we have considered, each subsequent appearance of a new card affects the probability of the outcome of the next event.

Therefore, using the mathematical formula we can calculate the probability of a positive result of the event when each of the 3 random cards is an Ace. The probability of this combination will be: 4/52 × 3/51 × 2/50 = 0, 000181.

Mathematical expectation