Mathematics

# How Probability is used in Card Games

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Everyone knows there is some form of probability involved with card games but most do not know the actual probability or how it relates to the game. To fully understand how probability affects certain situations in games we must know what this probability actually is.

By definition probability is the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences. To anyone that hasn’t taken a statistics course lately this definition may seem a little fuzzy but I will explain it more thoroughly. The probability of something happening is (Desired Solutions)/(All possible Solutions). For example the probability of drawing a king out of the deck with 52 cards is 4/52 or in simplified form 1/13. This is because out of all of the 52 cards we want to draw one of the four kings in the deck.

Now we know what the probability of a card being pulled is we can apply this to card game situations. Of course not all card game players are mathematicians so it is impossible to do all of the exact calculations so quickly but with a general knowledge you can determine whether you have a (Large/Decent/Small) chance of winning. In Texas Hold’em lets imagine a situation where you have a two diamonds and there are three diamonds on the flop; we know that there are two cards yet to be flipped so let’s find the probability of there being another diamond and completing your flush. But to do this we must first find our desired solutions and all of our possible solutions.

To find all of the possible solutions we will list them.

Diamond:D
Heart:H
Club:C

Here are all of the possible solutions: (9)

DD,DH,DS,DC,HH,HS,HC,SS,SC

We desire all solutions with at least one diamond so we have 4 desired sets. This means our probability of having this flush is 4/9 or 44.4% which means our flush is less likely then calling a coin flip but since this is a good hand it may be worth pursuing because if you are successful the only a few hands can beat you; and you can also calculate the odds of someone getting a straight flush or a full house but it will be much easier and quicker to just assume that probability in relation to your own. So with this relationship between your odds of winning and the odds of someone having a better hand then you can determine how much you should bet.

Now just because you can determine the probability of one game does not mean you can predict them in every game. For example you cannot predict the outcome of the winning color on a roulette wheel. The average human will have a natural intuition or superstition that if the ball lands of red 50 times in a row the next ball must land on black. Mathematics does not agree with this assumption because this situation shows correlation without causation. In simple terms this means just because there is an obvious pattern the color of the last ball does not actually influence or affect the color of the next ball.