The Mathematics of Poker !!

maths

Poker, like any other casino game, is all about odds. And when you talk about odds, probability invariably comes into the picture. And when we talk about probability, is when the Mathematics of Poker comes into play. If you want to understand how these odds can be used to help you improve your game, I’ve prepared just the perfect little guide for you.

About Probability

Probability is a whole section of mathematics devoted to finding out how likely a certain event is to occur as opposed to another event. The best example of this is a coin flip. There’s a 50% chance of you getting heads or tails, since there are two sides to any coin.

Probability when it comes to cards

While a coin just has two sides, a typical poker deck has 52 cards in it. Therefore, the Mathematics of Poker involve a bit more complicated number of likely outcomes when a card is dealt. Each of these cards belong to one of four suits: diamonds, clubs, spades or hearts. And each of these suits have cards of thirteen ranks, starting from number two to the Ace, which is the highest ranking card. The probability of your being dealt an Ace as your first card is one in thirteen, which works out to 7.7%. The same way, your probability of being dealt a club as your first card is one in four, which works out to 25%.

Once you are dealt a card, such as an ace, there are only three other aces left in the deck that can be dealt. Therefore, the probability changes for the next round. The new probability of being dealt an ace now becomes three in fifty one, which works out to 5.9%; this a lower probability than when there were no aces dealt.


Hole Pair probability

The probability of receiving a hole pair is 0.45% for each card. The probability of receiving any of the thirteen hole pairs is 5.9%.

Hand probability
The probability of winning when it comes to beating your opponent’s hand is:

  • If you have a high pair and your opponent has two low cards, you have an 83% chance of winning
  • If you have a high pair and your opponent holds a low pair, you have an 82% chance of winning
  • If you have a middle pair and your opponent holds one high card and one low card, you have a 71% chance of winning
  • If you have two high cards and your opponent holds two low cards, you have a 63% chance of winning
  • If you have two high cards and your opponent holds a low pair, you have a 55% chance of winning

Knowing a bit of the Mathematics of Poker and understanding probability can help you to make smarter changes to your strategy during a game so that you have a better chance of winning. Even if you hate the subject, the Mathematics of Poker is far more interesting and easy to comprehend!