The Relationship Between Mathematics and Poker

Playing cards have been around for centuries. They are one of the longest-lasting forms of entertainment, and millions of people all over the world still enjoy a variety of different card games. Whether it be poker, blackjack, bridge, or a variety of other titles, playing cards are a universal game that anybody can enjoy.

A standard deck of cards has 13 cards in each suit, made up of:

  • Hearts
  • Diamonds
  • Spades
  • Clubs

The deck contains 52 cards, which all have the same chance of being dealt out during a poker game. As each suit has a set denomination, the chances of having certain hands can vary wildly, depending on how rare of a combination it is. The concept applies to poker games in both land-based and online casinos alike, as you can check at https://www.cafecasino.lv/casino/video-poker.

How The Mathematics Work

Due to the high number of potential hands that can be dealt, it can be difficult to use mathematical probabilities to your advantage. Poker players who operate at the highest level are able to roughly calculate the probability of their hand being the one that scoops them the prize.

Using mathematics whilst playing poker is an element of strategy that can make up part of a bigger strategy that turns out to be a success. The area has been widely studied, and there is plenty to suggest that getting your head around the mathematics involved in poker can bolster your technique and give you a better chance in the heat of a game.

The odds of obtaining a Royal Flush are so astronomical as you require a combination of 10, Jack, King, Queen and Ace, all from the same suit. Likewise, the possibility of getting a straight flush is also so rare that you don’t really need to work out the mathematics for it, as there’s an incredible chance that you have the winning hand.

The table below shows the return percentage for each hand. It also calculates the likelihood of it being dealt to you during a poker game.


Poker HandsProbabilityLikelihood of return
Royal Flush0.002%0.619%
Straight Flush0.011%0.547%
Four of a Kind0.236%5.906%
Full House1.151%10.361%
Three of a Kind7.445%22.334%
Two Pair12.928%25.856%
Jacks or Better21.459%21.459%


As we go further down the table, you can see the probability of each hand becoming greater. All of the odds are calculated using a standard 52-card deck. This was something we touched on in the opening stages of this article. To be precise, there are 2,598,960 possible variations of hands you could end up with.

So, the chances of getting a royal flush are exactly 4 in 2,598,960. Whereas a standard flush, for instance, has 5,108 potential avenues. So, the odds and probability are much better given the fact there’s a multitude of different variations.


Do You Have to Be Good at Mathematics to Be Good At Poker?


While it doesn’t hurt to be competent at maths, you don’t have to be a maths professor to play at the highest level. Sometimes, having a strong hand can work against you if your body language is easy to read and you don’t read the session as effectively as other players.
Intuition definitely comes in handy, when you have to deal with an opponent who’s bluffing or takes advantage of a strong hand. Being able to interpret the game in an intuitive fashion will make you stand out from the competition.

Some professional players have walked away with huge sums by bluffing their way through games with hands that aren’t even that strong. A great example of a player who knew how to throw up smokescreens and throw his opponents off was poker legend, Phil Ivey.

The psychology of great players like Ivey and the fact they can do the maths make them formidable opponents. It is a similar story to Dan Cates, who became one of the top players in the world by his early thirties by putting a weighted emphasis on his poker psychology.

Likewise, some players can fold whilst having the strongest hand in the game. The maths explains, in theory, why certain hands are more lucrative than others and hold the possibility of the best returns.

However, it doesn’t completely dictate the direction of the play. The reason is because of other factors that need to be thrown into the equation. This includes whether or not you are up against a strong player.

This is true especially if you are competing against somebody who knows how to read body language or bluff their way out of a tricky situation. It doesn’t matter how good your hand is if your opponent can read you and throw you off with their own body language and signals.


You may also like