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# The Mathematics of Poker: How can Maths help you at the Card Table?

From Robin, published on 27/06/2017 > > > Mathematics: An Asset in Poker?

Whoever said that maths doesn’t have everyday applications?

One of the most compelling and entertaining examples is the connection between this reputedly difficult discipline, and poker.

Is it possible win at poker without integrating maths into your game?

While a good level of maths may not be necessary to win in a poker tournament, a good knowledge of probability can certainly give you an edge over those who don’t use it.

Use maths and win real money….. intriguing, isn’t it?

Emma

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## Poker: a Game of Combinations

Poker is not a game of chance and there is more to it than the variant known as “Texas Hold’Em” – one of the best-known and most played styles in the world. Instead, it involves making combinations, and bears much in common with bridge.

It is not luck that prevails in poker, but rather the richness of combinations employed as well as a perfect mastery of one’s emotions, a few tactics and a dash of well-placed opportunism.

So could poker be considered a maths puzzle?

## Should we learn Maths to Play Poker?

There are many different applications of maths and maths lessons to be found in poker.

Basically, in the first instance, it is a question of calculating the probability of the pot and considering questions like “do I have a chance to win this hand?”

There are as many sides to both poker and maths (Source: Flickr.com – Jim Sher)

You can not escape the aspect of probability, as a good knowledge of numbers provides an essential basis for playing poker well.

So, theoretically, fear of maths is illogical at the poker table.

There will always be players, especially older ones, who will try to convince you that poker is, above all, a game of wills and that intuition counts for everything.

While there’s no need to have the genius of Einstein to play poker, this is not a piece of advice to be followed blindly: How can you let your gut feeling determine your chances of winning a big pot? It’s impossible; in this respect, at least, poker is purely mathematical.

This may seem a little abstract to non-poker players, but the key lesson is this: In poker, the most important thing to know is the frequency with which a certain draw will appear based on the hand you are holding.

## Psychology and Maths in Poker

If poker were simply a game of chance, it would not attract so many followers all over the world.

The dynamics of this game are primarily driven by strategy, which depends on two essential factors: Maths and psychology.

It is certainly possible that mathematicians have a slight advantage over other players. Among the great “poker mathematicians”, are players like Andy Block, Paul Magriel and Chris Ferguson.

But it is surely the mathematical genius John Forbes Nash (played by Russell Crowe in “A Beautiful Mind”), a specialist in game theory, who solidified the link between poker and maths.

There are maths games, then there’s poker (Source: Pixabay.com – quinonesnaomy)

## From Counting Games…. to Poker

The mathematical principles generally applied to poker are fairly basic and accessible to most people.

Among the most important are:

• The context on which the poker odds rest, i.e. the cards: There are 52 cards in a pack, and 13 in a suit.
• There are the odds and the probabilities: These are concepts that it is imperative to know your way around. There is a simple rule of thumb that can give you an idea of your draw’s chances: Multiply the number of “outs” on the flop, using the “turn” and the “river”. (In Texas Hold’Em and Omaha poker, a flop is the first 3 cards of the board, this draw coming after the first round.)
An out is one of the cards, potentially in the deck, that can improve your hand (the 2 closed cards). By knowing your outs, you can calculate your chances of getting one of the cards still in play that will give you a strong hand and a winning combination.
• Calculating life expectancy (or predicted gain): This is the profitability of a play, which a bet can bring you. It may be negative or positive. By calculating this chance, you can anticipate potential changes in the situation, and in so doing determine your actions and style of play.

As an example: If you toss a coin, you may bet £1 on heads and the same amount on tails. The odds are then 1: 1.

The mathematically predicted gain is therefore zero, because it is very unlikely that you will either be ahead or behind, whether after 2 or 200 coin tosses.

How can you calculate life expectancy?

You subtract the amount you bet in the pot from the probability of winning the pot.

If the result is positive, then you will have a greater chance of winning in the long run. If the result is negative, you can still win at the table, however the more you play the lower your chances of winning, in the long run, will be.

## Maths is not Everything in Poker

But beware, maths lessons won’t do everything for you in poker: One mustn’t forget that it is a game you never have all the information necessary to be certain of your chances of winning the bet.

Maths can be counterproductive if it takes precedence over experience and intuition. All it takes is one little mistake at the start of a game, and maths won’t be of any help during the rest of the poker game or the tournament.

If there’s one thing to remember about maths and poker, it would be that it doesn’t help with all parts of the game: It can help you estimate the profitability of risk in your poker games, over the long term, and nothing more.

Even basic maths concepts can boost your game (Source: Commons.wikimedia.org – Johnny Blood)

## Maths Skills useful in Poker

### Percentages and probabilities

A good poker player knows percentages and probabilities, he knows that he has one chance in eight of having three of a kind if he holds a pair, and that he has one chance in three of a flush on the flop.

### The importance of “outs”

A poker player knows the importance of “outs”: The number of cards that will improve your hand strength.

How’s it done? Count your outs, multiply by two, add two and you get the chance of landing a great poker hand.

### Pot odds

A mathematically strong poker player knows how to calculate the pot odds.

This is an essential factor in making your decisions in poker.

Pot odds refers to the relationship between the size of the pot and the size of the stake. For example, if there are £10 in the pot and you placed £2, the odds are 5 to 1.

If you saw a bet of £5 in the pot at £10, then the pot is at 2 to 1.

Even if it sounds a little complex at first, calculating the pot odds is essential for playing in the medium to long term.

Whatever happens, you should always be aware of the size of the pot.

## Maths Essential in Poker

Using maths in poker is not a must, but it becomes a necessity if you want to progress and succeed in the game.

This is especially true if you play online poker (against a computer). And yes, maths and computer science are also related.

It is not always easy to master, because you need to know in real time your chances of winning or losing depending not only on your cards, but on those in the deck as well.

An average poker player usually doesn’t calculate anything, and avoids headaches by going “all-in“, i.e. placing all remaining chips on the table as soon as he gets a pair or has a big hand.

There are, however, some numerical benchmarks to be kept in mind: For example, if you have a pair, your chances of having three of a kind are 1/12. You should know how much you’ll win if you get such a hand – This amount should be greater than the sum of the other 11 bets.

Most of these mental calculations are nevertheless quite simple to master. While not necessary if you are playing inexperienced opponents, but if you want to become a top poker player, maths and knowledge of these rules is a must.

In the same way that you can’t write words and phrases without knowing the letters that make them up, it is impossible to play poker well without understanding principles like pot odds, for example.

Learn to master certain mathematical concepts, learn how to handle the “bankroll” (the total amount that a player has available to wager) and how to keep your cards balanced.

And above all, you will have to progress in mental calculations!

Luckily, most mathematical concepts related to poker can be easily learnt by memorising tables.