Mathematics and poker. First steps.

Mathematics? But this is poker. This is for fun and I’m going to have to go to school to study math. But is it essential? If I have been playing for a long time and I have not had to use them. This is luck, you go with the good ones, if your desires fall and if the ones of the others fall, you lose, but as you go with good ones, you will win more times.

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Many of you will be thinking this. And the truth is that it is not very attractive to start studying mathematics to play poker; but a minimum must be known and it is so minimal that it is embarrassing to call it mathematics. It is adding and multiplying, nothing more.


Mathematics and poker. First steps.

All the games in which chance intervenes can be explained with mathematics, and poker is no less. If you get to know how chance influences poker and how we can control it, we will be better than rivals who ignore this data.


The first step you are going to take is to calculate if you have to pay an all-in on the turn, when there is only one card remaining.


The table of 2

If you know how to multiply by two, you have everything done. You do not have to know more math to decide if you’re going to pay an all-in on the turn.

When the opponent makes a bet that is all-in, it does not matter if they are all your chips or all of the opponent’s; You will have to calculate the percentage of times you will win the hand, to know if you are going to take a correct amount of chips when you get a better hand than the opponent.

The calculation is simple, of all the cards that are left in the deck, there will be some that make you win the hand and others that make you lose it. I’ll give an example so you can see it clearly:

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You have A ♠ Q ♠ in your hands and the community ones are K ♠ 8 ♠ 3 ♥ 2 ♦. You have maximum project of color, if in the river a pica leaves, it is almost sure that you are going to win the hand.

If you have two spades in your hand and there are two spades on the table, there are four spades that can not appear on the river. Since each suit has thirteen cards, there are nine spades in the deck that if they appear on the river, will make you the winner of the hand. In the deck there are 52 cards, you have two and there are four on the table, so you do not know where the 46 missing cards are.

So from 46 cards, they’re worth 9. This means that your cards have almost a 20% chance of appearing on the river.

But there is a simpler way to calculate this. If you keep in mind that each card has a little more than 2% chance of being the one that comes out on the river; you can multiply by two the number of cards that you consider that make you the winner of the hand and so you have the percentage of times we will take the hand.


And what is the use of knowing that we are going to win the hand 20% of the time?

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Pot Odds

Now we have to see what benefit you are going to get with your bet. When you pay a bet you do it hoping to take the boat.

Imagine you are on the turn with a pot of 1,000 points and the opponent goes all-in for 500 points. It’s your turn, no one else is in your hand. If you throw the opponent takes the pot and ends the hand. If you pay, the river comes out and the one with the best hand takes the pot. You are risking 500 points (the ones you have to pay) to win 1,500 (1,000 in the pot plus 500 that the opponent bets).

This is a pot odds of 500 to 1,500, which you can simplify and stay in 1 to 3. It means that you are risking one to win three, so with winning one out of four times this situation is repeated, you will have a positive balance.

You always have to think long term, think that you will be presented with a multitude of similar situations and that if you act correctly you will have benefits. If this situation were repeated, you would need to win one out of four times to recover the bet. Every four times, three of them would lose 500 points and the fourth would gain 1,500 points so you would be at peace. If you could win more times, you would have benefits; On the contrary, if you win less than one every four times, you would have losses.


If you put the two concepts together, you can easily calculate whether a bet is profitable or not. In the example we have put, you would get color, and you would win the hand, 20% of the time, or what is the same 20 out of 100 times. This can be expressed in odds such as 20 to 80. In one hundred percent of the cases, you win in 20 and in the other 80 you lose. If you simplify, you would have odds of 1 to 4.

So you have odds, or odds of winning the hand, from 1 to 4, then you need the pot to have better pot odds from 1 to 4 so that it is profitable to pay the bet.

In this case, the pot gives pot odds from 1 to 3, which are odds worse than the times you will win the hand (1 to 4). If you repeat this move for a considerable number of times, you will lose 500 points four out of five times (the times you pay the 500 points and the color does not come out) and the time you win you will only take 1,500 chips (the chips of the pot plus the opponent’s bet), so in summary you will lose 500 points every five hands, meaning that this bet is costing you 100 points each time you do it.


In summary

To know if you must pay a bet on the turn, you have to calculate how many times you will win the hand and compare them to the pot you can win. If the benefit of the pot compensates for the times you are going to lose your hand, you are interested in paying the bet, otherwise you will have to throw yourself away.

Remember that the pot you win in proportion to your bet must be greater than the odds you have of winning the hand.

This is the simplest case for calculating odds and pot odds. If you want to continue learning, do not miss the following deliveries. And, as always, practice at, without practice there is no improvement.

Paul Perkins

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