Poker is a purely mathematical game, even if it doesn’t look like it on the surface. Everything at the poker table is based on math, and if you learn how to use this math the right way you’re guaranteed to win in the long run.
I know it’s a big promise to guarantee that you can win, but that’s the way that math works. If you use math facts the right way, there’s nothing that can change them.
This article serves as an introduction to basic poker math that you need to know about. It’s not everything that you need to know, but you can’t learn more advanced techniques correctly until you learn these 6 poker math facts.
1 – Basic Poker Card Math
Everything that you need to know about using math when you play poker starts with the way the cards that are used are designed and how they work. All of the most common poker games use the same deck of 52 cards.
Poker uses both the 13 card ranks and the 4 card suits to build hands. The harder a poker hand is to complete, the higher it ranks.
The power of poker math and the deck is about what can and can’t happen when the next card or cards are dealt. You know what’s left in the deck and what’s not in the deck based on what cards you have and what cards you’ve seen.
If you have a pair of jacks in your hand in a Texas holdem game before the flop, you know that there are 50 cards that you haven’t seen and that exactly 2 of those cards are jacks. The deck only has 4 jacks, and you have 2 of them.
The rest of this article goes into more detail about different situations at the poker table. But you need to spend some time thinking about what you learned in this section. Every time you play a hand of poker think about what can happen, what can’t happen, and how you can use this information to make better decisions.
2 – Odds on the Flop
In Texas holdem and Omaha poker, the 2 most popular poker variations, there’s a flop containing 3 cards, followed by a turn and river. The odds of things happening are slightly different in Texas holdem than Omaha because you start with 2 cards in holdem and 4 in Omaha. I’m using Texas holdem for the odds discussions on this page.
When you start a holdem game with 2 cards and stay in the pot to see the flop, you can get an idea of the odds of improving your hand on the flop. This is important because once you learn how likely or unlikely a hand is to improve it helps you learn when to stay in a hand and when to fold.
If you have a pair in your hand, the best thing that can happen on the flop is to get quads or a set. The odds of flopping quads are very low. The odds of flopping a set aren’t great, but they’re better than flopping quads.
You have to look at each card on the flop to consider odds. The odds of getting a set on the first flop card are 2 out of 50. The odds on the second card are 2 out of 49, and the odds on the third card are 2 out of 48.
This averages out to basically 6 out of 49. In other words, you’re going to flop a set almost 1 out of every 8 times you have a pocket pair.
This is just 1 example of using odds on the flop. Deal out practice hands and determine the odds of improving using this method until you understand how likely your hand is to improve.
3 – Odds on the Turn and River
Using odds on the turn and river is easier than determining them on the flop. You know the value of more cards and there’s only 1 card on the turn and 1 on the river.
On the turn, there are 47 cards that are possible. On the river there are 46 possible cards.
All you have to do is figure out how many cards help your hand in total.
If you have a flush draw with 4 cards of the same suit and 2 high cards that can form a high pair if you match 1, you have 9 cards that can make the flush and 4 cards that can match either of your high cards, for a total of 13 cards.
The odds of getting 1 of these 13 cards on the turn are 13 out of 47. If you don’t get 1 of these cards on the turn, the odds on the river are 13 out of 46.
Run the odds for every hand as you practice. This is going to help you learn which hands are worth drawing to and which ones you should fold.
4 – Odds of Completing a Flush
A flush draw is a common draw in poker. I touched on it in the last section and it’s a good example of using odds so I want to cover it more here. And this same method can be used for any type of draw once you see how it works.
On a flush draw you have 4 cards of the same suit out of a total of 13. This means you have 9 chances left in the unseen cards to complete the flush. This means that you’re never the favorite to complete a flush because there are always more cards left that don’t complete it.
But this doesn’t mean you should always fold when you have a flush draw. Sometimes it’s profitable in the long run to draw. You’re going to learn more about this in the next section.
On the turn you have 9 out of 47 chances to complete your flush, and on the river you have 9 out of 46 chances.
Pot odds compare the odds of completing your hand and hopefully winning against the amount of money you can win. When the amount of money you can win is better than the odds of drawing the card you need you stay in the pot, and when the money you can win is worse than the odds you should fold.
Look at the odds of completing your hand. In the case of a flush on the river, you have a 9 out of 46 chance. Now look at how much is in the pot and how much you have to put in to see the river.
For example, the pot has $400 in it and your opponent bets $50. This means you have to call $50 and the pot now has $450 in it. This is a ratio of 1 to 9. Your odds of hitting the flush are 1 to 5.11. This is better than the ratio of money you call against the money in the pot, so the pot odds say this is a profitable call in the long run.
6 – Poker Expectation
Poker expectation is a way to determine the average profit or loss for situations in poker. In the last section you saw an example of pot odds. Here’s how you can determine how much this situation is worth in the long run.
The deck has 46 unseen cards. So you’re going to run the exact same situation 46 times using each of the possible cards on the river to see the average profit per hand.
It’s going to cost you $50 for each of the 46 hands for a total of $2,300. You lose 37 times out of the 46. On the 9 times that you hit your flush you’re going to get $500 each time. This is a total return of $4,500.
This is a total profit of $2,200 on 46 hands. This is an average profit of $47.83 per hand. This is how you use expectation in poker to make better playing decisions.
Poker math starts with an understanding of the cards used in the games. The deck of cards unlocks all of the secrets about poker math you need to use.
A deck of poker cards is built in a way that lets you determine odds of what can happen on the flop, on the turn, and on the river. It also lets you use 2 powerful mathematical concepts called pot odds and expectation.
With these poker math tools you can quickly learn how to be a profitable poker player.
Michael Stevens has been researching and writing topics involving the gambling industry for well over a decade now and is considered an expert on all things casino and sports betting. Michael has been writing for GamblingSites.org since early 2016. ...
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