Texas Holdem Probability Of Hands

4/15/2022

In the previous article on working out preflop hand probability, we worked out the likelihood of being dealt different combinations of starting hands before the flop.

In this article, I will cover the basics of working out the probabilities behind various possible flops. I'll go ahead and cover the probability basics first in case you missed it in the preflop probability article.

Best Free Poker Training Options in 2020. Why spend any money if you are just starting out with many free poker training classes and other material available for free on YouTube and online poker. Poker is any of a number of card games in which players wager over which hand is best according to that specific game's rules in ways similar to these rankings.Often using a standard deck, poker games vary in deck configuration, the number of cards in play, the number dealt face up or face down, and the number shared by all players, but all have rules that involve one or more rounds of betting. Using The 'Outs' To Calculate Texas Hold'em Poker Odds. We have already determined that you have nine 'outs'. Now there are 52 cards in a deck and two of those are in your hand, leaving 50.

In the case of Texas Hold'em, there's the 2 pocket cards and 5 on the board. This way of working out the probabilities would be the more accurate way - however, just to note, the probabilities worked out on 5 of 52 are practically the same, and far easier to calculate. Number of possibilities. When you see players limping on 4-5 hands an orbit you just need to bet your hands. The math will take care of them, but you really need to use caution. LAG is a style because if you have AK the.

Probability calculations quick links.

A few probability basics.

When working out flop probabilities, the main probabilities we will work with are the number of cards left in the deck and the number of cards we want to be dealt on the flop. So for example, if we were going to deal out 1 card:

The probability of dealing a 7 would be 1/52 - There is one 7 in a deck of 52 cards.
The probability of dealing any Ace would be 4/52 - There four Aces in a deck of 52 cards.
The probability of dealing any would be 13/52 - There are 13 s in a deck of 52 cards.

In fact, the probability of being dealt any random card (not just the 7) would be 1/52. This also applies to the probability being dealt any random value of card like Kings, tens, fours, whatever (4/52) and the probability of being dealt any random suit (13/52).

Each card is just as likely to be dealt as any other - no special priorities in this game!

The numbers change for future cards.

A quick example... let's say we want to work out the probability of being dealt a pair of sevens.

The probability of being dealt a 7 for the first card will be 4/52.
The probability of being dealt a 7 for the second card will be 3/51.

Notice how the probability changes for the second card? After we have been dealt the first card, there is now 1 less card in the deck making it 51 cards in total. Also, after already being dealt a 7, there are now only three 7s left in the deck.

Always try and take care with the numbers for future cards. The numbers will change slightly as you go along.

Working out probabilities.

Whenever the word 'and' is used, it will usually mean multiply.
Whenever the word 'or' is used, it will usually mean add.

This won't make much sense for now, but it will make a lot of sense a little further on in the article. Trust me.

Total number of flop combinations.

First of all, lets work out the total number of possible flop combinations. In other words, we will just be working out the probability of 'any random flop'.

To work out this probability we simply multiply the probability of 3 individual cards being dealt.

(random card) * (random card) * (random card)
(1/52) * (1/51) * (1/50) = 132,600 possible flops.

Pretty big combination of cards huh? However, we've omitted the fact that we know our 2 holecards, so there will be two less known cards in the deck when we are dealing the flop. So if we amend this calculation by starting at 50 instead of 52:

P = (1/50) * (1/49) * (1/48)
P = 1/117,600.

Better, but this 1/117,600 probability is with exact cards in order. In Texas Hold'em it does not make a difference whether the flop comes A K Q or A Q K. So to account for this we multiply this fraction by 6 (1*2*3 = 6).

P = 1/117,600 * 6
P = 1/19,600.

The order of cards on the flop makes no difference, so multiply the probability by 6 to account for this (1 * 2 * 3 = 6 - this is math probability stuff). Don't worry if you don't know why we do this, just take it as it is.

This means that the probability of the flop being A K Q in any order is 1/19,600 - which is exactly the same probability as the flop coming something like 2 5 9 in any order.

So in total there are 19,600 different possible flops in Texas Hold'em.

Probability of specific flops.

To work out the probability of specific flops with the cards in any order we simply multiply the probabilities of each of those cards being dealt.

Multiply the 3 probabilities together.

So let's say we want to find the probability of flopping a heart flush.

There are 2 hearts in our hand.
There are 11 hearts left in a deck of 50.

P = (11/50) * (10/49) * (9/48)
P = 990/117600 = 1/119

In this example we do not need to multiply the final probability by 6. This is because the order of the cards and their probabilities are important, as the overall probabilities decrease as each heart is dealt.

What Are The Texas Holdem Hands

Overview of working out flop probabilities.

This is a really basic article for working out flop probabilities in Texas Hold'em. Think of it as more of a taster for working out probabilities on the flop to help you get your feet wet.

If I were to continue with probabilities, I would be delving deeper in to mathematics and further away from poker. That wouldn't necessarily be a bad thing, but my maths is a bit rusty and it's not going to directly improve your game, so I'll stop for now. Maybe I'll address it in a future article, but for now this is as far as I'm going to go.

If you're really interested in the mathematics of the game, try the book: The Mathematics of Poker by Bill Chen. It's definitely not a light read, but it's very interesting if you enjoy the maths side of the game. For other books, try the poker books section.

Did You Know?

A pocket pair is cards of the same rank, which means if your two cards have the same number, from 2-2 all the way up to A-A, this is called a pocket pair.

The odds of receiving any pocket pair is 5.9% which is 16 to 1. These are also the same odds of receiving a pocket pair of 2’s.
The odds of receiving a specific pocket pair: 0.45% or 220 to 1 These are the same odds for receiving a pocket pair of A’s.
The odds of receiving a pocket pair of A’s twice in a row is 0.002047% or 48,840 to 1.
The odds of receiving a pocket pair of K’s is 0.9% which is 220 to 1.
The odds of receiving a pocket pair of Q’s is 1.4% which is 73 to 1.
The odds of receiving a pocket pair of J’s is 1.8% which is 54 to 1.
The odds of receiving a pocket pair of 10’s is 2.3% which is 43 to 1.
The odds of receiving a pocket pair of 9’s is 2.7% which is 36 to 1.
The odds of receiving a pocket pair of 8’s is 3.2 which is 31 to 1.
The odds of receiving a pocket pair of 7’s is 3.6% which is 27 to 1.
The odds of receiving a pocket pair of 6’s is 4.1% which is 24 to 1.
The odds of receiving a pocket pair of 5’s is 4.5% which is 21 to 1.
The odds of receiving a pocket pair of 4’s is 5.0% which is 19 to 1.
The odds of receiving a pocket pair of 3’s is 5.4% which is 17 to 1.

Poker Fast Facts

The total number of possible royal flush hands in a standard 52 card deck is 4.

And the odds of making a royal flush is 649,739 to 1.

This is correct assuming that every game plays to the river.

In poker terms, the river is the name for the fifth card dealt, face-up on the board.

In total, there are 2,598,960 possible poker hands with 52 cards.

The odds of getting four of a kind in Texas Hold ‘Em is 4164 to 1.

Casinos normally change decks after 15 minutes of steady play, so that the cards can always be fresh and unmarked, as many professional players would be able to remember the certain markings on cards and use that to their advantage.