Posted 4/12/2022 by admin

How To Calculate Texas Holdem Odds

How To Calculate Texas Holdem Odds Rating: 9,0/10 3180 votes

The odds in this Texas Hold'em odds table are unlikely to directly help your overall strategy, but they are pretty interesting nonetheless. The Texas Hold'em odds for each of the different situations have been given in both percentage and ratio odds, so use whichever format you feel comfortable with.
Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush.

The odds in this Texas Hold'em odds table are unlikely to directly help your overall strategy, but they are pretty interesting nonetheless. The Texas Hold'em odds for each of the different situations have been given in both percentage and ratio odds, so use whichever format you feel comfortable with.

The following Texas Holdem odds table highlights some common probabilities that you may encounter in Hold'em. It is not vital that you learn these probabilities, but it is useful to be aware of the chances of certain situations arising.

Texas Hold'em odds chart.

Situation	Percentage Odds	Ratio Odds
Preflop Probabilities:
Dealt AA.	0.45%	220 to 1
Dealt AK.	1.2%	82 to 1
Dealt AKs.	0.3%	331 to 1
Dealt 72o.	0.9%	109 to 1
Being dealt AA vs. KK (heads up).	0.004%	22,559 to 1
Dealt a pocket pair.	6%	16 to 1
Dealt suited connectors.	4%	24 to 1
Flop Probabilities:
Flopping a pair.	32.4%	2.2 to 1
Flopping a set (with pockets).	11.8%	7.5 to 1
Paired Board:
2 players, probability of trips.	17%	4.8 to 1
3 players, probability of trips.	26%	3 to 1
4 players, probability of trips.	34%	2 to 1
5 players, probability of trips.	43%	1.4 to 1

How to use Texas Hold'em odds.

Other poker odds charts.

For more useful odds charts that you can use for when you are working out whether or not to call when on a drawing hand, use the following tables:

Both of these tables give the odds for completing your draw depending on how many outs you have. You can find out more on how to work out odds and all that mathematical stuff in the article on pot odds.

Go back to the poker odds charts.

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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.

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.

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.

Odds Of Texas Holdem Hands