Ever wondered where some of those odds in the odds charts came from? In this article, I will teach you how to work out the probability of being dealt different types of preflop hands in Texas Holdem.

It's all pretty simple and you don't need to be a mathematician to work out the probabilities. I'll keep the math part as straightforward as I can to help keep this an easy-going article for the both of us.

Poker odds calculate the chances of you holding a winning hand. The poker odds calculators on CardPlayer.com let you run any scenario that you see at the poker table, see your odds and outs,. How To Work Out Hand Probability In Texas Holdem. Ever wondered where some of those odds in the odds charts came from? In this article, I will teach you how to work out the probability of being dealt different types of preflop hands in Texas Holdem. It's all pretty simple and you don't need to be a mathematician to work out the probabilities. Mar 21, 2018  I've been asked several times about the probabilities of each poker hand in multiple-deck games. Although I strongly feel poker based games should be played with only one deck, I will submit to the will of my readers and present the following tables. The first table shows the number of raw combinations, and the second the probability.

• Probability calculations quick links.

A few probability basics.

When working out hand probabilities, the main probabilities we will work with are the number of cards in the deck and the number of cards we want to be dealt. 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.

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Probability of being dealt two exact cards.

Multiply the two probabilities together.

So, we want to find the probability of being dealt the A and K. (See the 'and' there?)

• Probability of being dealt A - 1/52.
• Probability of being dealt K - 1/51.

Now let's just multiply these bad boys together.

P = (1/52) * (1/51)
P = 1/2652

So the probability of being dealt the A and then K is 1/2652. As you might be able to work out, this is the same probability for any two exact cards, as the likelihood of being dealt A K is the same as being dealt a hand like 7 3 in that order.

But wait, we do not care about the order of the cards we are dealt!

When we are dealt a hand in Texas Hold'em, we don't care whether we get the A first or the K first (which is what we just worked out), just as long as we get them in our hand it's all the same. There are two possible combinations of being dealt this hand (A K and K A), so we simply multiply the probability by 2 to get a more useful probability.

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P = 1/2652 * 2
P = 1/1326

You might notice that because of this, we have also worked out that there are 1,326 possible combinations of starting hands in Texas Holdem. Cool huh?

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Probability of being dealt a certain hand.

Two exact cards is all well and good, but what if we want to work out the chances of being dealt AK, regardless of specific suits and whatnot? Well, we just do the same again..

Multiply the two probabilities together.

So, we want to find the probability of being dealt any Ace andany King.

• Probability of being dealt any Ace - 4/52.
• Probability of being dealt any King - 4/51 (after we've been dealt our Ace, there are now 51 cards left).

P = (4/52) * (4/51)
P = 16/2652 = 1/166

However, again with the 2652 number we are working out the probability of being deal an Ace and then a King. If we want the probability of being dealt either in any order, there are two possible ways to make this AK combination so we multiply the probability by 2.

P = 16/2652 * 2
P = 32/2652
P = 1/83

The probability of being dealt any AK as opposed to an AK with exact suits is more probable as we would expect. A lot more probable in fact. Also, as you might guess, this probability of 1/83 will be the same for any two value of cards like; AQ, JT, 34, J2 and so on regardless of whether they are suited or not.

Probability of being dealt a range of hands.

Work out each individual hand probability and add them together.

What's the probability of being dealt AA or KK? (Spot the 'or' there? - Time to add.)

• Probability of being dealt AA - 1/221 (4/52 * 3/51 = 1/221).
• Probability of being dealt KK - 1/221 (4/52 * 3/51 = 1/221).

P = (1/221) + (1/221)
P = 2/221 = 1/110

Easy enough. If you want to add more possible hands in to the range, just work out their individual probability and add them in. So if we wanted to work out the odds of being dealt AA, KK or 7 3..

• Probability of being dealt AA - 1/221 (4/52 * 3/51 = 1/221).
• Probability of being dealt KK - 1/221 (4/52 * 3/51 = 1/221).
• Probability of being dealt 7 3 - 1/1326 ([1/52 * 1/51] * 2 = 1/1326).

P = (1/221) + (1/221) + (1/1326)
P = 359/36465 = 1/102

This one definitely takes more skill with adding fractions because of the different denominators, but you get the idea. I'm just teaching hand probabilities here, so I'm not going to go in to adding fractions in this article for now! This fractions calculator is really handy for adding those trickier probabilities quickly though.

Overview of working out hand probabilities.

Hopefully that's enough information and examples to allow you to go off and work out the probabilities of being dealt various hands and ranges of hands before the flop in Texas Holdem. The best way to learn how to work out probabilities is to actually try and work it out for yourself, otherwise the maths part will just go in one ear and out the other.

I guess this article isn't really going to do much for improving your game, but it's still pretty interesting to know the odds of being dealt different types of hands.

I'm sure that some of you reading this article were not aware that the probability of being dealt AA were exactly the same as the probability of being dealt 22! Well, now you know - it's 1/221.

Other useful articles.

• Poker mathematics.
• Pot odds.
• Equity in poker.

Go back to the poker odds charts.

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In our poker math and probability lesson it was stated that when it comes to poker; “the math is essential“. Although you don’t need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it’s all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.

In this lesson, we’re going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We’ll start with some basic math before showing you how to correctly calculate your odds. Don’t worry about any complex math – we will show you how to crunch the numbers, but we’ll also provide some simple and easy shortcuts that you can commit to memory.

Basic Math – Odds and Percentages

Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn’t mean “a quarter”. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5). Niagara falls ny gambling age.

Here are some examples:

• 2-to-1 against = 1 out of every 3 times = 33.3%
• 3-to-1 against = 1 out of every 4 times = 25%
• 4-to-1 against = 1 out of every 5 times= 20%
• 5-to-1 against = 1 out of every 6 times = 16.6%

Converting odds into a percentage:

• 3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
• 4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%

Converting a percentage into odds:

• 25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
• 20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.

Another method of converting percentage into odds is to divide the percentage chance when you don’t hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:

• 25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
• 30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).

Some people are more comfortable working with percentages rather than odds, and vice versa. What’s most important is that you fully understand how odds work, because now we’re going to apply this knowledge of odds to the game of poker.

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Counting Your Outs

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. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.

Probability Of Poker Hands

Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there’s room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .

The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:

Table #1 – Outs to Improve Your Hand

The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:

Table #2 – Examples of Drawing Hands (click to enlarge)

Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:

Don’t Count Outs Twice

There are 15 outs when you have both a straight and flush draw. You might be wondering why it’s 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.

Anti-Outs and Blockers

There are outs that will improve your hand but won’t help you win. For example, suppose you hold on a flop of . You’re drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.

It’s generally better to err on the side of caution when assessing your possible outs. Don’t fall into the trap of assuming that all your outs will help you. Some won’t, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.

Calculating Your Poker Odds

Once you know how many outs you’ve got (remember to only include “good outs”), it’s time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we’ll explain three methods. This first one does not require math, just use the handy chart below:

Table #3 – Poker Odds Chart

As you can see in the above table, if you’re holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you’re 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.

We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You’ll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.

Doing the Math – Crunching Numbers

There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.

Let’s again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let’s take a look…

Casino niagara pac free parking. With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:

(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.

This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:

9 x 38 ≈ 342.

Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:

36 + 342 ≈ 380.

The total number of turn and river combos is 1081 which is calculated as follows:

(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.

Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:

380 / 1081 = 35.18518%

This number can be rounded to .352 or just .35 in decimal terms. You divide .35 into its reciprocal of .65:

0.65 / 0.35 = 1.8571428

And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.

The Rule of Four and Two

A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.

Imagine a player goes all-in and by calling you’re guaranteed to see both the turn and river cards. If you have nine outs then it’s just a case of 9 x 4 = 36. It doesn’t match the exact odds given in the chart, but it’s accurate enough.

What about with just one card to come? Well, it’s even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that’s 16% (8 x 2) – which is almost 17%. Again, it’s close enough and easy to do – you really don’t have to be a math genius.

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Conclusion

In this lesson we’ve covered a lot of ground. We haven’t mentioned the topic of pot odds yet – which is when we calculate whether or not it’s correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we’ll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.

As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we’ll get to in the next lesson.

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By Tom 'TIME' Leonard

Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.

Probabilities Of Poker Hands