Poker Hand Probability Calculator
admin 4/7/2022
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.
The Poker Odds Calculator will help you calculate your chances on a given hand, in any situation. One of the most interesting features of the PokerNews Poker Odds Calculator is the guide on the. As a poker player, knowing poker hand odds and rankings is crucial to knowing where you stand when calculating your odds of winning. This guide is for players from beginner to intermediate level – meaning those with a basic knowledge of poker but who don’t know how best to calculate poker odds to gauge the chances of success – and will give you everything you need to beat others when.
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.
- 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.
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.
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?
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...
Poker Hand Probability Calculator Estimate
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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Online poker odds calculators are poker software tools that automatically calculate the poker odds for a hand, using the information that is available. These poker statistics that the poker odds calculators generate are especially useful as a tool for beginner poker players who are not completely familiar with the odds of making different poker hands. Advanced poker players will be more interested in products such as Holdem Ranger that allowed for detailed calculations of equity using hand ranges. If you are interested in extremely detailed mathematical projections of poker situations and aren't afraid to get elbow deep in formulas then check out Pokerazor. Simple Free Poker Calculators can be found on sites like PocketFives.com and CardPlayer.com.
Most poker calculators will display your odds of making a variety of hands such as straights, flushes, full houses, etc. as well as your opponents' odds of having those hands. In most poker odds calculators, all of these statistics are combined to give you an estimated win percentage as well as a recommended action. Some poker odds calculators run in real time and read the cards that are on the table to gather the data. Others, such as PokerStove, are used on their own and require the user to enter all of the hand information.
When deciding what kind of Hold'em calculator you want to use, take into consideration what features you would like to have. If you are interested in getting probabilities and only play a single table, check out the Poker Wingman poker odds calculator. It attached to a single table and offers odds and advice based on customizable playing style settings. If you want to go through and analyze hands after they have been played to find out if you put your money in correctly vs. your opponent's range of hands, check out PokerStove or Hold'em Ranger. For a solid free poker odds calculator, check out Magic Holdem.
Poker odds calculators are extremely useful tools when used correctly. Do not make the mistake of choosing one that gives poor advice or incorrect statistics. Some calculators are banned at certain poker sites. This is usually because you are not allowed to use programs that give advice in real time. Another reason that online poker calculators such as Poker-edge are banned is because they used a central database of hand histories to calculate opponent's playing styles and makes recommendations based on that.
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