# Probabilities in Texas Hold'em

The number of distinct 5-card poker hands that are possible from 7 cards is 4, Multiply the two probabilities together. As you can see, this is a much easier method of finding your percentage odds. You can see these figures for yourself below:. 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.

## Poker Strategy

A 10 beats a 7 so player 2 wins. Q , J Player 2: Both have a two pair of aces and queens, with a king singleton. Only the top five cards matter. The jacks and deuce are irrelevant. One of the most important aspects of Texas Hold'em is the value of each two-card hand before the flop. The decision of how to play your first two cards is something you face every hand, and the value of your first two cards is highly correlated to your probability of winning.

The following table shows my power rating for each initial 2-card hand in a player game. The numbers are on a 0 to 40 scale. Basically, you should only play hands that are dark green, blue, or purple. Of course you should be more be more liberal in late position and picky in early position. If forced I would say you should need 10 points in late position and 19 points in early position to call the big blind. If your table is loose, as if often the case online, you can play a bit looser yourself.

Use the top table if you have a pair, the middle table if your cards are suited, and the bottom table if your cards are unsuited. Except for a pair,look up your high card along the left and your low card along the top. Following are the links to my tables of the value of each intial hand according to the number of players.

The player section explains the methodology for creating the table table. The following table shows the probability of making various hands after the flop and the correct "pot odds. This table is a good starting point the player should make mental adjustments for the probability of winning without making the hand, losing with making the hand, and expected future bets. The odds of a two pair improving to a full house are the same as those for four to an inside straight.

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The answer is yes and no! If you know for sure that someone else is holding a spade, then you will have to count that against your total number of outs. However, in most situations you do not know what your opponents hold, so you can only calculate odds with the knowledge that is available to you.

That knowledge is your pocket cards and the cards on the table. So, in essence, you are doing the calculations as if you were the only person at the table - in that case, there are 9 spades left in the deck. When calculating outs, it's also important not to overcount your odds. An example would be a flush draw in addition to an open straight draw. In addition to this, sometimes an out for you isn't really a true out.

Let's say that you are chasing an open ended straight draw with two of one suit on the table. In this situation, you would normally have 8 total outs to hit your straight, but 2 of those outs will result in three to a suit on the table. This makes a possible flush for your opponents.

As a result, you really only have 6 outs for a nut straight draw. Another more complex situation follows:. Once you know how to correctly count the number of outs you have for a hand, you can use that to calculate what percentage of the time you will hit your hand by the river. Probability can be calculated easily for a single event, like the flipping of the River card from the Turn. This would simply be: This can be calculated as shown below:. Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game.

To illustrate, here is a two-overcard draw, which has 3 outs for each overcard, giving a total of 6 outs for a top-pair draw:. However, most of the time we want to see this in hand odds, which will be explained after you read about pot odds. To change a percentage to odds, the formula is:. Now that you've learned the proper way of calculating hand odds in Texas Hold'em, there is a shortcut that makes it much easier to calculate odds:. After you find the number of outs you have, multiply by 4 and you will get a close estimate to the percentage of hitting that hand from the Flop.

Multiply by 2 instead to get a percentage estimate from the Turn. You can see these figures for yourself below:. As you can see, this is a much easier method of finding your percentage odds. But what about ratio odds? This is still done using this formula:. We minus 1 from that and get a rough estimate of our odds at about 3: Let's try this all the way through with an example:. If the 1 out of 5 doesn't make a ton of sense to you, think about the 1: Now that you know how to calculate poker odds in terms of hand odds, you're probably wondering "what am I going to need it for?

Pot odds are simply the ratio of the amount of money in the pot to how much money it costs to call. The higher the ratio, the better your pot odds are. Pot odds ratios are a very useful tool to see how often you need to win the hand to break even. The thinking goes along the lines of: The usefulness of hand odds and pot odds becomes very apparent when you start comparing the two.

As we now know, in a flush draw, your hand odds for making your flush are 1. Your answer should be: This means that, in order to break even, you must win 1 out of every 5 times. However, with your flush draw, your odds of winning are 1 out of every 3 times! You should quickly realize that not only are you breaking even, but you're making a nice profit on this in the long run. Let's calculate the profit margin on this by theoretically playing this hand times from the flop, which is then checked to the river.

As you can see, you have a great reason to play this flush draw, because you'll be making moneyin the long run according to your hand odds and pot odds. 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. You might notice that because of this, we have also worked out that there are 1, possible combinations of starting hands in Texas Holdem.

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

However, again with the 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.

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. What's the probability of being dealt AA or KK? Spot the "or" there?

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 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.

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.