Texas Holdem Pot Odds and Probability - Poker Probabilities

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Poker Odds for Texas Holdem - Do the math

"Do you know what the odds are in flopping 2 to a flush when you hold two of the same suit in your hand?" - Michael

"Um, no." - Me looking embarrassed.

"Well then my friend, you need to go read a few books before we talk more." - Michael

That conversation really sums up how I think about poker odds now. There�s really no getting around understanding some basic math in poker if you want to win. In this article I�ll explain how I think about the odds to make certain hands in Texas Hold'em and provide some useful data points which you should memorize for your everyday play. First I�ll discuss poker pot odds and a very simple way to figure out the odds of improving your hand.

Important preflop odds in Texas Holdem:

If you hold the following hands this is the percent of the time that you will improve your poker hands preflop to what is listed below:

The odds in Texas Holdem that you will improve the following hands:
You start with: After the flop you will: Likelihood:
Holding a Pair flop three of a kind or better 12%
Holding A/K flop an Ace or a King 32%
2 suited cards flop a flush less than 1%
2 suited cards flop 4 to a flush 10%
2 unmatched cards flop 2 pair 2%
Holding 2 A's or K's How often preflop for A's or K's 0.9%

See more Poker Probabilities

Calculating Poker Pot Odds

Let�s assume your hand is comprised of 2 spades and and the flop has 2 spades. How do you determine your pot odds to make your flush with 2 cards left?

Well first you must consider the fact that there are 13 spades in the whole deck. Out of these 13 spades we know there are 4 already out there because you have 2 spades in your hand and there are 2 spades on the flop. 2 + 2 = 4. Since there are 4 spades out of the deck already that means there are 9 left. 13 spades in deck - 4 spades seen = 9 spades left.

That's the first part you must quickly compute. Now consider the fact that you have seen a total of 5 cards. By this I mean that you have seen the 2 cards in your hand and you know what the 3 on the flop are. 2 cards in your hand + 3 cards on the flop = 5 seen cards. There are a total of 52 cards in the deck. Since we have seen 5 cards we know that 47 are left unseen. 52 cards in deck - 5 seen cards = 47 unseen cards.

In order to calculate the percent of the time we will make our flush you have to do a little bit of math. Take the cards that are left that will improve your hand and divide them by the unseen cards. This is the calculatation for calculating your odds in poker that you will improve any hand. In this example we see that we have 9 spades cards which will give us our flush to improve and there are 47 unseen cards in the deck. The math is: 9 cards to improve / 47 unseen cards = ~19%. This 19% is the percent of the time that we will make our flush on the turn. Always remember the following poker odds formula:

Cards to improve your hand / unseen cards = percent of time you will make your hand.

What are the Texas Holdem pot odds that you will make this flush if you see the turn and the river? Since the calculations are difficult I won�t go into details here as to why you can�t simply double the 19% chance you make your hand in the next card by 2. For now, I�ll just tell you it�s ~36% of the time.

How does this math need to factor into your play? Well, let�s say that you are playing in a $1-2 game and the pot has $2 in it (both blinds check/call). Let�s say you flop 4 to a flush and you check. Your opponent bets and you are sure he has a hand which beats your flush draw and he will call if you raise. What should you do? You should fold. You need to call your opponents bet of $1.00 for a chance to win a pot which has a total of $2 in it. We need to do some simple math now. There is a total of $2 in the pot and you are putting in another $1. Your $1 to call / $2 in the pot = 50%. This means that you will have to contribute 50% of the total pot by calling and you only have a 19% chance to potentially make a winning hand. If you have to put in a higher percent into the pot than your chances of winning are offering you then you�re in a long term losing position.

To further clarify my point let�s say that in our example you make this call 5 times. You make your hand 20% (we'll use 20% instead of 19% to make it simple) of the time in this situation. 20% of 5 times is one. So you'll win one time out of 5 and therefore win the $2 that was in the pot. Since you've won 20% of the time the other 80% of the time you've lost the hand. You've won once and lost 4 times. In the other 4 times that you miss your hand you�ve lost $4 by calling and not making your hand. Since you've won $2 in the one time you won the hand and lost $4 in the other times you have lost money. $2 by calling and winning - $4 by calling and losing= $2 loss.

This is just the beginning. Pot odd math really gets a little bit trickier than this when you factor in implied odds.

Calculating Implied odds in Texas Holdem

Implied odds is simply taking into consideration how your opponents will react. For example, if I have a flush draw and there are 2 passive players who have both checked to me and I think there is more than a 12% chance I can win the pot with a bet (meaning that for every 100 times I bet I will win the pot 12 of them) than I may bet and try to steal the pot right here. Now let's add the percent of the time I will win simply by bluffing to the percent of the time I will make my flush and win in order to decide if I should try and make a bluff at the pot. If I win the hand over 12% of the time with a bet and when I get called I make my hand 19% (recall that we will make our flush 19% of the time in our example earlier) of the time I will either win the pot outright or make a winning hand 33% of the time. 12% of the time everyone folds when I bet + 19% of the time they call and I make my flush for the winning hand. Now If the pot is bigger than my 33% chance that I will win then I should absolutely bet. I'm getting the right pot odds.

As you can see the pot odd calculations can get somewhat complex as you look into the deep mind game that is poker. However, the basic thought process is simple. Take the outs you believe will make you the winning hand, divide by the unseen cards and this is the odds that you will complete your hand in the next card.

Final Thoughts on Poker Odds:

There are so many thoughts which come to my mind when I think about drawing hands that I can�t put them all into 1 article. However I will make a few quick points which I hope you will consider when considering when to draw in Texas Holdem. Don�t draw to the dummy end of the straight (ie. You hold 6,7 and the flop is 8, 9, A) as you may be drawing dead and don�t have overcard draws either. By overcard draws I mean that if you hit your 6 or 7 you will probably still lose. Think about how much stronger your draw is if you had 10, J on a flop that is 8,9, 2. In this scenario you might hit the jack and still win the pot. See Poker Draws for an advanced discussion on how to play your draws. Additionally, always take into consideration what your opponent is thinking and what he will do. Often a call is not correct due to our pot odds formula but if you were to bet and combine your expected odds that you will make him fold with the fact that if called you may make your hand you may come up with a winning formula.

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