# Texas Hold ’em - Probability - General

Texas Hold'em Odds "Outs" are unseen cards that will make any hand you expect will win the pot if they come off on the turn or river. Enter your email address below to subscribe to our weekly newsletter along with other special announcements from The Wizard of Odds! Every hand is exactly 5 cards. What are the odds of having two four of a kinds and a straight flush dealt to the same player in a Texas hold 'em game with ten players in 50 hands? This means if the absolute best five-card hand a player can make is by using the five cards on the board, then that is his or her final hand this is known as playing the board. Texas hold 'em fool?

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In order for a flush or straight flush to be possible there must be at least three cards of the same suit on the board. If the board is unpaired at the end there is usually one or more straights possible. In a low limit game you should train yourself to look for straight possibilities especially when a passive opponent suddenly wakes up on the turn or river with a raise. These tips will help you determine quickly the highest possible hand at the moment the nuts. Suppose the board after the turn looks like this: Single Card Straight Flushes The most common example of this is a board like the following: The Beaten Boat Suppose the following flop is dealt Flop when you hold The colors are red and black for historical purposes and so the same deck can be played for other games where that might matter.

Does any single player have a straight? If yes, he wins the pot. Do multiple players have straights? If so, the player with the highest straight wins.

A is the lowest straight, while J-Q-K-A is the highest straight. If multiple players share the highest straight, they split the pot. Does any single player have a 3 of a kind? Do multiple players have 3 of a kind? If yes, the player with the highest 3-set wins the pot. If multiple players have the highest 3-set, the player with the highest kicker wins the pot. If multiple players tie for highest 3-set and highest kicker, the player with the next highest kicker wins the pot.

If the players tie for the highest 3-set, highest kicker, and highest second kicker, the players split the pot. Does any single player have 2-pair? Do multiple players have 2-pair? If yes, the player with the highest pair wins the pot. If multiple players tie for the highest pair, the player with the second highest pair wins the pot.

If multiple players tie for both pairs, the player with the highest kicker wins the pot. If multiple players tie for both pairs and the kicker, the players split the pot. Does any single player have a pair? Do multiple players have a pair? If yes, the player with the highest pair win. If multiple players have the highest pair, the player with the highest kicker wins. Compare second and third kickers as expected to resolve conflicts, or split if all three kickers tie.

At this point, all cards are kickers, so compare the first, second, third, fourth, and if necessary, fifth highest cards in order until a winner is resolved, or split the pot if the hands are identical. Thunderforge 6, 3 23 Nothing can be more accurate and complete answer. Thank you very much! There is no hand composed of five of a color.

However, this answer omits five of a suit, which is a flush, and ranks above a straight and below a full house. I'm confused then - why does that need to be evaluated first? Quite simply, each player evaluates their hand individually, and the first person or people to have one according to the algorithm above win the hand.

I suppose you could optimize it by saying "can anyone beat the five card community hand? In essence, your comment adds more confusion than it solves. Paparazzi This answer is intended to be and indeed is used as a canonical answer. It is used to answer any question that uses the standard poker resolution. I've done a bit of reformatting to help improve clarity. Feel free to make further changes or undo it entirely if you don't like it.

Steven Stadnicki 4, 1 17 This was also the type of bad beat in the video; in fact, these were the exact cards. One player has two to a royal flush T-K , the other has one ace and a "blank" card, and the board contains the other three aces and the other two cards to the royal. One player has one to a royal flush T-K and a blank card, the other has two aces, and the board contains the other two aces and the other three cards to the royal flush.

The following table shows the number of combinations for each case for both players and the board. The lower right cell shows the total number of combinations is 16, However, we could reverse the cards of the two players, and still have a bad beat. So, we should multiply the number of combinations by 2. The probability of just a case 1 bad beat is 1 in million.

The simple reason the odds are not as long as reported in that video is that the two hands overlap, with the shared ace. In other words, the two events are positively correlated. For example, in video poker if you are initially dealt a four of a kind and you discard them all, it will reappear as a winner, since the central computer was programmed for your machine to get a four of a kind.

Therefore, any strategy is useless. Regardless of what cards the player keeps, he can not avoid his fate. If the player tries to deliberately avoid his fate, the game will make use of a guardian angel feature to correct the player's mistake.

I completely agree with the author that such games should warn the player that they are not playing real video poker, and the pay table is a meaningless measure of the player's actual odds.

It also also be noted these kinds of fake video poker machines are not confined to New York. Hello, I am a seventh grader from Hawaii. I am doing a science fair project on poker and shuffling. I was hoping you could answer a few questions that would help me with my project:. How did you come up with the percentages found in the charts? If you used a computer program, how did you develop it and how long did it take?

You stated that you started the Wizard of Odds as a hobby. Did experimenting change as your site became more well-known? Why or why not? The two-player table was done by a brute-force looping program, that cycled through all possible opponent cards, and 1,, possible community cards.

For three to eight players, looping would have taken a prohibitive amount of time, so I did a random simulation. I mostly copied and pasted code from other poker-based programs. The new code only look about a day to write. Yes, I started my site as a hobby in June It has gone through three different domains over the years.

Here is what it looked like in May The purpose of the site has always remained the same, a resource for mathematically-based gambling strategy. Through the years, I have just been adding more games and material. One experiment was providing my NFL picks for the season , which was an abject failure. How did you come up with that figure? Thus, the probability of getting at least one ace or king is I was involved in a hand of online poker and would like to know the odds of this happening, please:.

Normally I'm sick of bad beat questions, but this one was too painful to ignore. In a six-player game, the probability is 15 times higher, or 1 in 58,, After the indicated hole cards are dealt, and before the flop, the probability is 1 in 38, that the hand will finish as it did.

There is a promotion being advertised by a Las Vegas card room: You have to use both of your hole cards, and there is a five-hour time limit. Assuming 35 hands per hour, and that the clock starts with the first flush, what is the probability of achieving the other three flushes within five hours? At 35 hands per hour, in five hours hands could be played. You then have hands to make a flush in hearts, diamonds, and clubs.

In the next hands the probability of missing a heart flush would be However, that would incorrectly over-subtract the probability of not making all three flushes. So you should add back in pr no club, diamond, or heart flush. I would like to thank dwheatley for his help with this problem. It is discussed on my bulletin board at Wizard of Vegas.

Each time he held as hole cards, and both times he made a full house on the river. What are the odds of that? Given two cards of different ranks, the probability of making a full house are 1 in The odds of making it on the river are 1 in The odds of this happening with the same two starting cards, in rank only, are 1 in 3,, Wizard of Odds uses cookies, this enables us to provide you with a personalised experience.

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The Wizard of Odds. Paul from Toronto, Canada The probability of a four of a kind in seven cards is 0. Kevin from Richmond, USA You can refer to my section on probabilities in poker to see the probability is 3.