# Poker probability

This article possibly contains original research. You need a [A] overcard to make top pair. Even though there might not technically be 47 cards remaining, we do calculations assuming we are the only players in the game. Another more complex situation follows:. Your answer should be: It has gone through three different domains over the years.

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What if there are only 2 or 3 or x spades larger than my largest hole card? Thanks for your help and the great site. The following table shows the probability for 1 to 8 higher ranks and 2 to 10 players, including yourself. In the case of your example of 4 higher ranks and 9 total players, the probability is The way I calculated these probabilities assumed independence between hands, which is not a correct assumption, but the results should be a close estimate.

Asking this for my own personal knowledge. I was dealt pocket aces. I got the royal flush on the river. I was wondering what the odds are of making the royal flush on the river with aces to start?

This would be the two suits in your pocket aces and the 46 possibilities for the extra card. If the flop comes up three of the same suit and I do not have a suit that matches the flop, and there are ten players left at the table, what is the probability of someone having a flush?

So the probability of at least one player having a flush is This is just a quick estimate. If I did a random simulation I think the probability would be just a little bit higher, because of the dependence between hands. Wizard, I have been recently trying to calculate the probability of getting a flush in Texas Hold 'Em if dealt two suited hole cards?

My answer keeps on coming out to be 5. Add this all up and you get 0. That is, five cards on the board where no pair exists, no flush is possible and no straight is possible. Combin 4,2 is the number of ways to choose two suits out of four for the suits represented twice. Combin 5,2 for the number of ways to choose two ranks out of five for the first suit of two cards. Combin 5,2 is the number of ways to choose two ranks out of five for that suit of two cards.

The number of these combinations in which no three ranks are within a span of 5 is There is no easy formula for this one. I had to cycle through every combination. They have a Bad Beat Jackpot, which is now quads or better being beat. Both players have to play both hole cards, and there must be four players dealt cards. My question is, what is the probability of any hand being a bad beat hand, assuming all players stay until the end?

My new Bad Beat Jackpot section shows the probability of this kind of bad beat in a player game to be 0. In this case, the player is stuck with bad odds on the Ante and Blind. However, his odds are favorable on the Play. That value would be even less with a smaller raise. I have a simple question about the odds of this occurring.

ESPN and others quoted it as 1 in approximately 2. It appears to me that they simply took the published odds of quads occurring, and multiplied them by the odds of a royal flush occurring.

Is this the correct method of calculation? I disagree with the 1 in 2. As you said, they seemed to calculate the probabilities independently for each player, for just the case where both players use both hole cards, and multiplied. Using this method I get a probability of 0. Maybe the one in 2. They also evidently forgot to multiply the probability by 2, for reasons I explain later. One player has two to a royal flush, the other has two aces, and the board contains the other two aces, the other two cards to the royal, and any other card.

In most poker rooms, to qualify for a bad-beat jackpot, both winning and losing player must make use of both hole cards. 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. Perhaps surprisingly, this is fewer than the number of 5-card poker hands from 5 cards because some 5-card hands are impossible with 7 cards e. Some variants of poker, called lowball , use a low hand to determine the winning hand. In most variants of lowball, the ace is counted as the lowest card and straights and flushes don't count against a low hand, so the lowest hand is the five-high hand A , also called a wheel.

The frequencies given are exact; the probabilities and odds are approximate. As can be seen from the table, just over half the time a player gets a hand that has no pairs, three- or four-of-a-kinds.

If aces are not low, simply rotate the hand descriptions so that 6-high replaces 5-high for the best hand and ace-high replaces king-high as the worst hand. In some variants of poker a player uses the best five-card low hand selected from seven cards.

The table does not extend to include five-card hands with at least one pair. Its "Total" represents Bluffing frequency can affect the probability of an opponent calling a bet or folding. From Wikipedia, the free encyclopedia. This article has multiple issues. Please help improve it or discuss these issues on the talk page. Learn how and when to remove these template messages.

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