# Texas hold 'em

Thanks again and keep up enlightening the masses! There is no limit to how much someone can bet. Counterfeited — The unfortunate role reversal which can occur when the board cards nullify certain cards in your hand. News specific to the online poker world including big scores, new promotions and new legislation. Should I have accepted the bet? This is where true strategy and comparing pot odds to the actual odds of hitting a better hand come into play.

## Holdem Basics

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. 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 Rags have almost no equity ; therefore they are a losing proposition unless you have reasons for wanting to play them that trump winning the current pot.

This is one of the most important and difficult strategies to master in pre-flop play and it's where the Gap Concept comes into play. The gap concept is simple: Poker can get a little counterintuitive when there are pre-flop raises.

Unless you have reason to believe otherwise, when someone raises you have to assume they have a premium hand.

This means that calling with marginal hands containing high cards can be a very big mistake. For a beginner, it can be less disastrous to call a raise with a rag hand than to call with a high marginal hand. If we assume the original raiser has a premium hand then you would make a call against them strictly to try and "crack" the hand they have. So three of the five most probable hands the raiser holds have you absolutely dominated. If you're against KK you're in better shape than against any of the last three hands, but you're still a major dog.

The only hand you have a chance with is JJ. Now, on paper suited against all five of the premium hands is a serious dog. The difference is it's cheap. It's an easy fold; you lose nothing. On paper you win more hands with A-Q than with suited. The difference is that you win smaller pots with A-Q and lose your entire stack when it goes bad. With suited you win very large pots or lose almost nothing. At a full-table cash game with a tight table image, in the long run you can make more money with the suited hands than with A-Q.

It's possible but very difficult to fold KK pre-flop. When KK runs into AA, one person usually ends up very upset. The calls or folds you make in these situations are what separate a good poker player from a great one. It's different every time; every hand is up for debate. But, as a general rule:. With KK behind a raise, most of the time you will come over the top. The rationale for doing so is the same as that for making the original raise: You don't want any players behind you to call.

If you're the last player to act pre-flop, and you're already isolated, it's not a bad idea to smooth-call and hide the strength of your hand. The disadvantage to this play is that you get no more information from the opponent. If he holds AA, you are in a world of pain. If he has QQ, you're one happy sunnuvagun. By re-raising the original raiser pre-flop you will learn a lot about his hand.

Against weaker players, AA will push all-in or immediately call. Anything else will usually fold or have to take a long think before they make any play. Every hand, table and player is unique.

These are guidelines, not rules. The gap concept applies even more strongly to overcalling then to calling an original raiser. Once there is a raise and a re-raise, as a tight-aggressive player it becomes very difficult to do anything but fold. Calling a raise and a re-raise pre-flop with a hand such as suited is also usually a mistake.

A raise and a re-raise usually mean you'd be cold-calling six big bets. It also means that the betting has been reopened. The original raiser is going to call, fold or push all-in. Unless it was a strict bluff the original raiser will almost never fold in this situation. If he does have AA he will most likely move all-in. Players can make that move with all five of the premium hands as well as with some marginal ones. This means you're running a very large risk that you're throwing away the call.

If the original raiser moves all-in you're forced to muck your hand, losing the chips invested in the original call. Another powerful move you can make pre-flop is the limp re-raise.

Having a premium hand in early position it can pay well to limp with the intention of coming over the top of anyone who makes a raise. This works best at a very active and aggressive table. If there have been no raises on the table for the last hour, such a move is simply reckless. Limp re-raising does one of three things:. For this reason alone it's almost always a mistake to play into or against a limp re-raise by a weak-to-average player.

The disadvantage to this maneuver comes when no one raises. In this scenario you'll find yourself in a multi-way pot, out of position. If you're playing AA and don't hit a set on the flop then you have to remember that all you have is one pair. Anyone willing to call any large bets at this point has a decent chance at having a random two pair or made hand.

If you play the hand hard and fast you will lose a big pot against anything other than an overplayed top pair. When you fold a hand, pre-flop or post-flop, it doesn't mean you're finished playing the hand.

Every hand that plays out at the table is laden with valuable information. It's usually easier to pick up information on how a person is playing when you're not in the hand. You don't have to worry about how to play your hand; this in turn allows you to concentrate on how they're playing theirs.

The more information you can gather on someone the further in advance of having to face a difficult situation against them, the more likely you are to make the right decision.

The story is very different if you're playing in a tournament as opposed to in a cash game. All of the previous advice becomes completely obsolete in certain tourney situations. Cash games stay rather constant; in a tournament, the pressure of mounting blinds adds different elements to the game that are not present in a cash game.