Pot Odds

The pot odds (English for pot - odds ) are used by poker players calculations, which indicate whether the numbers of inserts is statistically profitable. They are usually stated as a percentage or ratios and are part of a poker strategy. While the pot odds only describe a relationship between use and maximizing profits, the term odds used in the context denotes a real probability value. The odds are the probabilities to improve his previous hand, which can be estimated with the outs. The outs denote the number of cards that improve your hand. By comparing the odds the pot odds, one can determine the extent to which the payment of the insert is profitable.

It should be noted that the assessment of this article, due to the empirical law of large numbers, are only valid on average for a sufficiently large number of games. Considering only a single game, so you can not make any statements due to the random factor.

Pot odds of the poker variant Texas Hold'em

Calculation of outs, odds, and odds

As outs refers to the number of capable to improve the current hand of cards to get a winning hand eligible.

If you have for example on the hand A ♥ K ♥ and the flop are 3 ♠ 5 ♥ 7 ♥, so you need another heart card to make the flush draw a complete flush. Throughout the game there are 13 cards with the color of the heart. Four of them (two on hand, two on the board ) are already available. The remaining nine heart cards are now the outs.

As odds is defined as the probability of getting one of the missing Out ​​Cards.

Since you know your hole cards and the flop, even 47 cards left after the flop from formerly 52 in which the outs are included.

The chance to improve his cards by the turn card are:

If the Turn on the table, so are still 46 cards unknown. This is true for the chance to improve his cards by the river card, is almost the same:

From the number of outs, one can determine the so-called rule of thumb, the probability in percent to get these outs:

Because chances are especially interesting with about 8 outs, the first formula is a good approximation both after the turn and after the river card. The chances for an improvement through the turn or river card be derived later. The following table gives an overview but already the rules of thumb to the particularly interesting in poker hands:

Important chances for improvement after the flop / turn

When a combination of cards like a flush draw and an open ended straight draw may be the cards that improve both draws, just simply count. In our example, the 7 ♥ and ♥ D improves both the flush and the open-ended straight draw. So you have not 17 outs, which are obtained when one adds the nine from the flush draw plus eight from the open-ended straight draw. In many outs are obtained with the rule of thumb for the turn or the river (one card ) too high a (small ) percentage.

The probability of an improvement by the turn or river card is obtained over the counter event. So you calculate the probability that both the turn and the river no outs ( which we denote here with O) can be seen:

47 cards are still unknown after the flop cards do not improve the hand. After the turn, only 46 cards are unknown, it maps not improve his hand. The chance to improve his cards on the turn or river, is:

Once you have determined the probability to win against a suspected when opponents hand like top pair top kicker, you have this yet against the amount to be used, relative to the targeted profits, set to determine whether the effort is worthwhile.

Odds spelling of the winning probabilities

It is simply a different notation for the probabilities introduced above:

Odds = not known cards without improvement: useful maps.

An open -ended straight draw ( after the turn ) has the following odds: as eight are helpful, of the 46 unknown cards. The advantage of this notation is that you can easily determine whether a going along makes sense. If the pot is in relation to the use that is to bring out greater than the odds as shown, so the hand is playable. In the first example 5 € in the pot and you would have to bring € 1 to play along profitably. So you have pot odds of 5:1, which corresponds to the odds of 5:1. Decision-making is so ( if you have the odds noticed in this way ) easier to apply in practice. Here is an overview of a few interesting hands:

Pot Odds

As pot odds is the ratio between the amount necessary to pay a bet and the current value of the pot. In contrast to the odds the pot odds are not probabilities, but only to the relationship between the successful use and the possible profit. The lower the value of the pot odds is, so the less money you have to put in to win a certain amount, the better.

Gambles an opponent after the flop in a 5 € 1 € big pot, then the current value of the pot is 6 €. You yourself should now also pay € 1 to stay in the game. The pot odds are 1:6 so here. Our commitment would be one-seventh of the resulting pots, or as a percentage expressed 14.29%.

Odds and pot odds to the Call

Comparing the odds with the pot odds, so you can make it easier to put (call) or exit ( Fold ). If the probability to improve his hand greater than the relative share of the total pot, so you should set. In the long term it will thus be on the winning side.

Small rule of thumb:

• Are the odds greater than or equal to the pot odds, so you should set.
• Are the odds smaller than the pot odds, so it is better to get out.

Example:

It has an open-ended straight draw on the turn with odds of 17% according to the rule of thumb (or 17.39 % in real terms ). The pot is € 4 large. Someone has 1 €, ie a quarter of the pot. Does it make sense to call this application, under the assumption that the opponent has one or more pair ( s), or three of a kind and we are the last player who can put / call? With a bet of € 1 also you get the chance to win € 6. The application is therefore 1 / ( 4 1 1 ) = 1 /6 = 16.67% of the resulting pot. The odds are therefore greater than the pot odds, and it makes sense to go with this application. In 100 games this situation would be 100 times 1 €, that is 100 €, deploy, and in 17.39 % of cases, a pot of 6 €, ie € 104.34 win. The expected profit is positive at € 4.34.

With the odds notation can be more easily determine whether a call is profitable. The odds refer to 4.8: 1 is a somewhat greater probability 1 / (4.8 1 ) = 17.2 % less than the pot odds of 5: 1 ( 1 / ( 5 1) = 16.67 %).

If the pot is just 3 € large ( and someone also has 1 € ) would be a call not profitable because of the use of the total pot to 1 / (3 1 1 ) = 1 /5 = 20 % increase. The pot odds are higher than the odds of 17%. In 100 games this situation, one would again 100 times 1 €, that is 100 €, deploy, and but win in 17.39 % of cases, this time only a pot of € 5 for a total of only € 86.95. So we lose a hundred games ( and 100 € total bet ), total € 13.05. The pot odds are now 4: 1 and thus indicate a greater ratio than the odds of 4.8: 1

If more betting rounds are excludable, so often come the odds after the turn and river to the application. After the flop you hold a flush draw with odds of 36 % according to the rule of thumb (or 34.97 % in real terms ). The pot is 1 €. An opponent places a bet equal to the pot. Does it make sense to call this application when it needs to go all-in? With a win, the stack would triple. With 36% probability of winning a playable situation. Again we make the odds of writing the decision easier. The odds of 1.9: 1 denote ( 34.5 %) more likely than the pot odds with 2: 1 ( 33.3%).

Odds and pot odds when setting

In the above calculations, you go for simplicity assume that you are behind an opponent and he has a winning hand. In general, you can win the following ways:

The odds only consider the probabilities in the last case, when we complete our paper. So there are additional opportunities to win, and it makes sense mathematically, to make even higher stakes. The sum to releasing ( generation) amount must

Taken into account. If there is only one opponent, it is often profitable ( just after the flop ) a bet (bet or call) to choose the the size is double or even two and a half times as the actual odds. This means a bet the size of 3 /4 or half the pot in a draw. Due to the increased use, it is hoped to increase the likelihood of a fold of the opponent. Due to the increased probability of the fold of the opponent, the probability of an immediate profit increases. In the case that one already has a better hand, increasing the expected gain.

Implied odds

In this bill not the current pot is involved, but appreciated how high the final pot will be. The difference is caused by the expected operations of the other players in the following betting rounds.

Implied Odds therefore always contain a speculative element, namely the question: By how the pot will be much greater if I komplettiere my draw in the end?

S - The maximum amount to be paid C - likely to improve the hand, in percent P - Estimated, final pot size

Moves in no- limit games, for example, are often given to justify with implied odds, since it can be at best of winning the entire stack of the opponent during the game. For this reason, puts or calls you at a draw is usually higher than the odds would suggest (eg 3/4 pot size ).

Reverse implied odds

With reverse implied odds is defined as the probability not to hold the winning hand, even though you get one of the cards you one of his outs. In these situations, the outs are devalued or reduced. In the example to the open -ended straight draw in the table. Hand: 10 ♥ ♣ flop B: 8 ♠ 9 ♥ 2 ♥ Here you can see the outs 7 ♥ D ♥ because of an impending flushes not fully credited. This danger it is important when considering whether a call is profitable to consider. For this, the outs are reduced depending on the hand -held, the flop and the number of opponents. With a flush draw, higher flushes possible, we reduced his outs accordingly. The outs ( the enemy ) can lead to a higher road, you also do not fully priced. The so-called texture of the sheet must be observed. If you have a straight draw, so you should also reduce his outs on the flop with at least two cards of one color. Climbing many opponents in the hand of one, so the probability that at least one opponent has a better hand.

Protection of a hand

It is a use at a hand that is strong, but can be beaten later in the game, such as an impending flush or a straight. One should put as much that the opponent must make a bet, to which they do not have the necessary odds. If you hold ( on the turn ) the highest pair with the highest card ( top pair top kicker ), but two cards of one color lie on the table and you take a bet the size of a quarter of the pot, so get someone to matching flush draw has a playable situation. He gets pot odds of 5: 1, a flush draw but has odds of 4.1: 1 He has to use only one-fifth of the pot, but gains in (slightly less than) one in four cases the pot. Against an opponent in case of imminent flush you should bet more than the 3.1- most part of the pot (the probability odds in writing by one decreases so ), then the call is no longer profitable playable for the opponent. If the opponent calls every time he loses money in the long run. When protecting one hand, it is therefore necessary to assess the possible pot odds your opponent.