In poker, pot odds are the ratio of the current size of the pot to the cost of a contemplated call.[1] Pot odds are often compared to the probability of winning a hand with a future card in order to estimate the call's expected value.
- 3Implied pot odds
- 4Reverse implied pot odds
- 5Manipulating pot odds
Converting odds ratios to and from percentages[edit]
Odds are most commonly expressed as ratios, but converting them to percentages often make them easier to work with. The ratio has two numbers: the size of the pot and the cost of the call. To convert this ratio to the equivalent percentage, these two numbers are added together and the cost of the call is divided by this sum. For example, the pot is $30, and the cost of the call is $10. The pot odds in this situation are 30:10, or 3:1 when simplified. To get the percentage, 30 and 10 are added to get a sum of 40 and then 10 is divided by 40, giving 0.25, or 25%.
Texas Hold'em Pot Odds
To convert any percentage or fraction to the equivalent odds, the numerator is subtracted from the denominator and then this difference is divided by the numerator. For example, to convert 25%, or 1/4, 1 is subtracted from 4 to get 3 (or 25 from 100 to get 75) and then 3 is divided by 1 (or 75 by 25), giving 3, or 3:1.
Dec 29, 2008 Understanding and calculating the pot odds, though, will only get you halfway to where you need to be. Once you have the odds (and the implied odds), you need to calculate your equity in the pot and then compare the two to see what the correct play is in each situation.
Using pot odds to determine expected value[edit]
When a player holds a drawing hand (a hand that is behind now but is likely to win if a certain card is drawn) pot odds are used to determine the expected value of that hand when the player is faced with a bet.
The expected value of a call is determined by comparing the pot odds to the odds of drawing a card that wins the pot. When the odds of drawing a card that wins the pot are numerically higher than the pot odds, the call has a positive expectation; on average, a portion of the pot that is greater than the cost of the call is won. Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and the expectation is to win less money on average than it costs to call the bet.
Implied pot odds[edit]
Implied pot odds, or simply implied odds, are calculated the same way as pot odds, but take into consideration estimated future betting. Implied odds are calculated in situations where the player expects to fold in the following round if the draw is missed, thereby losing no additional bets, but expects to gain additional bets when the draw is made. Since the player expects to always gain additional bets in later rounds when the draw is made, and never lose any additional bets when the draw is missed, the extra bets that the player expects to gain, excluding his own, can fairly be added to the current size of the pot. This adjusted pot value is known as the implied pot.
Example (Texas hold'em)[edit]
On the turn, Alice's hand is certainly behind, and she faces a $1 call to win a $10 pot against a single opponent. There are four cards remaining in the deck that make her hand a certain winner. Her probability of drawing one of those cards is therefore 4/47 (8.5%), which when converted to odds is 10.75:1. Since the pot lays 10:1 (9.1%), Alice will on average lose money by calling if there is no future betting. However, Alice expects her opponent to call her additional $1 bet on the final betting round if she makes her draw. Alice will fold if she misses her draw and thus lose no additional bets. Alice's implied pot is therefore $11 ($10 plus the expected $1 call to her additional $1 bet), so her implied pot odds are 11:1 (8.3%). Her call now has a positive expectation.
Reverse implied pot odds[edit]
Reverse implied pot odds, or simply reverse implied odds, apply to situations where a player will win the minimum if holding the best hand but lose the maximum if not having the best hand. Aggressive actions (bets and raises) are subject to reverse implied odds, because they win the minimum if they win immediately (the current pot), but may lose the maximum if called (the current pot plus the called bet or raise). These situations may also occur when a player has a made hand with little chance of improving what is believed to be currently the best hand, but an opponent continues to bet. An opponent with a weak hand will be likely to give up after the player calls and not call any bets the player makes. An opponent with a superior hand, will, on the other hand, continue, (extracting additional bets or calls from the player).
Pot Odds Poker
Limit Texas hold'em example[edit]
With one card to come, Alice holds a made hand with little chance of improving and faces a $10 call to win a $30 pot. If her opponent has a weak hand or is bluffing, Alice expects no further bets or calls from her opponent. If her opponent has a superior hand, Alice expects the opponent to bet another $10 on the end. Therefore, if Alice wins, she only expects to win the $30 currently in the pot, but if she loses, she expects to lose $20 ($10 call on the turn plus $10 call on the river). Because she is risking $20 to win $30, Alice's reverse implied pot odds are 1.5-to-1 ($30/$20) or 40 percent (1/(1.5+1)). For calling to have a positive expectation, Alice must believe the probability of her opponent having a weak hand is over 40 percent.
Manipulating pot odds[edit]
Often a player will bet to manipulate the pot odds offered to other players. A common example of manipulating pot odds is make a bet to protect a made hand that discourages opponents from chasing a drawing hand.
No-limit Texas hold 'em example[edit]
With one card to come, Bob has a made hand, but the board shows a potential flush draw. Bob wants to bet enough to make it wrong for an opponent with a flush draw to call, but Bob does not want to bet more than he has to in the event the opponent already has him beat.
Assuming a $20 pot and one opponent, if Bob bets $10 (half the pot), when his opponent acts, the pot will be $30 and it will cost $10 to call. The opponent's pot odds will be 3-to-1, or 25 percent. If the opponent is on a flush draw (9/46, approximately 19.565 percent or 4.11-to-1 odds against with one card to come), the pot is not offering adequate pot odds for the opponent to call unless the opponent thinks they can induce additional final round betting from Bob if the opponent completes their flush draw (see implied pot odds).
A bet of $6.43, resulting in pot odds of 4.11-to-1, would make his opponent mathematically indifferent to calling if implied odds are disregarded.
Bluffing frequency[edit]
According to David Sklansky, game theory shows that a player should bluff a percentage of the time equal to his opponent's pot odds to call the bluff. For example, in the final betting round, if the pot is $30 and a player is contemplating a $30 bet (which will give his opponent 2-to-1 pot odds for the call), the player should bluff half as often as he would bet for value (one out of three times).
However, this conclusion does not take into account some of the context of specific situations. A player's bluffing frequency often accounts for many different factors, particularly the tightness or looseness of their opponents. Bluffing against a tight player is more likely to induce a fold than bluffing against a loose player, who is more likely to call the bluff. Sklansky's strategy is an equilibrium strategy in the sense that it is optimal against someone playing an optimal strategy against it.
See also[edit]
Notes[edit]
References[edit]
- David Sklansky (1987). The Theory of Poker. Two Plus Two Publications. ISBN1-880685-00-0.
- David Sklansky (2001). Tournament Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-28-0.
- David Sklansky and Mason Malmuth (1988). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1.
- Dan Harrington and Bill Robertie (2004). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume I: Strategic Play. Two Plus Two Publications. ISBN1-880685-33-7.
- Dan Harrington and Bill Robertie (2005). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume II: The Endgame. Two Plus Two Publications. ISBN1-880685-35-3.
- David Sklansky and Ed Miller (2006). No Limit Hold 'Em Theory and Practice. Two Plus Two Publications. ISBN1-880685-37-X.
Pot odds, equity and expected value are important interrelated concepts in poker. As a beginner it is important that you understand the basics if you want to get ahead of your opponents.
The math side of poker is often ignored by a lot of new players but by simply spending a bit of time learning these simple concepts you will be able to improve your game drastically.
So we will first go through each of them individually and then a full example to tie it all together in the next few articles.
Table Of Contents
Pot Odds: The Definition
The odds which are being offered to you when your opponent bets are called pots odds. Essentially it is how much you will win vs how much you have to risk – your risk to reward ratio.
This is particularly useful when in a situation where you’re facing a bet with a drawing hand (such as a flush draw). Pot odds will tell you whether is it correct for you to call or fold based on what size our opponent bet and how many cards that will improve our hand.
Basic Poker Odds
We can also use pot odds to determine whether or not we can call a river bet based on how often we expect our opponent to be bluffing.
Pot Odds: Using Ratios
To take an example of when we are facing a bet on the river when we have A9 of diamonds:
On the river our opponent bets $26 into a $41.5. If we called would be risking $26 and our reward is $41.5 already in the pot plus our opponents bet of $26.
This means that we are getting odds of 67.5: 26 (67.5 = 41.5+26). This is approximately 2.6:1.
Pot Odds: The Percentage Method
We can also convert that into a percentage (percentages are typically more intuitive) the result is 28%.
So if we expect to win 28% of the time or more we can call profitably.
How did we get that number?
Take the amount we have to call ($26) and divide it by the amount we have to call plus how much is in the pot:
Pot odds percentage = 26/(26+67.5) = 27.8%
Here is a summary of the numbers of outs and the pot odds associated for number of outs:
Why Are Pot Odds Useful?
It first lets us determine our risk to reward ratio. We can then use this along with the strength of our and our opponents potential hands in order to make better decisions.
Poker Pot Odds Table
If we have a very weak hand we should not be willing to call very large bets, only smaller bet sizes; in other words we must have very good pot odds in order to call.
This makes sense – if someone was to bet $1 into a $100 pot on the river we will continue with almost all of our range.
Pot Odds Poker Probability
The greater the pot odds (the smaller our opponent bets) the more likely we should be to continue with our hand. Conversely, the smaller the pot odds (the larger our opponent bets) the less likely we should be to continue with our hands. The larger our opponent bets the more the requirement for an extremely strong hand.
Implied Pot Odds
Implied odds is simply the additional chips we expect to win when we hit our hand.
For example if we were to hit a flush on the turn or river, the hand won’t just end – we still have an opportunity to win more money from our opponent.
This will reduce the pot odds we need to call profitably. The exception to this is when our opponent has pushed all in – we call we cannot win any more chips.
The reason we call preflop with small unpaired hands is not because we expect to have the best hand all that often; but because we expect to win a large pot when we hit a big hand such as three of a kind.
The reason we call is because with a hand like three of a kind, we have large implied odds and if we hit our hand we expect to win a big pot.
Here is an explainer video of implied odds from GreenBeanVideos:
A Real World Example of Implied odds:
The reason you go to College or University and get a degree is not because of the return you would expect immediately after graduation. It is because of the additional value a degree would bring you in the years after gradation through income, job opportunities etc. The same applied to poker.
Unfortunately implied odds cannot be directly calculated like pot odds – we have to guesstimate the amount our opponent will be willing to pay us off after we make our hand.
If we think our opponent has a very strong hand, and we stand to make a better one, we will have large implied odds.
If our opponent has a weak hand, we will have little implied odds.
Additionally, if we believe our opponent is a very bad player we will usually have large implied odds as he will be more likely to make mistakes and pay us with hands that he shouldn’t have.
Finally, if he is a good player we will have significantly less implied odds.
Here is a quick recap on everything we covered on pot odds:
Pot Odds Calculator
You do not need a fancy piece of software to work out your pot odds. As we have seen, it is simply the ratio of the bet you have to call to the size of the pot (including your opponents bet). You can also use a calculator to calculate the the percentage odds (or roughly do it in your head, you don’t need to be extremely accurate)
However, on of the best pieces of software you can use in conjunction with calculating pot odds from cardschat.com.
This piece of software can be used to work out your pot equity which we have discussed in detail in other lessons.
Conclusions
You should now be able to work out pot odds and when coupled with our other lessons, you should have a basic grasp on the math of poker.
Follow up this lesson first with Pot Equity and Expected Value (EV)