Dec 29, 2008 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. Pot odds refers to the relationship between the size of the pot and the size of the bet.
Calculating pot odds is a basic skill that most poker players learn soon after they take up the game. Almost all introductory poker books feature a section on pot odds, but they don’t go into too much depth. The truth is that pot odds and equity calculations are at the heart of being a successful poker player and if you wanted to, you could write a book on the subject. In fact, Bill Chen did just that; his book The Mathematics of Poker doesn’t make for light reading though. In this article we’ll go a little beyond the basics of pot odds, but not far enough so that you’ll have to stop and get a PhD in math to continue half way through.
The Basics of Pot Odds
Poker is a game of betting, and all betting revolves around odds. If your opponent bets $100 into a $100 pot, then you have to put in $100 to call. This means you’re risking $100 to win $200, representing odds of 2/1. To figure out if a call is profitable, you need to convert the odds on offer to an implied chance of winning. To do this, you simply add the numerator (above the line, 2 in this case) and the denominator (below the line, 1 in this case) and put the denominator above the sum giving you 1/3, or a 33% chance. Taking another example, let’s say your opponent bets $30 into a $70 pot, meaning you must risk $30 to win $100, so your odds are 100/30. Following the same formula as last time, we end up with 30/130, an implied chance of 23%.
So how does this relate to the cards in your hand? The gravest mistake that bad poker players make is continuing with their hand when the pot odds dictate that they should fold. Again, the easiest way to illustrate this is with an example:
Say you’re playing a tournament and you’re holding 7h8h and there are 5000 chips in the pot on the flop which reads AhTs2h and your opponent goes all in for 5,000 chips. When your opponent bets the size of the pot, we found out already that this gives you odds of 2/1 and you need a 33% chance of winning for you to justify continuing with the hand. If you’re certain than your opponent holds AK in this spot then you know that a flush will beat him if you make it.
If you know how to count outs and how the rule of 2 and 4 works, you’ll know that your flush draw has about a 36% chance of hitting on or before the river. The fact that your chances of winning are greater than the pot odds on offer means that a call will show a long term profit and that you can make it in this spot. In fact you can even calculate how many chips you’ll make from the call on average by adding the average chips gained when you hit, to the chips you lose when you miss. 36% of the time you’ll hit, and win 10,000 chips for a total of 3600, and 64% of the time you’ll lose 5000 chips for a total of -3200. The overall total gives you an expected value of +400 chips on average by making the call.
Let’s imagine the stack sizes are changed and your opponent surprises you by betting all-in for 10,000 chips on the flop. How does that change things? Now you’re risking 10,000 to win 15,000 giving you odds of 15/10 meaning that you need to win [10/(10+15)] = 40% of the time to break even. In this situation if you call, you’ll win 15,000 chips 36% of the time (5400), and you’ll lose 10,000 chips 64% of the time (-6400), so your expected value is now -1000 chips with this call.
In poker, you win when your opponent makes mathematical mistakes. If you bet a tiny amount relative to the size of the pot, you give your opponent very good pot odds and they can very often make a mathematically correct call. If you bet a bigger amount, they’ll generally not be getting the right price to call, and so if they do they’re making a mistake, which means a profit for you in the long run.
Implied Odds
In the examples we’ve discussed so far, the bets we’ve had to call have been all-in bets, and our pot odds calculations have been straightforward. Of course in deeper stacked cash games or early in tournaments, we’ll rarely be facing an all-in bet on the flop. Imagine you’re holding the same 7h 8h on a flop of AhTs2h in a $1/$2 cash game with stacks of $200 and $6 in the pot on the flop. Say your opponent bets $10, giving you odds of 16/10. If his bet was all-in, you’d need a 10/26 = 38% chance of winning the hand to call this bet. Your flush draw doesn’t quite make it, and so if his bet was all-in you should fold. However, with more money to into the pot, you can factor in money you could still possibly win before deciding whether to call or to fold. Let’s say you know this opponent will never fold AK and you’ll stack him if you hit your flush. Now when he bets $10, you’re really being offered his entire stack should you hit, so you need to call the $10 to prospectively win $200 plus the $6 in the pot meaning you’re getting odds of greater than 20/1. In this spot it’s clear that you should continue with your flush draw.
Let’s imagine that the turn comes down the 4d and your opponent bets $20 into the $26 pot, can you still continue. At this stage when implied odds are factored in, you’re being offered the $26 that was initially in the pot, plus his remaining $190 and you need to call $20 to see the river, representing odds of 216/20 or a little better than 10/1, meaning you need to win 9% of the time or more to show a profit.
With just one card to come, you have about an 18% chance of hitting your flush and so you can profitably call again.
Of course this is an extreme example, you can never be 100% sure that you’ll stack your opponent or that you’ll have the winning hand by the river. Even if you make your flush, your opponent could easily fold when you show a lot of strength or show down a higher flush or a full house, which brings us to the subject of reverse implied odds.
Reverese Implied Odds
Our examples above took into account the potential for winning money on later streets if we make our hand. However there are a number of situations in poker where we stand to lose out on money that goes into the pot on future streets. These are known as reverse implied odds situations. An example of reverse implied odds would be calling a re-raise from a tight player with a hand like KQ. If the player has a tight re-raising range then we’ll be put in a lot of difficult spots if we make a hand which we think could be good. For example if he has AK, then we’re in a reverse implied odds spot, as we’re likely to call him down if the flop comes King high, but we’re drawing very thin. Hands where you’re likely to be dominated if you make a pair represent the most common type of reverse implied odds situations.
The most costly scenarios are where you’re drawing to a strong hand but your opponent has a stronger draw, such as a better flush draw or the higher end of a straight. Reverse implied odds situations are particularly difficult to deal with when you’re out of position and will find it difficult to control the size of the pot.
Tue, May 28, 2:37am by Charlotte Lee
Last Updated Tue, Oct 8, 12:21am
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Calculating the pot odds in Texas holdem helps a gambler know when to fold or raise. The pot odds are a ratio between the current size of a poker pot and the cost of a call. Calculating this ratio allows gamblers to make informed decisions on the probability of winning and whether betting is worth the cost.
Once a player knows the pot odds, they can calculate the expected value of betting. This is helpful in several situations, none more so than when a player holds a drawing hand. This is a hand in which you are behind at the moment, but your have the promise of drawing a winning hand later.
Example of Pot Odds
To give an example, let’s assume the raise in front of you is $10. If the pot is $40, then the pot odds would be calculated like so: 40:10. Players often shorten this to 4:1. Converted to a ratio, you would have 1/5 or 20%. You would be putting in twenty percent of the pot.
Expected Value
Earlier we mentioned “expected value“. Expected value is a comparison between the pot odds and the chances you’ll draw the card you need. To calculate this ratio, you’ll need to figure out how many cards remain in the deck which might improve your hand.
Drawing Hands and Outs
“Outs” is the term used for the number of cards still in the deck which give you the winning hand. Besides your two hole cards and the community cards, you might know what 7 of the 52 cards are. If you have a straight draw of A-K-Q-J, then you need a 10 to make your straight. If no 10’s are in your hand or among the community cards, you have 4 outs. If one 10 was showing, you have 3 outs. This isn’t always the case with straight draws, though. For instance, if you hold a 6-7-8-9, you could win if you collected either a 10 or a 5. If neither card is showing, you have 8 outs.
A flush draw gives a player 9 outs (assuming you have 4 to a straight), if none of your suit have been drawn. It’s more likely one or two of your outs are gone, though. Let’s say you have the 3-6-9-Q of diamonds. You have 9 outs, but if you see the jack and 5 of diamonds among the community cards, you only have 7 outs. A straight flush is best, since you have 9 potential outs for suit and either 4 to 8 outs for card rank.
Calculating Outs
Once a player knows how many outs there are, they can calculate a ratio. If you have 4 outs after the flop, then you have a 4/46 chance of collecting an out (or just under a 9% chance) of hitting the card you need on any given dead. Keep in mind you’ll have two more cards drawn, instead of just one. The odds are 8.69% you’ll hit the card you need.
Calculating the outs you have produces a ratio of the chances you improve your hand. Since you can’t know what your opponent has in their hand, the math isn’t as cut-and-dried as it is on television, where the broadcasters have up-to-the-second information on hand composition and strength. Professional players often have an idea what their opponent is holding, depending on their tendencies and how they’ve played the hand.
Rule of 4 and 2
If you aren’t a math whiz and you need an easy way of calculating the outs, use Phil Gordon’s “rule of 4 and 2” (found in Gordon’s The Little Green Book). This rules states that you multiply your outs by one of these numbers to calculate the percentage odds of getting the card you need. If you’re on the flop waiting for the turn, multiply your outs by 2. If you’re on the turn waiting for the river, also multiply the outs by 2. If you’re on the flop waiting for the river–that is, your opponent is all-in–multiply the outs by 4.
Texas Holdem How To Calculate Pot Odds Chart
Two things need to be emphasized. This is meant to be a shorthand, so it’s not entirely accurate. In the example above, the 8.69% becomes 8%. Those dividing 46 by 4 might round up to 9%, if they’re an optimist, so understand you lose a little something in perspective by using a quick method. Also, a gambler is going to be divining their outs by 2 most of the time, because they won’t be all-in on the flop that often. Some players mistakenly use the 4 every time they’re on the flop, which causes a whole lot of busts. If you don’t like fractions and long division, Phil Gordon’s method should help you get pretty close at a fast rate.
Implied Odds
Simply figuring out the current set of probabilities is not always enough. Sometimes, you want to calculate the probable future bets, too. Since gamblers calculating pot odds are dealing with probability and possibilities anyway, it’s sometimes a more accurate measure to project what’s likely to be the odds next round. Let’s use an example.
If you have a drawing hand, then you are going to fold if you miss the card you want. Therefore, you know you won’t be betting any higher in that scenario. At the same time, if you hit the card you want, your opponent or opponents are likely to bet and you’re likely to make money off them. You need to calculate the odds not just of the current ratio, but implied future odds.
Why Make Calculations?
Any time you fold, raise, or make a call in Texas holdem, you’re weighing the odds (in some informal fashion) of what you should do. Pot odds let you do the same thing in a formal, mathematical way. If guesswork is a pitfall in gambling, then odds calculations takes some of the guesswork out.
Risk versus Reward
Texas Holdem Odds And Probabilities
The more information you have and can process, the better for you. Most of the time, you’ll have a vague idea of when it’s good to raise a bet and when it’s a bad idea. That’s not always the case, though.
Calculating Pot Odds In Texas Holdem
When you don’t use precise math, you can make all sorts of mistakes and simply have fallacies about the game you just played. By doing the math on your pot odds, you eliminate some of the supposition. All of this can best be summed up as the risk/reward factor. Players want to know how much they need to risk and how much they’ll rake in if they win, so pot odds help you play a more mathematical game of Texas hold’em.
Texas Holdem Poker Odds
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