When we talk about poker there is something that we must always take into account, the chances of winning a hand. The poker equity is one of the most important concepts that we can find in this popular card game because it allows us to know the odds we have of winning a hand against another player or the rest of the players at a given time. Equity in poker is the share of the pot that is yours based on the odds that you will win the pot at that point in play. Equity changes after each street – pre-flop, flop, turn and river. Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily. What I really want to know is how is the procedure that pokerstove like software use to calculate the equity of one hand against another. Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build.

What is Equity?

Equity is best defined as the the share of the pot that you can expect to win in the long run, based on the strength of your hand versus that of your opponent, with cards still to come. If you get all in pre-flop with AA and your opponent holds KK and there’s $400 in the middle, a tool like Pokerstove will tell you that you’re an 82% shot to win the hand when the flop, turn and river are dealt. What that means is that you can expect to take $328 of the $400 in the long run, and so your equity in the pot is $328.

However, the community cards can quickly change your equity in a hand. If a K comes down on the flop, your equity quickly drops to less than 10%. When you get to the river, your equity is always 100% when you’re ahead, 0% when you’re behind and 50% if you have the same holding as your opponent.

Why Calculate Equity?

Calculating your equity in a hand is a key skill in poker. Its imperative that you know your chance of winning the hand at showdown as the action progresses and to be able to compare this to both the pot odds and implied odds on offer, so you can make good, positive expected value decisions on every street in the hand. Bad or inexperienced players will often make decisions based on ‘feel’, or what hand they think their opponent might have. They give little consideration to the fact that their opponents could be making a certain move with a wide range of hands, and they also ignore the pot odds being offered to them. Playing poker in this manner is a sure way to go broke quickly and equity calculations are something you must do if you want to be a winning player.

How to Calculate Equity

A simple, and very commonly encountered example of how to calculate equity would be when you have a flush draw on the flop and you think your opponent has top pair or an over-pair. Consider the following hand:

The game is $1/$2 6-max no limit holdem. Your opponent is a very straightforward player.
Stacks:
SB: $170
BB: $209
UTG: $425
HERO (MP): $200
CO: $200
BTN: $145

Preflop: Hero is MP with Js Ts
UTG raises to $6, Hero calls $6, 4 folds.

Flop: ($15) Ks 8s 3c (2 players)
UTG bets $15, Hero raises to $50, UTG goes all in ($144 to hero)
Pot size: $259

Imagine we know for certain that our opponent holds AK in this situation. We have to calculate our equity before we decide if the pot is laying us the correct price to make the call. Using an equity calculator such as PokerStove, we can deduce that versus AK we have 38% equity.

A quick way to make a rough calculation of your equity is to count the number of cards still in the deck which will give us the winning hand, in this case 9, and multiply it by 4 (or 2 if we are on the turn). Armed with this information about our equity we now decide if we are getting the right price to call. In this case we have to risk our remaining $144 to win $259 so we divide the bet we are facing by the total pot size including our bet [144/(144+259)] to deduce that we need just under 36% equity to make the call breakeven in the long run. As you can see, we have more equity than this so we should call.

Of course, in reality you’re never going to know exactly what your opponent’s holding is. The best you can hope for is to put him on a narrow range of hands and calculate your equity against that range. In the hand above for example, your opponent will be going all-in on the flop when you raise with more hands than just AK. His range for doing this also includes all of the possible sets: KK, 88 and 33 as well as the nut flush draw combinations in his under the gun range and AA.

It’s reasonable to assume that he raises suited aces down to about ATs under the gun if he is a straightforward player. We have the J and T however, so his only likely flush draw holding other than AK is AQ. Our equity versus this range of nut flush draws ,sets and AA is 33.5%. Earlier we said we need 36% equity to call and against this range we do not have the required equity and so should fold.

Clearly it’s difficult to make an exact equity calculation versus an opponent’s range at the table, but if you get into the habit of running such calculations when reviewing your play after a session, you’ll find that you can intuitively make a good estimate.

In our poker math and probability lesson it was stated that when it comes to poker; “the math is essential“. Although you don’t need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it’s all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.

In this lesson, we’re going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We’ll start with some basic math before showing you how to correctly calculate your odds. Don’t worry about any complex math – we will show you how to crunch the numbers, but we’ll also provide some simple and easy shortcuts that you can commit to memory.

Basic Math – Odds and Percentages

Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn’t mean “a quarter”. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5).

Here are some examples:

• 2-to-1 against = 1 out of every 3 times = 33.3%
• 3-to-1 against = 1 out of every 4 times = 25%
• 4-to-1 against = 1 out of every 5 times= 20%
• 5-to-1 against = 1 out of every 6 times = 16.6%

Converting odds into a percentage:

• 3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
• 4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%

Converting a percentage into odds:

• 25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
• 20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.

Another method of converting percentage into odds is to divide the percentage chance when you don’t hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:

• 25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
• 30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).

Some people are more comfortable working with percentages rather than odds, and vice versa. What’s most important is that you fully understand how odds work, because now we’re going to apply this knowledge of odds to the game of poker.

The right kind of practice between sessions can make a HUGE difference at the tables. That’s why this workbook has a 5-star rating on Amazon and keeps getting reviews like this one: “I don’t consider myself great at math in general, but this work is helping things sink in and I already see things more clearly while playing.”

Instant Download · Answer Key Included · Lifetime Updates

Counting Your Outs

Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.

Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there’s room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .

The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:

How To Calculate Pot Equity In Poker

Table #1 – Outs to Improve Your Hand

The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:

Table #2 – Examples of Drawing Hands (click to enlarge)

Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:

Don’t Count Outs Twice

There are 15 outs when you have both a straight and flush draw. You might be wondering why it’s 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.

Anti-Outs and Blockers

There are outs that will improve your hand but won’t help you win. For example, suppose you hold on a flop of . You’re drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.

It’s generally better to err on the side of caution when assessing your possible outs. Don’t fall into the trap of assuming that all your outs will help you. Some won’t, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.

Calculating Your Poker Odds

Once you know how many outs you’ve got (remember to only include “good outs”), it’s time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we’ll explain three methods. This first one does not require math, just use the handy chart below:

Table #3 – Poker Odds Chart

As you can see in the above table, if you’re holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you’re 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.

We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You’ll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.

How To Calculate Equity Percentage

Doing the Math – Crunching Numbers

There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.

Let’s again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let’s take a look…

With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:

(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.

This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:

9 x 38 ≈ 342.

Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:

36 + 342 ≈ 380.

The total number of turn and river combos is 1081 which is calculated as follows:

(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.

Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:

380 / 1081 = 35.18518%

This number can be rounded to .352 or just .35 in decimal terms. You divide .35 into its reciprocal of .65:

0.65 / 0.35 = 1.8571428

And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.

The Rule of Four and Two

A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.

Imagine a player goes all-in and by calling you’re guaranteed to see both the turn and river cards. If you have nine outs then it’s just a case of 9 x 4 = 36. It doesn’t match the exact odds given in the chart, but it’s accurate enough.

What about with just one card to come? Well, it’s even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that’s 16% (8 x 2) – which is almost 17%. Again, it’s close enough and easy to do – you really don’t have to be a math genius.

Do you know how to maximize value when your draw DOES hit? Like…when to slowplay, when to continue betting, and if you do bet or raise – what the perfect size is? These are all things you’ll learn in CORE, and you can dive into this monster course today for just $5 down…

Conclusion

In this lesson we’ve covered a lot of ground. We haven’t mentioned the topic of pot odds yet – which is when we calculate whether or not it’s correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we’ll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.

As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we’ll get to in the next lesson.

By Tom 'TIME' Leonard

Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.