How to Calculate Pot Odds and Equity: Pot Odds
Having the ability to quickly and accurately calculate odds at the table can be crucial to your long-term success as a poker player.
True or false?: All of the decisions you make at a poker table can be made by feel, without any serious consideration for the actual numbers you face.
The answer is, absolutely false. There are a select few decisions at the table which require no consideration of odds, such as calling an all-in bet while holding the nuts on the river. Outside of plays made purely on a read of your opponent, all decisions in poker are made through an evaluation of the odds.
Even players playing by feel, who never actually make any calculations at the table, are still playing the odds. They just don't know the numbers associated with what looks and feels like a good decision to them.
In order to use the numbers to evaluate the quality of your decisions, you need to calculate the pot odds and your equity, and then compare the two. If the odds are greater than your equity, you're making money; if the odds are less, you're losing money.
It doesn't matter whether you start with the pot odds or your hand equity. Each of these numbers are independent of each other, but are completely useless until you have them both to evaluate.
In this article we'll look at pot odds, and in part two, hand equity.
Pot Odds
Count the pot: Actually counting the pot is incredibly difficult to do once it's grown large, especially when there are chips of multiple denominations piled together. The best idea is to keep a running count of the total pot as the hand progresses.
$2/$5 game: UTG raises to $15; folded to the cut-off, who calls. The button calls as does the small blind; the big blind folds.
What's the pot? Trying to add it up now is a little bit of a task, whereas if you keep a running total in your head as you go, it will be much simpler.
When you're keeping track of the pre-flop action, it helps to ignore the blinds until after they have acted; otherwise you have to subtract from your total what they already had in from the amount they called, adding the difference to your total. That's just too much work.
If you start at UTG, it's pretty simple: UTG raises to $15, cut-off calls ($30), button calls ($45), small blind calls ($60), big blind folds ($65).
Create a ratio: In the same scenario as above, the pre-flop raiser bets out $50. What are the pot odds to the player in the cut-off?
First, you have to add the bet to the total pot, making the total pot $115. The player must call $50 for a pot of $115. This creates your first ratio: $115-$50. Now to make things easy to work with, we want to make the right side of the ratio 1. Since I'm sure you've all forgotten your grade nine math:
115-50: If you want to turn the right side into a 1, you need to divide it by itself (50/50=1). What you do to one side of a ratio, you must do to the other, so 115/50 = 2.3. This makes your new ratio 2.3-1.
The cut-off's pot odds are 2.3-1.
Here's a trick to doing that last calculation in your head. At the table you don't need to be exact; getting yourself close will do just fine. To divide two numbers, take out the largest possible chunk that the divisor goes into without a fraction.
We know that 100/50 = 2, and 150/50 = 3. Since 150 is larger than the number, the largest chunk we can take out is 100. We now know out first number is a 2. That just leaves us with 15 (115 - 100).
Approximately how many times does 15 go into 50? 15*3 = 45. That's as close as we can get, since 45 is closer to 50 than 60. That gives us our second number (the remainder) of 3. Put the two together and we have: 2.3. It just so happens that in this example, the shortcut method brings the actual correct example.
Let's say the cut-off calls. What are the pot odds to the button now? Try to do that up in your head right now. If you're having trouble, here's a step-by-step numbers walk-through:
Pot = $115 + $50
Pot = $165
Odds = $165/$50
50 * 3 = 150 (first number is 3)
165 - 150 = 15
50/15 = close to 3
Odds = 3.3:1
Hopefully you caught on to the most important shortcut. Once we calculated the odds for the cut-off, and he calls, the odds to the button will be exactly better by one: 2.3 + 1= 3.3. There is no need to recalculate if a player only calls; just add one. Once another player raises, only then must you recalculate.
If what you just read has really confused you, you can check out this more basic article on the same topic. Between this one and that one, you should have odds figured out in no time.
In part two, you will learn how to evaluate hand equity, and finally how to compare the two numbers to get your result.
More articles about odds:
- Calculating Pot Odds: A Beginner's Guide
- The Turn: Pot Odds for Fourth Street
- Reverse Implied Odds Explained
Comments
12adam
2011-08-16Sean-
First off, great articles, your website is very helpful! But, I think the way you are calculating the pot odds in this one is a little off. You get the close to the right result since 50/15 ~= 3 and 15/50 ~= 0.3, which end up looking similar, but your method only works for that specific case. Morten mentioned this in his 1st comment but you didn't really address it.
Here's what I mean-
> From the article:
Pot = $165
Odds = $165/$50
50 * 3 = 150 (first number is 3)
165 - 150 = 15
50/15 = close to 3 (3.3) <<< this ratio needs to be flipped - it should be 15/50
Odds = 3.3 : 1
> calculating remainder the correct way:
Pot = $165
Odds = $165/$50
50 * 3 = 150 (first number is 3)
165 - 150 = 15
15/50 = 0.3
Odds = 3.3 : 1
> Comparison: your method gives 3.3:1, other method gives 3.3:1
> Ok, it seems to work for this case. However….
> Changing the numbers makes the problem a bit clearer:
Pot = $175 <<< change the pot size to 175
Odds = $175/$50
50 * 3 = 150 (first number is 3)
175 - 150 = 25 <<< now remainder is 25
> now, with your method:
50/25 = 2
Odds = 3.2 : 1
> calculating remainder the correct way:
25/50 = 0.5 <<< flipping the ratio
Odds = 3.5 : 1
> Comparison: your method gives 3.2:1, other method gives 3.5:1. hmmmm……
The size of the pot has increased, but the bet size has stayed the same. Therefore, you should be getting better pot odds than in the first case. However, your method tells you that your odds decrease, from 3.3: 1 in the first example down to 3.2: 1 in the second. Do you see the problem? I know it's been a while since this article was published, but you really might want to update it, pot odds are confusing enough to learn as it is. :)
Mar0cR3am
2010-05-14Hey guys, if you play online poker, an easy way to calculate the pot odds and your equity is using a small application. I wrote a small program in C, nothing complicated. Just compile it and run it ;)
The source code follows...
#include <stdio.h>
int main()
{
int outs, round, equity, multiplier;
float potsize=0.0;
float bet=0.0;
float potratio=0.0;
float equityratio=0.0;
printf("This small application calculates your pot odds, then calculates your equity and makes the comparison between the two ratios, allowing you to decide more easily if you should make the call.\n");
printf("This app keeps on repeating itself. To exit, use <CTR>-C\n");
while(1)
{
printf("\n\nWhat is the number of your outs?\n");
scanf("%d", &outs);
printf("\nAre you on the Flop or on the Turn?\n");
printf("If on the Flop press 1, else if on the Turn press 2.\n");
scanf("%d", &round);
printf("\nWhat is the pot size in $$?\n");
scanf("%f", &potsize);
printf("\nWhat is the required bet to keep on with this hand in $$?\n");
scanf("%f", &bet);
potratio = potsize/bet;
if (round==1)
multiplier = 4;
else
multiplier = 2;
if (outs>8 && round==1)
equity = outs*multiplier - outs + 8;
else
equity = outs*multiplier;
equityratio= (100.0-equity)/equity;
printf("\nYour equity is: %d%% \n", equity);
printf("The Pot Ratio is: %f : 1\n", potratio);
printf("The Equity Ratio is: %f : 1\n", equityratio);
if (potratio>=equityratio)
printf("\nYour estimated value is: %f +EV.\nYour pot odds suggest that you should make this call.\n", potratio-equityratio);
else
printf("\nYour pot odds suggest that you should not make this call. Proceed at your own risk!!!\n");
}
}
Sean Lind
2010-02-08Dudesomeguy,
Hey, props on crushing to 10 million by feel. Playing by feel is not incorrect, in fact many professional players do just that. But if you want to learn the math, it takes just a little effort. I'd say read the How not to suck a poker series, the article on Outs will pretty much answer all your questions on that, and the next article in the series go over some basic maths. Hopefully you find what you need here:
http://www.pokerlistings.com/strategy/how-not-to-suck-at-poker-count-your-outs
Dudesomeguy
2010-02-06So basically, I've made over 10million in chips by doing everything by feel. and the basic ' fold more, play less ' approach.
I rarely bluff.. but I run with chance often.
This is totally new stuff to me and it's confusing; I have no idea what the term ' Out ' means.. nor do I know what are the importance of these formulas...
it's a lot to digest, and in short sight, it appears as if it's just used to calculate the 'pot?' .. what's the significance in knowing this .. especially in online games..
Maybe it's not significant to me because I have no idea what the meaning of ' Equity ' is.
Anyone want to lay it out in crayon for me ?
Morten Hard
2009-08-18Hi Sean. It gladdens me to hear that you found it useful :D. I've been trying to apply those calculations we talked about, to my game over the last 3 days now, and with the new 'finding', I finally got it! I can make both the pot odds and the equity, thus giving the EV+, before the timer runs out! (online). And still get to think about my move towards the river. So i'm on a little high today ;P
How can I contact you personally? I have an idea for an article, if you're interested. It's about cheating your opponent into believing exactly what cards you're holding and how to take advantage of it. We could call it your "card image". If there isn't already one out there, written on the topic! lol. Maybe your e-mail address?
Sean Lind
2009-08-18Nice, thanks for that Morton, I like that a lot actually. Gets you the same result, but is a little simpler to explain and understand.
Thanks again, I'll be using this in the future.
Morten Hard
2009-08-18Hi Sean. Thanks for the answers. What a relief that you're able to improve on the math of odds :) Now I'll get on to practicing.
I thought your "math" example was very difficult for me to comprehend. But by coincidence I found a method I believe is much easier (this is just for sharing) ;).
Here's how it goes.
You have the 130/70= 1. As we both know.
Now we have the 60 left.. Under normal circumstances we would say 60/70 but that would become a number below 1, probably with a lot of digits and hard to precisely get a picture of fast. A much easier approach is to "omit tens" so you would get a number above 1. 60/7= 8,something. Now you "give back" the tens. 0.8. So 1.8 all of a sudden. If you were to work with odd numbers like 60/76 it would just be 60/7.6. Again by "borrowing tens" you could have VERY large numbers quickly concluded in your head like a remainder of 23500/36500 <-> 23.500/3.6500= 7.something. So around 0.7. What do you think of this? :) I must say I like it.
Sean Lind
2009-08-17Hey Morten,
Good questions, let's see if I can clear this up for you.
Firstly, your second question. Yes, this is a lot to calculate on the spot, but the more you do it, the easier it gets. Counting outs becomes second nature after a while, and figuring your equity in the hand the same. In fact, you end up memorizing most of it, so you know your equity without almost any effort.
The pot odds just takes work, but like I said you have no need to get really accurate, just close is good for this game.
Now the math:
You're thinking about the math "properly", the way you're taught to do it. When doing math in your head, you need to forget everything you know, and work backwards.
for your example of $70 to call into a $130 pot, here's how it works my way, without using a calculator.
70 goes into 130 only once, so the first number is a 1 (no matter what we do next, this number never changes).
We're now left with 60, you want to figure out how many times 60 goes into 70. We know that half of 70 is 35, and all of 70 is 70. 60 is exactly in the middle of 35 and 70, so what's the middle of 0.5 and 1?
0.8
now just put the two numbers together
1.8
Use a calculator and you'll get 1.85, so our cranium math is close enough.
The math is really that simple, it just takes a little bit of practice to understand the backwards thinking.
Morten Hard
2009-08-17Another thing concerning this article..
Is it even possible to calculate pot odds to equity, ALONGSIDE potential outs and anti- outs, during the flop and turn in online poker?
I tried applying these readings for my first time today and I found it nearly impossible to do all four readings, in addition to noticing the betting structure and trying to read the hand of my opponents and on top of that, having time to make a decent and thought- through choice, before the timer ran out, forcing me to fold.. or make a stoopid move. I guess it's a matter of practice. But still.. to me it seemed too overwhelming! I only managed to do the expected value reading and a bit of my possible outs. Felt like I was tossed around. And i even had my calculator in use at the table! Maybe i shouId isolate one reading at a time starting with, for instance, my own outs?
I believe that in live poker, that extra time you have, even just 1/2 a minute, could give you those readings. Do you improve on this a lot with practice or is it not just possible online? Does it come with experience?
Sorry for bothering. Oh, and by the way. Incredibly interesting and giving site with tons of great articles. Has improved my playing a lot, but have a bunch yet to learn.
Morten Hard
2009-08-17Isn't there something wrong with the equation above?!
I agree to 115/50 equals times 2.
The remainder of 15 is supposed to be dealt with the same way, I guess. So how can you suddenly change sides?
It gives no sense to me that you look at how many times 15 goes into 50, but rather how many times 50 goes into the remaining 15! Using a calculator 50/15= 3.333333..... (rounded off)= 3.3
The other way around: 15/50= 0.3
Isn't that the right way to do it? It looks to me like its just coincidence that you got to a '0.3'
But in reality it was 3.3, was it not? That would give 2 + 3.3= 5.3 instead of the intended 2.3.
I checked out this ex.: 130/70 (imaginary blinds 'n calls)= 1.857.... or just 1.8
Doing it your way the odds would be.: 130/70= 1. The remainder is 130- 70= 60. Then you say 70/60= 1,1666....
1+1.2(rounded off)= 2.2
1.857 vs. 2.2 are to me HUGE differences? Am I wrong in this? Mistaken? The least to say, is that I am confused.
Sean Lind
2009-07-24Wade,
Preflop action:
UTG raises to $15, cut-off calls ($30), button calls ($45), small blind calls ($60), big blind folds ($65).
Pot before the flop = $65
UTG bets $50 on the flop, $65+$50 = $115
Wade Sparks
2009-07-24In the second example, why was the total pot 115? That number seems to be an error because if UTG raises to $50, and we ignore the blinds, then the cut-off's pot should only be $100. And if the small blind calls, big blind folds, then the total pot should be $155