Quick reference guide on calling when pot odds are good

Abramo Della Luce

Abramo Della Luce

Rock Star
Silver Level
Joined
Jan 2, 2016
Total posts
498
Awards
4
Chips
0
When thinking about calling an opponents bet or raise, it is always interesting to know what your equity is.
This is done by counting your outs, calculating your odds and calculating your pot odds.
If your odds are higher than your pot odds, it is a good idea to call, so in the long run you will be winning money.
Now, one issue with this, is that it takes some time to make all these calculations (even when you're using the rule of four).
To make it faster, I have made some calculations and an overview that I find easier to use.
The only thing you still have to do, is counting your outs and seeing how big the opponent's bet or raise is according to the pot.

In the table below, the first column is the number of outs you have
Second column is the bet or raise size made by your opponent on the flop (counting with still 2 cards to come).
Third column is the bet or raise size made by your opponent on the river (counting with still 1 card to come).

If the betsize made is smaller than the number in the second or third column, you can call.

Example 1:
You have 6 outs (two overcards) and the opponent bets on the flop 1$ in a pot of 2$. This means 0.5 times the pot.
Looking in the table next to 6 outs, it says 0.46.
0.5 is not lower than 0.46, so you should fold.

Example 2:
Same as above, but the pot is 3$
This means 0.33 times the pot.
0.33 is lower than 0.46, so you should call.

Example 3:
You have have 15 outs on the flop (OESD + flush draw).
It doesn't matter how much the opponent bets, you are ahead, so you can call everything.

Example 4:
You have 4 outs (gutshot) on the turn. The opponent bets 1 dollar in a pot of 10 dollar. You can call here, even though on the long term, this is a break even point.
Code:
Number of outs    betsize on flop    betsize on turn

22                all                10.86
21                all                5.31
20                all                3.34
19                all                2.37
18                all                1.79
17                all                1.42
16                all                1.14
15                all                0.93
14                all                0.77
13                12.65              0.65
12                4.5                0.54
11                2.51               0.45
10                1.58               0.38
9                 1.16               0.32
8                 0.85               0.26
7                 0.62               0.21
6                 0.46               0.17
5                 0.34               0.13
4                 0.24               0.1
3                 0.16               0.07
2                 0.1                0.04
1                 0.04               0.02
If you find something that is not correct, or suggestions, please let me know.
 
W

WisdomMan87

Enthusiast
Silver Level
Joined
Apr 14, 2017
Total posts
67
Chips
0
to paint a better picture you should add some parts about, Reverse implied odds, and implied odds for they kind of go hand in hand. but nice work keep up the good job:)
 
Abramo Della Luce

Abramo Della Luce

Rock Star
Silver Level
Joined
Jan 2, 2016
Total posts
498
Awards
4
Chips
0
to paint a better picture you should add some parts about, Reverse implied odds, and implied odds for they kind of go hand in hand. but nice work keep up the good job:)
I know that would be more complete, but I just wanted to have a fast chart to look at when playing. It was not really my goal to explain the theory.
I just noticed for myself that I took to much time thinking about calling or not in certain situations and I found this really handy in making better decisions, so I thought, why not sharing it with the others here :)
 
MoeJurphy

MoeJurphy

Legend
Silver Level
Joined
Aug 12, 2015
Total posts
1,159
Chips
0
I'm probably just being stupid but are the bet sizing shown as %?
 
P

ph_il

...
Silver Level
Joined
Feb 5, 2005
Total posts
10,128
Awards
1
Chips
25
It looks like you made a very common mistake a lot of players do when using the rule of 2 and 4 when calculating their outs.

On the 2nd column, you used the rule of 4 instead of the rule of 2. You should be calculating for 1 card to come, not 2.

As a basic guideline:

-If there is a possibility of future bets, use the rule of 2 and calculate for a single card for flop-to-turn and turn-to-river bets.

-If there are no future bets to be made (a player is all-in) then you can use the rule of 4 since you are guaranteed to see the turn and river.

Your chart should have for columns: # of outs/odds for flop-to-turn[rule of 2]/odds for turn-to-river[rule of 2]/odds for turn and river [rule of 4].

If you'd like me to go more into this, I'll be happy to.
 
MoeJurphy

MoeJurphy

Legend
Silver Level
Joined
Aug 12, 2015
Total posts
1,159
Chips
0
I just meant was the "betsize on flop" units shows as % of flop or bb? :)
 
Abramo Della Luce

Abramo Della Luce

Rock Star
Silver Level
Joined
Jan 2, 2016
Total posts
498
Awards
4
Chips
0
It looks like you made a very common mistake a lot of players do when using the rule of 2 and 4 when calculating their outs.

On the 2nd column, you used the rule of 4 instead of the rule of 2. You should be calculating for 1 card to come, not 2.

As a basic guideline:

-If there is a possibility of future bets, use the rule of 2 and calculate for a single card for flop-to-turn and turn-to-river bets.

-If there are no future bets to be made (a player is all-in) then you can use the rule of 4 since you are guaranteed to see the turn and river.

Your chart should have for columns: # of outs/odds for flop-to-turn[rule of 2]/odds for turn-to-river[rule of 2]/odds for turn and river [rule of 4].

If you'd like me to go more into this, I'll be happy to.

You are totally right...
Such a pity that most sites that talk about this don't explain it well, but it's so clear how you put it here.
I suppose you can also use the rule of 4 if you play against a player that for some reason never bets the turn, but it might be a bit more risky in that case

So here is the updated version:
Code:
Number of outs    all in betsize on flop    betsize on flop    betsize on turn

22                all                       7.31               10.86
21                all                       4.21               5.31 
20                all                       2.87               3.34 
19                all                       2.1                2.37 
18                all                       1.63               1.79 
17                all                       1.31               1.42 
16                all                       1.06               1.14 
15                all                       0.88               0.93 
14                all                       0.73               0.77 
13                12.65                     0.62               0.65 
12                4.5                       0.52               0.54 
11                2.51                      0.43               0.45 
10                1.58                      0.37               0.38 
9                 1.16                      0.3                0.32 
8                 0.85                      0.25               0.26 
7                 0.62                      0.21               0.21 
6                 0.46                      0.17               0.17
5                 0.34                      0.13               0.13
4                 0.24                      0.1                0.1
3                 0.16                      0.07               0.07
2                 0.1                       0.04               0.04
1                 0.04                      0.02               0.02

Now, there is one thing that bothers me a bit when looking at this.
It feels super tight to follow this.
I mean, when someone bets half a pot, and I'm sitting there with an OESD + 1 overcard (so 11 outs), it feels strange to fold it.
Same for having a flush draw + 2 overcards (15 outs), and the opponents bets 0.90$ in a pot of 1$. According to this, it would mean that you don't even have enough outs to call!
Would it be a good solution for the second case, to just push all in, because this will bring you to the all in on flop column, meaning you're ahead?
Funny situation that I never thought about. Calling means you're not having good odds to win, but pushing all in makes you ahead (not even counting with the fold equity).
 
Abramo Della Luce

Abramo Della Luce

Rock Star
Silver Level
Joined
Jan 2, 2016
Total posts
498
Awards
4
Chips
0
I just meant was the "betsize on flop" units shows as % of flop or bb? :)
With betsize I mean how big the bet is compared to the pot.
So 0.73 means 73% of the pot. In a pot of 2$, this would mean that we can fold to a bet that is higher than 1.46$, and call one that is 1.46$ or lower.
3.34 would mean 334% of the pot, so in a pot of one dollar we can call a bet up to and including 3.34 dollar.
 
P

ph_il

...
Silver Level
Joined
Feb 5, 2005
Total posts
10,128
Awards
1
Chips
25
You are totally right...
Such a pity that most sites that talk about this don't explain it well, but it's so clear how you put it here.
I suppose you can also use the rule of 4 if you play against a player that for some reason never bets the turn, but it might be a bit more risky in that case

So here is the updated version:
Code:
Number of outs    all in betsize on flop    betsize on flop    betsize on turn

22                all                       7.31               10.86
21                all                       4.21               5.31 
20                all                       2.87               3.34 
19                all                       2.1                2.37 
18                all                       1.63               1.79 
17                all                       1.31               1.42 
16                all                       1.06               1.14 
15                all                       0.88               0.93 
14                all                       0.73               0.77 
13                12.65                     0.62               0.65 
12                4.5                       0.52               0.54 
11                2.51                      0.43               0.45 
10                1.58                      0.37               0.38 
9                 1.16                      0.3                0.32 
8                 0.85                      0.25               0.26 
7                 0.62                      0.21               0.21 
6                 0.46                      0.17               0.17
5                 0.34                      0.13               0.13
4                 0.24                      0.1                0.1
3                 0.16                      0.07               0.07
2                 0.1                       0.04               0.04
1                 0.04                      0.02               0.02

Now, there is one thing that bothers me a bit when looking at this.
It feels super tight to follow this.
I mean, when someone bets half a pot, and I'm sitting there with an OESD + 1 overcard (so 11 outs), it feels strange to fold it.
Same for having a flush draw + 2 overcards (15 outs), and the opponents bets 0.90$ in a pot of 1$. According to this, it would mean that you don't even have enough outs to call!
Would it be a good solution for the second case, to just push all in, because this will bring you to the all in on flop column, meaning you're ahead?
Funny situation that I never thought about. Calling means you're not having good odds to win, but pushing all in makes you ahead (not even counting with the fold equity).
You have to look at expected value.

With 11 outs, it looks like you win 43% of the time and lose 57%. If you're facing a half pot bet, say villain bet $5 into a pot of $10, you need to call $5 to win $15.

EV = [$15*.43] - [$5*.57]
EV = $6.45 - $2.85
EV = $3.60

Making your call profitable.

In fact, in this situation, you would only need 24% equity to break even. Anything less will be -EV.

However, I think your numbers are still off. With 11 outs, you should only have a ~23% chance to hit on the turn. And when we plug the corrected equity into the EV formula, we can see it's a -EV call. Not factoring implied odds, of course.
 
Last edited:
Abramo Della Luce

Abramo Della Luce

Rock Star
Silver Level
Joined
Jan 2, 2016
Total posts
498
Awards
4
Chips
0
You have to look at expected value.

With 11 outs, it looks like you win 43% of the time and lose 57%. If you're facing a half pot bet, say villain bet $5 into a pot of $10, you need to call $5 to win $15.

EV = [$15*.43] - [$5*.57]
EV = $6.45 - $2.85
EV = $3.60

Making your call profitable.

In fact, in this situation, you would only need 24% equity to break even. Anything less will be -EV.

However, I think your numbers are still off. With 11 outs, you should only have a ~23% chance to hit on the turn. And when we plug the corrected equity into the EV formula, we can see it's a -EV call. Not factoring implied odds, of course.

I didn't mean it to be a table that says how much times you will win or lose when you have a certain amount of outs, but how big you can call, so you don't have to do any calculation anymore, except for the one that says what the size of the bet is compared to the pot, which usually is really fast with standard betsizes of 2/3 pot, 1/2 pot or potsized bets.
I basically calculated the break even points for all the situations, and

Let me take the same example as you gave, with 11 outs.
I used 23.4% chance to hit on the turn in my calculations, so I'll use this now too.
In my (updated) table I say that you can maximum call a bet that is 0.43 times the potsize (in other words 43%).
In a pot of 10$ this would mean 4.30$

EV = (14.30$ * 0.234) - (4.30$ * 0.766)
EV = 3.35$ - 3.29$
EV = 0.06$

This should be 0, but because of rounding the 43% on 2 figures and rounding it down to be sure you're not calling too much, it is slightly different.
If I use a more accurate number this will be zero.

EV = (14.3985$ * 0.234) - (4.3985$ * 0.766)
EV = 3.37$ - 3.37$
EV = 0.00$

I never used these formulas before to calculate my EV, so I'm relieved that they confirm my calculations were correct :)

The way I calculated, was like this:
1 / 0.234 = 4.274 (chance of winning is 1 on 4.274)
4.274 - 2 = 2.274 (subtracting 2 for the bet of the opponent and your call at break even*)
1 / 2.274 = 0.43985 (maximum betsize you can call, in relation to the pot)
0.43985 => 43% (in percentage and rounded down, because we don't want a -EV call)

*This comes from the formula:
(x+x+1)/x=y, in which x = betsize and y = chance of winning (in a pot of 100% we add the bet x of the opponent + the call x from you)
We know y = 4.274 so
(2x+1)/x=4.274
<=> 1=4.274x-2x (here is where the 2 comes from)
<=> 1/2.274=x=0.43985


So indeed, a half pot bet (50%) will be -EV, because it is higher than the 43% I say in the table.
 
R

Running Nose II

Visionary
Silver Level
Joined
Mar 28, 2014
Total posts
572
Chips
0
Much of this stuff is seriously flawed!
 
R

Running Nose II

Visionary
Silver Level
Joined
Mar 28, 2014
Total posts
572
Chips
0
Sorry ohshootmubad, I thought that you would have figured it out for yourself. The premise is based on a rule of 4- 2 and the mathematics based on his rule is statistically flawed. Poker is such a simple game without going into calculations with outs verses bet sizes. You should know the number of your outs as soon as the flop goes down. You should also know, at the same time, the amount of money in the pot. It isn't difficult to calculate any increased money added when it is your turn to bet. You know your odds, you know the money in the pot and how much it will cost you to bet. What more do you need? Gold star for Abramo's efforts anyway
 
R

rhombus

Legend
Silver Level
Joined
Mar 1, 2012
Total posts
2,601
Chips
0
Rule of 4 and 2 is flawed once you get above 8 outs
i.e. 15 outs isnt 60% more like 54%
 
P

ph_il

...
Silver Level
Joined
Feb 5, 2005
Total posts
10,128
Awards
1
Chips
25
Sorry ohshootmubad, I thought that you would have figured it out for yourself. The premise is based on a rule of 4- 2 and the mathematics based on his rule is statistically flawed. Poker is such a simple game without going into calculations with outs verses bet sizes. You should know the number of your outs as soon as the flop goes down. You should also know, at the same time, the amount of money in the pot. It isn't difficult to calculate any increased money added when it is your turn to bet. You know your odds, you know the money in the pot and how much it will cost you to bet. What more do you need? Gold star for Abramo's efforts anyway
The rule of 2/4 is used as guide to quickly calculate the percentage chance of you hitting an out. While there are more accurate was to calculate your chance of hitting, this is just a quick and easy way to get really close.

So, I don't understand where you're saying it's flawed.

As far as Abramo's post, he simply showing the max bet size someone can call in a situation that'll still be profitable in the long run.
 
Abramo Della Luce

Abramo Della Luce

Rock Star
Silver Level
Joined
Jan 2, 2016
Total posts
498
Awards
4
Chips
0
Rule of 4 and 2 is flawed once you get above 8 outs
i.e. 15 outs isnt 60% more like 54%
True, that's why I used the exact percentages and not the rule of 4 and 2 in my calculations.
When having to make a fast decision, and I can only use my head and no other tools, I would still use it (carefully), being aware that it can be a few percentages of.
 
R

Running Nose II

Visionary
Silver Level
Joined
Mar 28, 2014
Total posts
572
Chips
0
The Rule of 4-2 may be quick way of calculating your outs, but it is flawed because it is mathematically inaccurate (well half of it is anyway). Perhaps it was the genius who thought it up arriving at a result then working backwards to find a suitable question, when they decided that because you had two cards to come after the flop, you can half the turn odds by 2. That is where it is flawed. They turn and the river are combined in their calculation, but they are mutually exclusive to each other. The river odds, by some fluke, resulted in being accurate enough. You put a lot of work into this Abramo and I applaud your effort.
 
P

ph_il

...
Silver Level
Joined
Feb 5, 2005
Total posts
10,128
Awards
1
Chips
25
The Rule of 4-2 may be quick way of calculating your outs, but it is flawed because it is mathematically inaccurate (well half of it is anyway). Perhaps it was the genius who thought it up arriving at a result then working backwards to find a suitable question, when they decided that because you had two cards to come after the flop, you can half the turn odds by 2. That is where it is flawed. They turn and the river are combined in their calculation, but they are mutually exclusive to each other. The river odds, by some fluke, resulted in being accurate enough. You put a lot of work into this Abramo and I applaud your effort.
Im not following you. Can you show an example?

Let's say you have 9 outs for the nut flush.

Can you show me how you would calculate your chances of hitting on the turn? On the river? On the turn or river?
 
R

Running Nose II

Visionary
Silver Level
Joined
Mar 28, 2014
Total posts
572
Chips
0
You have 9 outs, 2 clubs in your hand and 2 on the board after the flop. You know 5 of the 52 cards, with 47 unknown which contains your 9 remaining clubs. Of these 38 won't help, but 9 will, so the odds of hitting on the turn are 38/9 or 4.22/1. If the turn card isn't a club, you still have the river, but the unknown cards are now 46, (2 in your hand and 4 on the board). The 9 clubs are still there and the odds of hitting on the river are 37/9 or 4.11/1. Rule 4-2 has the odds on the turn as 1.9/1 and 4.1/1 on the river (I did say it was half right). Factor another 3 cards for the aces if you like, increasing your outs to 12, giving you odds of 35/12 and 34/12 respectively. Calculating odds for the turn OR the river is statistical nonsense. They are mutually exclusive and can never be calculated together if you want the correct odds.
 
P

ph_il

...
Silver Level
Joined
Feb 5, 2005
Total posts
10,128
Awards
1
Chips
25
Calculating odds for the turn OR the river is statistical nonsense. They are mutually exclusive and can never be calculated together if you want the correct odds.
So, if a player is all in on the flop and you only have v to call 1 bet to see the turn or river, it's statistical nonsense?

Tell me, how do you calculate the odds of hitting on either street if you don't calculate them together?
 
Last edited:
R

Running Nose II

Visionary
Silver Level
Joined
Mar 28, 2014
Total posts
572
Chips
0
What is it about mutually exclusive you don't understand? Reread the last sentence you wrote. If you don't understand the concept, there's not any point continuing this conversation, we are poles apart.
 
P

ph_il

...
Silver Level
Joined
Feb 5, 2005
Total posts
10,128
Awards
1
Chips
25
What is it about mutually exclusive you don't understand? Reread the last sentence you wrote. If you don't understand the concept, there's not any point continuing this conversation, we are poles apart.
Please explain why you would need to calculate the odds for the turn and river separately when a player is all in on the flop?
 
DrazaFFT

DrazaFFT

public static void
Bronze Level
Joined
Mar 9, 2013
Total posts
6,188
Chips
0
Rule of 4 and 2 is flawed once you get above 8 outs
i.e. 15 outs isnt 60% more like 54%

that is why you should (for rule of 4, not sure does it apply fop the rule of 2) take away 1% for each out above 9, and its pretty accurate up to 9 outs if i remember right, not 8, so the formula would be something like
odds=4*outs-(outs-9)
 
R

rhombus

Legend
Silver Level
Joined
Mar 1, 2012
Total posts
2,601
Chips
0
that is why you should (for rule of 4, not sure does it apply fop the rule of 2) take away 1% for each out above 9, and its pretty accurate up to 9 outs if i remember right, not 8, so the formula would be something like
odds=4*outs-(outs-9)
Yup think I posted awhile back about the modified rule of 4 and 2 anything above 8 subtract 1
i.e. 15 outs is 15 x 4 = 60 then subtract 7

https://www.cardschat.com/forum/learning-poker-57/rule-4-2-302941/post-3229963.html
 
R

rhombus

Legend
Silver Level
Joined
Mar 1, 2012
Total posts
2,601
Chips
0
Please explain why you would need to calculate the odds for the turn and river separately when a player is all in on the flop?
When all in on the flop its better to calculate odds of not hitting Turn or River then subtract from 100
 
Poker Odds - Pot & Implied Odds - Odds Calculator
Top