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.

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.

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

Originally Posted by WisdomMan87

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

I'm probably just being stupid but are the bet sizing shown as %?

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.

I just meant was the "betsize on flop" units shows as % of flop or bb?

Originally Posted by ohshootmybad

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:

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).

Originally Posted by MoeJurphy

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.

Originally Posted by Abramo Della Luce

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:

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.

Originally Posted by ohshootmybad

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.

Much of this stuff is seriously flawed!

Originally Posted by Running Nose II

Much of this stuff is seriously flawed!

What's the point of making such a statement and not even explaining why?

Or is this a "quality post"?

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

Rule of 4 and 2 is flawed once you get above 8 outs
i.e. 15 outs isnt 60% more like 54%

Originally Posted by Running Nose II

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.

Originally Posted by rhombus

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.

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.

Originally Posted by Running Nose II

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?

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.

Originally Posted by Running Nose II

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?

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.

Originally Posted by Running Nose II

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?

Originally Posted by rhombus

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)

Originally Posted by DrazaFFT

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/showpost3229963-post11.html

Originally Posted by ohshootmybad

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

Originally Posted by rhombus

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/showpost3229963-post11.html

If we had this conversation like year and a half ago i would be ready to bet that it's above 9, this way i have to say that everything i've learned or read slowly fading, its been more than a year since i played for real last time (cash) and even more since i read something or tried to discuss

You need to calculate the odds for the turn and the river separately because they are 2 different happenings. Calculating them together will give false odds. Again it depends on how much is in the pot and the size of the stack of the all in bet. An all in bet of $500 to a $500 pot, unless you have the nuts is a fold. However an all in bet of $100 to a $700 pot gives you 8/1 to call (or fold)

Originally Posted by Running Nose II

You need to calculate the odds for the turn and the river separately because they are 2 different happenings. Calculating them together will give false odds. Again it depends on how much is in the pot and the size of the stack of the all in bet. An all in bet of $500 to a $500 pot, unless you have the nuts is a fold. However an all in bet of $100 to a $700 pot gives you 8/1 to call (or fold)

My gosh. What do you not understand about it not being necessary when a player is all in? You are guaranteed to see both the turn and river, therefore, you don't need to calculate separately. The only way you won't be guaranteed​ to see either street in an all in situation, if you call, is if you plan on folding pre river... which would be really stupid.

Let's say you have 9 outs to the nut flush and a player is all in. If you call, you can either hit on the turn or river, so you calculate for hitting on either street and not separate. The odds of hitting on either turn or river is 1.86:1. If you calculate separately, it's 4.22:1 for the turn and 4.11:1 for river.

If the pot is giving you 3:1 odds in a situation where a player is all-in, (remember, you are GUARANTEED to see both turn and river if you call) then its a profitable call with 1.86:1 odds to hit on either street.

But, by doing it your way, you would be making a terrible fold since hitting on the turn is 4.22:1 and the pot is giving you 3:1. However, if it wasn't an all in situation, then you would be correct to calculate separately because you aren't guaranteed to see both streets.

Originally Posted by rhombus

When all in on the flop its better to calculate odds of not hitting Turn or River then subtract from 100

That wasn't what I was asking and that's exactly how i do it.

Great job. It could be improved by creating an method/formula to convert implied odds to extra outs.

Originally Posted by braveslice

Great job. It could be improved by creating an method/formula to convert implied odds to extra outs.

Implied odds might be too situational for this, but there is a formula you can do to see how much value you'd have to extract to profit with implied odds.


(Odds of making hand)-(pot odds) = X

X * $Bet = value required.

So, let's say you have a flush draw and the bet is $10, giving you 3:1 pot odds on flop. The odds of hitting flush on turn is 4.2:1

(4.2:1)-(3:1) = 1.2:1
$10 x 1.2 = $12.

So, you would have extract at least $12+ from your opponent to make your Implied odds call profitable.

Very nice graph to follow. I especially like how simple and easy it is to make for quicker decisions/finding things

I don't know how you can get 1 out. I'm intrigued, the lowest I can go is 2

Originally Posted by ohshootmybad

Implied odds might be too situational for this, but there is a formula you can do to see how much value you'd have to extract to profit with implied odds.


(Odds of making hand)-(pot odds) = X

X * $Bet = value required.

So, let's say you have a flush draw and the bet is $10, giving you 3:1 pot odds on flop. The odds of hitting flush on turn is 4.2:1

(4.2:1)-(3:1) = 1.2:1
$10 x 1.2 = $12.

So, you would have extract at least $12+ from your opponent to make your Implied odds call profitable.

Interesting, I didn't know about that, using ev you get:

EV=1/5.2*(30+X)-4.2/5.2*10 = 0 -> X= 12

Originally Posted by Running Nose II

I don't know how you can get 1 out. I'm intrigued, the lowest I can go is 2

Yes was interesting problem, at least one: hero AA, villain 77, flop A77.
Edit: this is too, hero Ah9h, villain 4h5h, flop 6h7h8h

Thanks for this. It's very clever, but what you are talking about is one out to WIN. The villain's cards are unknown and our hero, while flopping a boat, could still improve his hand with runner runner pairs between 8 and king (but lose). I know it seems ridiculous but that's 36 outs.

Yes, it seems ridiculous, good you explained.

Originally Posted by Running Nose II

Thanks for this. It's very clever, but what you are talking about is one out to WIN. The villain's cards are unknown and our hero, while flopping a boat, could still improve his hand with runner runner pairs between 8 and king (but lose). I know it seems ridiculous but that's 36 outs.

How is that 36 outs? Unless your opponent flopped quads vs your boat, they're either drawing to a better boat or quads, which is only 1-2 outs depending. They can only hit what they have in their hands and nothing else. So, if villain has 88, the board running 99-AA will be no help to villain.

As far as not knowing your opponents hand, that is true. Unless cards are flipped face up, there is no way of really knowing. You can definitely create a range of hands and shorten that range as the hand plays on, but most of the time-if its not blatantly obvious-you'll end up with a small range of possible hands. This is why if you're going to be playing draws, you need to play draws that'll be profitable for you if you hit and fold your other draws that aren't.

This is soooo clever. Both heroes have flopped great hands, but both don't know that they are beaten. What we are is left with is 1 WINNING out, and loads of other outs to improve their hands (but still lose).

Originally Posted by Abramo Della Luce

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.

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.

please make it simpler

This is soooo clever. I thank you for it. However the definition of 'outs' are the unseen cards that will complete or improve your hand. What we have here is a situation of the number of WINNING outs Our hero can improve his boat with any pair from 8s, 9s, 10s, Js, Qs, and Ks, - 36 outs(but still get stuffed). In the second he can improve with any 2 from 10, J, Q, or K of hearts - 6 outs, but again loses.

This is so clever and well thought out. However what we have here is the number of WINNING outs. The definition I know of 'outs' are the unknown cards that will complete or improve your hand, Our hero can improve his boat with any pair from 8s, 9s, 10s, Js, Qs or Ks - 36 outs.
He can improve his flush with any 2 from 10, J, Q or K of hearts - 6 outs.