How To: Analyze Calling An All-in

Introduction

A dozen or more times a week there are hands posted in this forum that are asking if Hero should call an all-in. I don't even have to scroll half-way down the first page of BC to see all of these threads that have a hand like this in them:

AKo vs relatively unknown player - Poker Forums
jj with king on the board 2nl - Poker Forums
a few hands 2nl - Poker Forums
Line check with AKs ($10NL) - Poker Forums
a few hands, first night of my op- 2nl - Poker Forums
2 QQ 6-max hands for review - Poker Forums

None of these hands were given with analysis. Instead, they're just dumped on the forums like "Hey guys which button do I mash here?" Deciding whether or not to call an all-in is pretty easy, so I'm going to show you guys how to put on your big girl panties and analyze your own hands a bit.

Required Software

Go here and download PokerStove if you don't already have it. PokerStove does equity calculations for us based on ranges against ranges so that we don't have to do them by hand. If you want to learn the keyboard shortcuts and whatnot to do complicated stuff in PokerStove, watch this 4-5 minute video that might be NSFW for language (link).

The Process

There is a pot size, you are facing a bet size, and you have an equity against your opponent's range. These are the three things that affect the EV of calling an all-in. The pot size and bet size are given to you, and you can use PokerStove or your own calculations to determine your equity. This creates a process that I'm going to overly exaggerate here into four steps for easy consumption:

Step 1: Identify the size of the pot. This is the size of the pot after your opponent has bet, including all of the money in the pot before your opponent bet and the amount he bet that you're allowed to call.

Step 2: Identify the size of the bet. This is how much you're calling.

Step 3: Determine your equity by one of the previously mentioned methods (using PokerStove or others).

Step 4: Figure the fraction bet size/(bet size + pot size). If your equity is larger than this, then a call is +EV. If your equity is lower than this, then a call is -EV. If your equity is exactly this, then a call has the same EV as a fold.

An Example

On the turn there is $8.50 in the pot and my opponent (who I have covered) shoves another $11.50. The board is AsThTc3s and I hold Td4d. I think my opponent's range (for the sake of this example) is {AA, 33, AK+, Tx}. Can I make a profitable call?

Step 1: What is the pot? There was $8.50 in the pot, and our opponent has bet another $11.50 that we can call, so the pot is $20.

Step 2: What is the bet? We are calling $11.50, so that's the bet size.

Step 3: What is our equity? Here's a quick screenshot of PokerStove:



So our equity is 39.394% against this range.

Step 4: The fraction bet/(bet+pot) is 11.5/(11.5+20), which is 36.5%. This is less than our equity of 39.394%, so it's a +EV call.

Where To Go From Here

Once you get this and regularly use it (both at the table with estimations and away from the table in your study and hand analysis) then you'll realize the only variable that changes is the range you put your opponent on. This is why estimating ranges is so important, so practice!

So from now on if someone posts a hand where they were facing an all-in, and they haven't shown the range they've put their opponent on, you should link them to this post and suggest they do their own analysis first.

Extra Credit: Finding The Exact EV

Like I mentioned earlier, when we're facing an all-in there are three factors that affect our EV: the size of the pot, the size of the bet we're calling, and our equity. While the shortcut I offered above (which I'll prove in a minute) will tell you if calling an all-in is +EV, sometimes it can be useful to know the exact EV of a call against a certain range. I'm going to quickly illustrate how to do this here.

There are two possible cases after we call. In the first case, we win the hand and win the amount of the pot. In the second case, we lose the hand and lose the amount we called. Our equity will tell us how often we'll pick up the full pot and how often we'll lose our bet as follows:

EV = (our equity)(pot size) - (our opponents equities)(bet size)

Keep in mind that our equity plus our opponents' equities will always equal 100%. So let's look at an example. Suppose that heads up after our opponent goes all-in for $4 the pot is $10 and we have 18% equity against his range. What is the EV of a call?

Our equity: 18% (or 0.18)
His equity: 100% - 18% = 82% (or 0.82)
Bet size: $4
Pot size: $10

EV = (0.18)(10) - (0.82)(4)
EV = 1.8 - 3.28
EV = -$1.48

So on average, this call will cost us $1.48.

Extra Credit: Proving The Shortcut

I said earlier that when our equity is greater than bet/(bet+pot) that the call will be +EV, when our equity is lesser than bet/(bet+pot) that the call will be -EV, and when our equity is equal to bet/(bet+pot) that the call will be 0 EV. Here I'm going to quickly prove that and show you where this comes from. Remember our equation from above?

EV = (our equity)(pot size) - (our opponents equities)(bet size)

Well let's call our pot size P, our bet size B, and our equity E for the sake of simplicity. This means our opponent's equity is (1-E) since our equity plus our opponent's equity has to add up to 100% (or 1). This gives us the following equation which we'll do a little algebra on:

EV = EP - (1-E)(B)

Now suppose a call is +EV. This would mean that

0 < EP - B + EB
B < EP + EB
B < E(P+B)
B/(P+B) < E

Which shows that our equity will be greater than bet/(bet+pot). Similarly we can show that the rest of this shortcut is correct.

Now go forth and do math.

lol wrong screen shot. good post though and should be put in the read this before posting HH's sticky

Thanks spoonitnow
did not now that bet/bet+pot part of the analysis
some practice
PokerStars No-Limit Hold'em, $0.10 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

CO ($10.25)
Button ($9.55)
SB ($14.20)
BB ($2.60)
UTG ($9.55)
Hero (MP) ($10)

Preflop: Hero is MP with ,
UTG calls $0.10, Hero bets $0.50, 1 fold, Button calls $0.50, 3 folds

Flop: ($1.25) , , (2 players)
Hero bets $0.90, Button raises to $9.05 (All-In), Hero calls $8.15

Turn: ($19.35) (2 players, 1 all-in)

River: ($19.35) (2 players, 1 all-in)

Total pot: $19.35 | Rake: $0.95

Opponent range a AA,88,22,AKs,AsTs,K8s,6s5s,AKo,K8o
against that range I have 46%equity
Pot:11.2
Calling: 8.15
Range: equity 46%
bet/[pot+bet] = 8.15/19.35= 42%
so EV+ call

I think you said something to this effect a year or more ago: putting people on ranges is the most underutilized skill in the poker universe.

Originally Posted by Robb

I think you said something to this effect a year or more ago: putting people on ranges is the most underutilized skill in the poker universe.

Well it's the basis of the vast majority of all poker decisions, so yeah.

Also I added the "Extra Credit" portions at the bottom of the OP for completeness.

Great post! I need to take this on-board

Thanks spoon for posting this!

spoon4mod

The position is filled. Sorry

Originally Posted by XxStacksxX

The position is filled. Sorry

well you voted me off irc, I vote you off the mod team

Originally Posted by iopq

Originally Posted by XxStacksxX

The position is filled. Sorry

well you voted me off irc, I vote you off the mod team

It was only a 24 hour ban in case you didn't know.

Originally Posted by spoonitnow

Originally Posted by iopq

Originally Posted by XxStacksxX

The position is filled. Sorry

well you voted me off irc, I vote you off the mod team

It was only a 24 hour ban in case you didn't know.

yeah but I'm going to be spiteful and leave for a week anyway

Originally Posted by iopq

Originally Posted by spoonitnow

Originally Posted by iopq

Originally Posted by XxStacksxX

The position is filled. Sorry

well you voted me off irc, I vote you off the mod team

It was only a 24 hour ban in case you didn't know.

yeah but I'm going to be spiteful and leave for a week anyway

It's not often that 25 people in the same IRC channel run good at the same time for a week straight.

lol

Originally Posted by spoonitnow

EV = (our equity)(pot size) - (our opponents equities)(bet size)

This is actually an equation I didn't know about. I'm excited to use this where I can find a true value for my plays.

I think one leak I have is just "oh plus++ EV so SHovveE". So thanks again for this.

There is another simpler equation that does the same thing.

EV = (our equity)(total pot) - (amount to call)

total pot = the size of the pot after our call is added to the pot

So using spoon's example:

Originally Posted by spoonitnow

So let's look at an example. Suppose that heads up after our opponent goes all-in for $4 the pot is $10 and we have 18% equity against his range. What is the EV of a call?

The other equation would look like:

EV = (0.18)($10 + 4) - 4
EV = 2.52 - 4
EV = -$1.48

Just thought I would throw that out there.

oh cool! Thanks for posting stax

Another equation for shoving all in as a bluff is to multiply our equity times the total pot and compare the amount of money we put into the pot to the amount of money we lose by shoving

imagine a scenario where you put in 12BB of your stack in and got raised to 24BB with 100BB stacks

so say we are shoving for 88BB into a total 200BB pot (when called) with 30% equity
the pot as it stands right now has 36BB
200BB * .3 = 60BB
our bluff costs us 28BB
therefore we're risking 28BB to win 36BB
so to break even on our bluff we need villain to fold 28/(28+36) = 43.75% of the time

you can do this calculation on flop/turn semi-bluffs and preflop semi-bluffs

Originally Posted by iopq

Another equation for shoving all in as a bluff is to multiply our equity times the total pot and compare the amount of money we put into the pot to the amount of money we lose by shoving

so say we are shoving for 88BB into a 200BB pot with 30% equity
the pot as it stands right now has 36BB
200BB * .3 = 60BB
our bluff costs us 28BB
therefore we're risking 28BB to win 36BB
so to break even on our bluff we need villain to fold 28/(28+36) = 43.75% of the time

you can do this calculation on flop/turn semi-bluffs and preflop semi-bluffs

This doesn't make any sense. How are we shoving 88bb into 200bb if the pot is 36bb? Even if you're saying 200bb is the pot after [if] we're called, 88 + 88 + 36 = 212.

Not to mention going all-in as a bluff is completely irrelevant to this thread.

Yes I know what you meant (Villain has already put in 12bb this street, etc.), but if you're going to post something off topic in a thread anyway, at least go for a little clarity.

yes, I realize this is how to analyze shoving all in instead of calling all in, but I didn't feel it deserved its own topic

the math is as follows: you put in 12BB, villain has put in 24BB, you shove over the top for 88BB more, villain can call for 76BB more
stacks are 100BB

pokerstove question: say on the board is ad 10h 4s, when i click a10 as one of their possible hands, does it automatically factor in the cards that or missing, i see there is a way to do that manually so i am assuming it does not factor those in.

Yes it factors it in. If Ad is already in use, it will factor out all combinations of AdTx.

How useful is it, while learning to put people on ranges, to start from the HUD percentages for VPIP (calling/limping range) and PFR (open range) plug those into Pokerstove and go from there?
Is there any value in this, say above 50-60 hands history on a player, at the micros?

Originally Posted by killnine

How useful is it, while learning to put people on ranges, to start from the HUD percentages for VPIP (calling/limping range) and PFR (open range) plug those into Pokerstove and go from there?
Is there any value in this, say above 50-60 hands history on a player, at the micros?

it's a rough idea, but not always right.
what if the villain limp/reraises AA and raises worse hands like A3s?

Originally Posted by iopq

it's a rough idea, but not always right.
what if the villain limp/reraises AA and raises worse hands like A3s?

In this case, I'd use PFR for the range. But I do see your point.
Am I correct in saying that while learning, the HUD values can be used as a starting point, IF I refine them after preflop action AND on the flop AND turn?
Or will this teach me a bad habit? Maybe it's best to assign the range myself and compare after the session how it relates to villain's VPIP/PFR and if I could have made a better decision using those?

Mind, I am currently grinding 2NL and there it might well pay more to just fold to strength (vs taggs/nits and mostly even loose/passives) and play the next hand.

yes, that's correct you can plug in some rough estimate in pokerstove and then on the flop you can mark the hands he continues with and possibly add a hand that you missed because fish play pretty hands like 75s while they might not be part of the top 40% hands or whatever but when he raises 752 flop you should add that back into his range (because remember our preflop range was really a rough estimate)

or you could start on the flop and start adding hands you THINK he will both play pf this way and that make sense

the best way(especially if it's a 3b pot and the pf range is tighter) is to start pf and mark all of the hands he would play, then go to the flop and mark all hands he continues with, etc. instead of relying on percentages

One thing to consider when calculating equity and ranges is that villain's bluff% is always > 0. For close EV situations, you have to consider some air in his range.

So, in the ATT3 hand, OP had the range as {AA, 33, AK+, Tx}, but I think you have to include *some* hands like JJ, QQ, KK or QJs as part of the range, because if you don't, you'll wind up folding close calls that may be more +EV than you think.

*Disclaimer* I have no idea how much bluff to assign to villains. Obv, you can read betting patterns to sniff these out, but even if you're just looking at the cold math, you could throw in 72o to allow for some bluffing %.

What do you guys with some actual skill think of this?

Dontezuma: Well in most spots obviously villain's have some bluffing frequency. However, it's always fairly hard to determine just how often villain is bluffing, and with what hands he is doing it with, without having played with that villain extensively.

Usually in spots where I think a decision is close, I calculate my equity against villain's value range. That is hands I highly suspect him to be doing this play with. If it's a call when he is only doing this for value, then it will be an even more +EV call if he is bluffing in this situation some % of the time. If it's a close fold when only analyzing his value range, then we can figure out how often he needs to be bluffing, and what hands he could possibly be bluffing with, to determine if a call is more correct than a fold.

Also, you must keep in mind what hands he is doing it with. in the ATT3 example, if he is bluffing, whether he is doing it with QJ or 72o does make a difference. If we have AK on that board, then his QJ has 3 outs against us, while 72o does not. Therefore, if he is bluffing with QJ his equity will be higher than if he is bluffing with 72o.

in line with the talk about bluffing, it is either in the super system or hoh1 that they say that they haev found that villains are bluffing 2% of the time, idk how that would translate into equity but i def agree with dontezuma that it needs to be a part of it...

stacks brings up a good point though, is it possible to do all of that while playing the hand or is that something you do in review? (talking about figuring out the value range then equity and then if its a close fold, going back and adjusting it to a potential bluff)


oh and i forgot to mention great post spoon, i knew this is what i should be doing but it really is a kick in the ass in the right direction

Stacks, I wasn't suggesting that you should throw QJ or 72 into that particular hand as bluffs interchangeably, because obv. QJ has 4 outs to a straight if you don't have a boat and 72 doesn't have that.

I was suggesting that when you are putting hands in your range for pokerstove calcs, you could throw a random air hand in to account for bluffs. If it's a value-betting nit, I ignore bluffing%, but for thinking players, donks, and maniacs, it's a very important piece of the equation, especially with any history at all with an opponent.

All in all, I agree with the thought of analyzing the equity in the value ranges, and calling the snap-offs profit, but in constructing your ranges, you have to include some air. Go to thinkingpoker.net sometime and read Andrew Brokos' stuff. There are some awesome articles on thinking about ranges, bluffing optimally, etc.

In the example step 4. Shouldn't the fraction be 11.5/(11.5+20)= 36.5% equity? Or am I doing something wrong?

Originally Posted by dontezuma

Stacks, I wasn't suggesting that you should throw QJ or 72 into that particular hand as bluffs interchangeably, because obv. QJ has 4 outs to a straight if you don't have a boat and 72 doesn't have that.

I was suggesting that when you are putting hands in your range for pokerstove calcs, you could throw a random air hand in to account for bluffs. If it's a value-betting nit, I ignore bluffing%, but for thinking players, donks, and maniacs, it's a very important piece of the equation, especially with any history at all with an opponent.

All in all, I agree with the thought of analyzing the equity in the value ranges, and calling the snap-offs profit, but in constructing your ranges, you have to include some air. Go to thinkingpoker.net sometime and read Andrew Brokos' stuff. There are some awesome articles on thinking about ranges, bluffing optimally, etc.

Yes you could, but this is inferior to the process of analysis that Stacks has briefly outlined.

WHY is it inferior to include non-value hands in the analysis? I could see how throwing a random hand, like 7-2 would be less precise, but Stacks says, "I calculate my equity against villain's value range...hands I highly suspect him to be doing this play with."

In the ATT3 case, we didn't see the betting that led to the final decision, but wouldn't KQ or QJ be in that range as well, for semibluff purposes? The semibluff is a pretty standard play, so I would think that most opponents have it in their repertoire. Adding likely bluffing hands to the pokerstove calculation seems to me to be important for narrowing the range enough to make an analysis of the profitability of your decision.

It may well be inferior, but just stating it's so without backing it up with a reason doesn't get the conversation any further down the road.

By saying "it's inferior because adding a random hand skews the results too much versus the reality that most villains are value betting and by only including specific, likely bluffing hands, you'll get better results," you force me to sharpen my thoughts around the process.

We're all trying to get better, and I know you weren't attacking me, but I am asking that the replies from all of us to all of us have a goal in mind, just like our bets.

Originally Posted by Tiresman

In the example step 4. Shouldn't the fraction be 11.5/(11.5+20)= 36.5% equity? Or am I doing something wrong?

Yes, fixed it. I caught this in my local copy of the OP but didn't fix it in the post. Thanks.

Originally Posted by dontezuma

WHY is it inferior to include non-value hands in the analysis?

It's inefficient for a number of reasons. First, if it's a call with no bluffing hands in his range, then you've wasted time on an extra step. Second, if it's not a call unless there are bluffing hands in his range, you can quickly figure out how many hands he has to be bluffing with to find the break even point. Then you make a decision based on if you think he's bluffing more often than that or not. This avoids the difficult (and unnecessary) decision of deciding exactly how many combinations of starting cards (clicky) he's bluffing with.

Originally Posted by dontezuma

It may well be inferior, but just stating it's so without backing it up with a reason doesn't get the conversation any further down the road.

Something to keep in mind is that every time someone provides you with helpful advice, it makes the games harder, which takes food directly off of the table of the person giving the advice.

Along that line of thought, a lot of things are left open-ended. While we're not going to intentionally give you bad advice, we're also going to hold your hand or spoon-feed you.

Spoon:

Thanks. I appreciate the somewhat self-defeating nature of blog posts on this and other sites. And I'm not asking you to spoon-feed me (!).

And I see what you're saying about the wasted time. I wasn't sure which route would prove more efficient. And really, this isn't something you do at the table, so I'm not sure it matters which is more efficient. The question is, how do you look back and analyze a hand to decide if your instinct at the table was correct, isn't it?

We don't run hands through the stove before the decision. We have to run it through our heads at the table (I think he's either got such and such, or this and that). As I see it, the whole math piece of it is to sharpen our instincts, because I can find a way to justify a lot of bad calls or bad folds by applying the wrong range to a villain. ("I put him on KK+ and that's why I laid down my QQ on a 58J flop to a raise...")

As for the food off the table, I think it's not a fair assessment to say that those who reply are "the teachers" and those who post the learners. I use the blog to sharpen my own analysis, because in verbalizing my process to others, I find holes in my own game. I want to advance the conversation as a whole for all of us, not just mooch off others' knowledge, so I hope I'm coming off that way. Collective learning is 1+1=3.

Originally Posted by dontezuma

As for the food off the table, I think it's not a fair assessment to say that those who reply are "the teachers" and those who post the learners. I use the blog to sharpen my own analysis, because in verbalizing my process to others, I find holes in my own game. I want to advance the conversation as a whole for all of us, not just mooch off others' knowledge, so I hope I'm coming off that way. Collective learning is 1+1=3.

well put dontezuma....while i am currently one of the leeches feasting on the overwhelming girth of knowledge here, i think that your sentiment about communal learning and what not is a great outlook to have.

Originally Posted by dontezuma

And really, this isn't something you do at the table, so I'm not sure it matters which is more efficient.

Actually it is.

Originally Posted by dontezuma

The question is, how do you look back and analyze a hand to decide if your instinct at the table was correct, isn't it?

No.

Originally Posted by dontezuma

As for the food off the table, I think it's not a fair assessment to say that those who reply are "the teachers" and those who post the learners.

If someone knows something I don't, and they tell me, that's +EV for me and -EV for them. Because of this, it's unfair for me to insist upon clarification of something I don't understand without a lot of effort into trying to figure things out on my own. That's all you need to assess.

mafff smafff. just click your way to the nosebleeds ldo

Originally Posted by dontezuma

One thing to consider when calculating equity and ranges is that villain's bluff% is always > 0. For close EV situations, you have to consider some air in his range.

So, in the ATT3 hand, OP had the range as {AA, 33, AK+, Tx}, but I think you have to include *some* hands like JJ, QQ, KK or QJs as part of the range, because if you don't, you'll wind up folding close calls that may be more +EV than you think.

*Disclaimer* I have no idea how much bluff to assign to villains. Obv, you can read betting patterns to sniff these out, but even if you're just looking at the cold math, you could throw in 72o to allow for some bluffing %.

What do you guys with some actual skill think of this?

first calculate your equity vs. his draws and value hands
say you have 30% and he's betting pot on the turn
estimate what he's going to do with his bluffs and when his draws miss on the river
if you think he's going to give up, then we probably can assign him 5-10% bluffing frequency and call once, fold river
if he's continuing to bluff on the river then we'll just fold turn

it makes it easier if you separate his value range and his bluffs because you can then make two different calculations and say "I can call here if he's bluffing 15% of the time, and I should fold if he's bluffing 5%, since he's not likely to be bluffing then I should probably fold"

Originally Posted by spoonitnow

Introduction

...watch this 4-5 minute video that might be NSFW for language (link).
..."

Dead link

Originally Posted by Sasquach991

Originally Posted by spoonitnow

Introduction

...watch this 4-5 minute video that might be NSFW for language (link).
..."

Dead link

Sucks for whoever missed it.

Originally Posted by spoonitnow

Introduction

(link).


.

He//o,

The video link appears to not exist.

Do we ever need to calculate the EV? Isn't it enough to state "our equity to win the pot is greater than the pot odds so it is +EV" when making our decisions? It is the same math and faster.

Originally Posted by Extremophile

Do we ever need to calculate the EV? Isn't it enough to state "our equity to win the pot is greater than the pot odds so it is +EV" when making our decisions? It is the same math and faster.

When calling an all-in, it's simply enough to know it's +EV since your only options are calling or folding (which we assume to have an EV of 0). Other times it's not necessarily sufficient to know that something is +EV since you could have multiple +EV options and would like to pick the MOST +EV one.

Is this in the digest yet? Tired of people coming in and asking whether they should call a shove with 12 outs.

Originally Posted by Extremophile

Do we ever need to calculate the EV? Isn't it enough to state "our equity to win the pot is greater than the pot odds so it is +EV" when making our decisions? It is the same math and faster.

You're correct.

Also here's a remake of the PokerStove video http://www.youtube.com/watch?v=oycsi9jQEOA

Very helpful to the newdonks like myself. Much thanks.

Bump just to say how goddamn awesome this dude's screenname is above me.

Nice video. Didn't know all the shortcuts.

I also didn't know spoon was a southern boy.
Terms like "stuff", "yallow" and "Woops, wut the hell did I pick?" show just how far south your roots go.

Personally I would have substituted the last one with "Wut the cornbread hell did I pick?" but my roots go pretty deep.

lol............

bump

Extremely useful post. I'll try and post a hand analysis later, determining whether I was +EV or -EV.

I recognize that this is a stupid question, but then I am clearly not up on the knowledge like you guys, so here goes:

How do you determine someone's range if it isn't someone you've played with a whole lot, or its someone that just came to the table?

Originally Posted by nprk

I recognize that this is a stupid question, but then I am clearly not up on the knowledge like you guys, so here goes:

How do you determine someone's range if it isn't someone you've played with a whole lot, or its someone that just came to the table?

You just estimate it the best you can. You'll very rarely be able to know exactly what your opponent's range is with 100% certainty, and that's okay. With total unknowns, you can use certain clues like what their buy-in size was and what the typical players are like at that level. With semi-unknowns, you take whatever small bits of information you have and try to extrapolate.

In general just do the best you can each time and you'll naturally get better at it, even with very small amounts of information.

Oscar directed me here earlier when I was asking about a shove call. I worked through it and thought this thread deserved a bump!

Thanks SPOOOON!

np chief

Step 4: The fraction bet/(bet+pot) is 11.5/(11.5+20), which is 36.5%. This is less than our equity of 39.394%, so it's a +EV call.

please help here: 11.5/(11.5+20) = 11.5/(31.5) = 13.239 where do we get 36.5%

You must be doing it wrong, because 11.5/31.5 is still 0.36507936507936507936507936507937 for me.

Originally Posted by spoonitnow

You must be doing it wrong, because 11.5/31.5 is still 0.36507936507936507936507936507937 for me.

yes I was. I was dividing 31.5 by 11.5. I need to do it the other way. Thanks

Originally Posted by mrhappy333

yes I was. I was dividing 31.5 by 11.5. I need to do it the other way. Thanks

Glad you found the problem. Best of luck.

Bump since apparently I linked to this thread in two different threads by the same person.

Also I forgot how big of a jackass dontezuma was.