Figuring out equity in your head, during a hand, w/out PokerStove (newbie question)

Newbie question here.... I've been doing a lot of postmortems lately on individual hands, using PokerStove to figure out my equity, posting them, etc. A lot of times the results don't surprise me at all, but often it does. I'm curious how people figure out equity (just roughly I mean) when you're playing a hand? If you don't have a read on your opponent, and you're just trying to get a ballpark idea of your equity before you play the rest of the hand, is there a way to crunch the numbers and come up with it w/out the luxury of PokerStove?

Here's an example. Keep in mind it's a math question here, not a strategy question.

On the flop I have Ahttp://forumserver.twoplustwo.com/im...lies/heart.gif Khttp://forumserver.twoplustwo.com/im...lies/heart.gif, there are 3 other opponents, and the board is Khttp://forumserver.twoplustwo.com/im...es/diamond.gif 8http://forumserver.twoplustwo.com/im...ilies/club.gif 3http://forumserver.twoplustwo.com/im...lies/spade.gif. With TPTK, no draws, and a safe board, it's not surprising that my equity is (apparently) 70% w/ the three other villains at 10%. Great, I'm a big favorite, no s--t. But is it feasible to come up with that 70% number on the fly while you're playing? I mean, is there a simple formula people use? I guess I'm asking in part because although I understand why certain hands dominate others, I kinda get how PStove gets it's #s, I don't how to come up with them w/ out software like this.

Again, I'm talking about coming up w/ rough estimates here and not about strategy. Am I just not good w/ numbers or is there something I'm missing. http://forumserver.twoplustwo.com/im...es/redface.gif

My opinion here doesn't count for much because I really don't know the answer, but I'm gonna try anyway.

Pokerstove gets its info by running a certain senario millions of times and giving a average of times hand1 beats hand2 in the form of a percentage. It would be impossible to do that in your head on the fly. The way to understand your equity in any given situation is to practice using stove vs villains range enough to make it second nature.

Hypothetically, if every time you had AK this same board flopped you would know you we're a 70% favorite because you practiced it and seen it enough times. So it's a matter of running all of your ranges vs all of villains ranges enough times to know what your equity is in any given situation.

Huh, so it's just a matter of having a lot general scenarios (like TPTK on rag board, or let's say a set w/ 4 flush on board, etc., common scenarios like that) committed to memory? at least more or less to memory?

Any good players out there find this to be true as well? Though I realize you don't have to be rainman to win, I guess I'm feeling a bit math-challenged these days and wondering if other folks out there are able to do things with their brain that I'm missin'.

Your equity is determined by how many hands you beat, how often you hold, how many hands we lose too, and how often we catch up.

Its 2 handed on the same K83r flop. We hold AK and shove the flop. Villain calls with exactly KQ, 88, and 33. What is our equity against that range? WHY???? Ignore fold equity.

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Originally Posted by rowhousepd

On the flop I have Ahttp://forumserver.twoplustwo.com/im...lies/heart.gif Khttp://forumserver.twoplustwo.com/im...lies/heart.gif, there are 3 other opponents, and the board is Khttp://forumserver.twoplustwo.com/im...es/diamond.gif 8http://forumserver.twoplustwo.com/im...ilies/club.gif 3http://forumserver.twoplustwo.com/im...lies/spade.gif. With TPTK, no draws, and a safe board, it's not surprising that my equity is (apparently) 70% w/ the three other villains at 10%.

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Can't believe no one has mentioned it yet but this makes no sense at all.

Are you assuming random hands for your opponents?

What ranges are you putting them on? Did you raise, flat a raise, or 3-bet preflop? Are your opponents loose, nitty, weak/passive, etc? Do you at least know their preflop VPIP and PFR stats? These questions are essential to determining your equity against your opponents' ranges.

In your example did you give each of your opponents a calling range? AK cannot be 70% v 3 ppls calling ranges.

Oh and the simple answer is lots of practice

Use stove hundreds of times, and get a feel for how the results come per situation. Also, you need a range to use pokerstove, so how are you going to get an answer assuming random opponents, and random ranges?

1)note your common situations
2)put opponents on ranges
3)enter into pokerstove to get results
4)do hundreds of times w/different situations
5)remember and use in play

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Originally Posted by rowhousepd

On the flop I have Ahttp://forumserver.twoplustwo.com/im...lies/heart.gif Khttp://forumserver.twoplustwo.com/im...lies/heart.gif, there are 3 other opponents, and the board is Khttp://forumserver.twoplustwo.com/im...es/diamond.gif 8http://forumserver.twoplustwo.com/im...ilies/club.gif 3http://forumserver.twoplustwo.com/im...lies/spade.gif. With TPTK, no draws, and a safe board, it's not surprising that my equity is (apparently) 70% w/ the three other villains at 10%.

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I still don't see how you got 70% without telling us the villains' ranges

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Originally Posted by JKDS

Your equity is determined by how many hands you beat, how often you hold, how many hands we lose too, and how often we catch up.

Its 2 handed on the same K83r flop. We hold AK and shove the flop. Villain calls with exactly KQ, 88, and 33. What is our equity against that range? WHY???? Ignore fold equity.

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This is a great example. If you can put your opps on a solid range, you can figure out where each hand lies in relation to your own holding.

In this example:
KQ: 8 combos that you beat
33+88: 6 combos that beat you

So, 8/(8+6) = 57% equity. It's approximate (the actual stove result is an even 50% due to the fact that the sets crush you more than you crush the KQ), but it's also doable at the table when you get good at estimating combos.

I know we don't have enough info but why are giving villain such a narrow range. @ 2nl (don't know ops stakes) QQ, JJ, is almost always continuing and TT, 99, AQ, AJ, are gonna stick around enough to exploit them too.

But I think ops original question is being over looked. JKDS gave a great explanation of what equity is but how do we do that on the fly? I still think that practice with a tool like pokerstove is the best way to get comfortable with understanding our equity vs any given range. No?

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Originally Posted by supahaole

I know we don't have enough info but why are giving villain such a narrow range. @ 2nl (don't know ops stakes) QQ, JJ, is almost always continuing and TT, 99, AQ, AJ, are gonna stick around enough to exploit them too.

But I think ops original question is being over looked. JKDS gave a great explanation of what equity is but how do we do that on the fly? I still think that practice with a tool like pokerstove is the best way to get comfortable with understanding our equity vs any given range. No?

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Obv i dont think thats actually anyones continuing range, but its a good exercise for figuring out our equity. Ya, pokerstoving things alot will get u a good feel...but only if you really understand why pokerstove says what it says. If you do understand, and you know your equity against every possible hand, then you can easily determine what your equity is without needing pokerstove if you really wanted to. Honestly, i dont really ever care what my equity is...and i rather just know that im beating so and so in villains range and behind so and so and hes folding so and so and raising so and so etc.

@nightgizmo: yup thats exactly why. KQ will suck out about 12% of the time, and we'll almost never improve against 33 or 88. So really its 8*88% : 6+8*12% which is about 50%:50%

Wow seems to me everybody is busy patting themselfs on the back for pointing out that he doesn't have his opponent on a range. The example is just an example. So the answer would be something like "Well first we put our opponent on a range. Then we figure out how often we get beat.............."

Rowhouse I wish I had the answer for you but I don't. Hopefully Spoon or somebody who actually knows will jump in soon and give you the math.

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Originally Posted by HarleyGuy13

Wow seems to me everybody is busy patting themselfs on the back for pointing out that he doesn't have his opponent on a range. The example is just an example. So the answer would be something like "Well first we put our opponent on a range. Then we figure out how often we get beat.............."

Rowhouse I wish I had the answer for you but I don't. Hopefully Spoon or somebody who actually knows will jump in soon and give you the math.

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LOL at not reading the thread and insulting everyone in it. Good job sir, good job.

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Originally Posted by HarleyGuy13

Wow seems to me everybody is busy patting themselfs on the back for pointing out that he doesn't have his opponent on a range.

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Originally Posted by supahaole

...I think ops original question is being over looked. JKDS gave a great explanation of what equity is but how do we do that on the fly? I still think that practice with a tool like pokerstove is the best way to get comfortable with understanding our equity vs any given range. No?

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This is me patting myself on the back for pointing out that I understood ops question.

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Originally Posted by JKDS

Ya, pokerstoving things alot will get u a good feel...but only if you really understand why pokerstove says what it says. If you do understand, and you know your equity against every possible hand, then you can easily determine what your equity is without needing pokerstove if you really wanted to. Honestly, i dont really ever care what my equity is...and i rather just know that im beating so and so in villains range and behind so and so and hes folding so and so and raising so and so etc.

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Now I'm patting JK on the back for giving a well thought out answer to said question.

Look at me. Now look at him. Now back at me.

I'm on a horse.

Point(s) well taken! I should have read deeper my sincere apology!

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Originally Posted by HarleyGuy13

Point(s) well taken! I should have read deeper my sincere apology!

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Graciously accepted.

@JKDS- Got any popcorn left?

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Originally Posted by supahaole

Graciously accepted.

@JKDS- Got any popcorn left?

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i got som box candeys

Sorry for the delayed response, guys.

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Originally Posted by JKDS

Its 2 handed on the same K83r flop. We hold AK and shove the flop. Villain calls with exactly KQ, 88, and 33. What is our equity against that range? WHY???? Ignore fold equity.

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Are you just asking a hypothetical here? Because realistically I'd put someone one AA, KK, AK (two of which crush me) before I'd put someone on 88 or 33.

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Originally Posted by Imthenewfish

I still don't see how you got 70% without telling us the villains' ranges

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This 70% from Stove assume 3 opponents play any random cards to the showdown -- which I do realize is what's going to happen very often. I put in random bc I was using a theoretical scenario where I have no reads on the villains and assume I could be up against anything. Remember, I was asking a hypothetical mathy question rather than one where you're reading players, etc.

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Originally Posted by JKDS

@nightgizmo: yup thats exactly why. KQ will suck out about 12% of the time, and we'll almost never improve against 33 or 88. So really its 8*88% : 6+8*12% which is about 50%:50%

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Uuug. Brain meltdown. So confused about this one. It's ok, you don't need to explain. Just realizing I need to work on this sort of thing. :confused:

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Originally Posted by supahaole

But I think ops original question is being over looked. JKDS gave a great explanation of what equity is but how do we do that on the fly? I still think that practice with a tool like pokerstove is the best way to get comfortable with understanding our equity vs any given range. No?

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That's right. In this thread I just kinda wanted to know what kind of calculations you do during the hand. Well I guess I wasn't sure if coming up with a raw # that reflects the probability of my hand winning was useful to know as a kind of, I dunno, basis for determining how to proceed in that hand. I was wondering if the thought process (in real time at the table) would be, like...

"Ok, I know that TPTK on a dry board vs 3 opponents is about ~70% ... and I know one of the villains has an average range and two of them are super nits ... so my equity is really got to be less than 70% ... probably more like 60% maybe ... I can't be sure (since I don't have PokerStove embedded in my brain) but it's definitely less ... so now if I bet, two will probably call, which give means my implied odds are ..." Well you get the idea.

Basically, I'm just wondering about how the thought process works as you play a hand, and whether you start w/ a raw math-based equity %, then work through the strategy stuff after that.

Im pretty stumped on how to quickly respond and change your thinking via a forum post alone. Hit up IRC and ask why

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Ok, I know that TPTK on a dry board vs 3 opponents is about ~70% ... and I know one of the villains has an average range and two of them are super nits ... so my equity is really got to be less than 70% ... probably more like 60% maybe ... I can't be sure (since I don't have PokerStove embedded in my brain) but it's definitely less ... so now if I bet, two will probably call, which give means my implied odds are ...

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this isnt great thinking.

JKDS was just creating a hypothetical situation, purely as an exercise to teach a concept. His example shows what you can actually do at the table.

Also -- please erase from your memory the erroneous thought that "TPTK has 70% equity vs 3 opponents". You will never use that in any at-the-table calculation ever.

Instead, you will use the same process you always use: figure out a range and then calculate equity. The only difference is that at the table, you use mental shortcuts to estimate your equity.

I know the next question: "What shortcuts?" Well, it depends. It depends on what works for you as a shortcut. For some people, they can quickly juggle a bunch of different numbers in their head and spit out an answer. For others, they can mentally sort the different hands in a range by strength, and then combine them to get an estimate of strength ("he has 8 dominated pairs and 6 sets, those end up canceling each other out to break even"). Maybe you just plug values into PokerStove, but before you ever hit the "Evaluate" button, you try to get your own estimate and see how close you get, then eventually just get good at intuitively knowing the equity.

Bottom line: whatever works for you, use it. It's one of those things that doesn't have a single, one-size-fits-all solution, because what works for some people will seem impossible to others that can still get the same results using different methods.

So what happens during live games? Do the top players know hundreds of equity values from memory or is equity not used as much when making decisions?

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Originally Posted by rowhousepd

This 70% from Stove assume 3 opponents play any random cards to the showdown -- which I do realize is what's going to happen very often. I put in random bc I was using a theoretical scenario where I have no reads on the villains and assume I could be up against anything. Remember, I was asking a hypothetical mathy question rather than one where you're reading players, etc.

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OMGWTFBBQ

There is so much wrong with this I don't know where to begin.

"70% assumes 3 opponents play any random to showdown and that's whats going to happen very often". Seriously? Do you think this is true?

Clearly you are not getting the point here. Using stove to figure out equity implicitly means we must put our opponents on ranges. Putting opponents on ranges is not necessarily based on 'having reads' on them. Seriously, you are going about this all wrong. The worst part about it is you're justifing it and trying to convince others what you're doing is correct.

Let me give you an example of a situation where I would use a random range to figure out my equity. Preflop, I`m a shortstack in a tournament in the small blind and will have to shovel my chips in regardess of what I hold once the action makes it`s way to me (assume I have like 1.5 BBs left).

Assume first that the action folds all the way around to me; I get my chips in, and the BB is now forced to call since my stack is so short and all the dead money in the pot.

Here we can assign a truly random range to our villain, because we know he`s calling even if he looks down at 72o (which, even if I held AKo, isnt that big a dog).
`
So we can see now that valuing our hand versus random ranges is fairly useless as it only really applies to few and infrequent situations.

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To get back to your example, you stated that stove told you that you had a 70% equity share of the pot while your three opponents had 10% each. But what happened preflop?

Let's assume that preflop, you failed to raise and instead decided to limp along with each of these players. So what cards are they limping with? AA? KK? no, probably not. But hands like 22-88, QTo, JTo might be in that range.

It's pretty obvious that even limping preflop involves some kind of hand selection. Why then, condemn ourselves to assigning 'random' hand ranges postflop?

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Originally Posted by Tasha

So what happens during live games? Do the top players know hundreds of equity values from memory or is equity not used as much when making decisions?

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only the top live players that are also the good/professional online players really have a lot of equity values memorized imo

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Originally Posted by Tasha

So what happens during live games? Do the top players know hundreds of equity values from memory or is equity not used as much when making decisions?

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I would assume that top players in live games, don't necessarily have to know equity values, but would think that they are putting their opponents on ranges, and comparing their strength to their ranges; i.e. how many combinations in their opponents ranges do they beat/how many of their opponents hands are strong drawing hands, etc?

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Originally Posted by bhaley66

I would assume that top players in live games, don't necessarily have to know equity values, but would think that they are putting their opponents on ranges, and comparing their strength to their ranges; i.e. how many combinations in their opponents ranges do they beat/how many of their opponents hands are strong drawing hands, etc?

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i thought a lot of good live players didn't know how to put people on ranges

I have no way of telling for sure, but I find that highly unlikely...

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Originally Posted by bhaley66

I would assume that top players in live games, don't necessarily have to know equity values, but would think that they are putting their opponents on ranges, and comparing their strength to their ranges; i.e. how many combinations in their opponents ranges do they beat/how many of their opponents hands are strong drawing hands, etc?

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So why don't online players do the same thing? Is it because equity can be used to calculate EV?

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Originally Posted by Tasha

So what happens during live games? Do the top players know hundreds of equity values from memory or is equity not used as much when making decisions?

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i think that the top players have too much experience and probably have hundreds of equity values from memory but tnote that they are playing live, hense there are a number of other things which are important for the game, like reading your oponent, being able to bluff and so on.

I want to simplify your example and calculate the equity only against one opponent for you to get a feel of it. Rest is up to you...

Here is how I do it at the table if needed:

First you have to have a range for your opponent. Say you bet the flop and got raised, and you put him on QQ, 88, 33, KQ, K8s.

QQ -> 6 combos (he needs another Q to win, his equity is ~9%, 0.5 combo beat you, you beat 5.5)
88 -> 3 combos (you have almost 0 equity, 3 combos beat you, you beat 0)
33 -> 3 combos (you have almost 0 equity, 3 combos beat you, you beat 0)
KQ -> 8 combos (he needs a Q to win, his equity is ~13%, 1 combo beats you, you beat 7)
K8 -> 1 combo (you need an A to win, your equity is ~13%, given that this is a tiny part of his range, we can ignore this 13%, 1 combo beats you, you beat 0)

So, there are 21 commbos in his range, 8.5 of them beat you and you beat 12.5.
Your equity is 12.5/21 =~ 60%

And if we put it in stove:

Text results appended to pokerstove.txt
20,790 games 0.040 secs 519,750 games/sec
Board: Kd 8c 3s
Dead:
equity win tie pots won pots tied
Hand 0: 60.055% 59.81% 00.24% 12435 50.50 { AhKh }
Hand 1: 39.945% 39.70% 00.24% 8254 50.50 { QQ, 88, 33, KQs, K8s, KQo }

The fact is that you're probably never going to get the exact numbers. Sure you can assign a range and then calculate the # of combos by using the rule of 16 combos per non PP hand and 4 combos per PP minus the # of combos that have blockers in your hand and on the board. Then it's a simple division problem to figure out your equity. However, doing all of these steps during full tilt's 15 second time bank is not usually going to be very easy to accomplish unless you're extremely good at quick math in your head.

So the real answer is pretty much just what yaawn said. Practice. Eventually you'll learn certain common numbers but a lot of the time you'll just have to ballpark things since ranges are never set in stone and may even be wrongly assigned.

First off, typo alert! My bad, sorry guys.

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Originally Posted by rowhousepd

This 70% from Stove assume 3 opponents play any random cards to the showdown -- which I do realize is what's going to happen very often

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I meant to say: "which I realize is NOT what's going to happen often." Big difference. Think that lead to some confusion. (Promise I'll preview my posts from now on.) ;)

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Originally Posted by JKDS

Im pretty stumped on how to quickly respond and change your thinking via a forum post alone.
....
this isnt great thinking.

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I do know that. In fact what I mean to illustrate (though it may have come across differently) was one possible way of thinking through the decision making process, starting w/ a pre-memorized equity # specific to that TPTK dry board scenario, then changing that number depending on what kind of range I thought my opponent had.

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Originally Posted by NightGizmo

Also -- please erase from your memory the erroneous thought that "TPTK has 70% equity vs 3 opponents". You will never use that in any at-the-table calculation ever.
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Instead, you will use the same process you always use: figure out a range and then calculate equity. The only difference is that at the table, you use mental shortcuts to estimate your equity.

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I'm wiping my mental hard drive clean of the above line of thinking. The advice to figure out range and then equity pretty much gets to the crux of my original question. Mostly I'm trying to figure out which part of the puzzle to begin with.

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Originally Posted by Penneywize

"70% assumes 3 opponents play any random to showdown and that's whats going to happen very often". Seriously? Do you think this is true?

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Nope, as I said it was typo. I was just trying to imagine theoretical, no-reads situation. Like I mentioned, I've been wondering which comes first in your head as you play a hand -- a calculation of equity (based purely on the scenario), or a guess about the villain's range. Obviously it sounds like figuring out the range precedes the equity estimate. About the other things pointed out, Penneywize, your point is taken. Thanks for the help.

From what most of you guys said, it sounds like if the villain's range contains hands that, for the most part, the hero is a big favorite over, the equity is high. But when his range consists largely of hands that crush the hero, the equity is probably bad. Is this more or less accurate?

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Originally Posted by Belt

So, there are 21 combos in his range, 8.5 of them beat you and you beat 12.5.
Your equity is 12.5/21 =~ 60%

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So once you narrow down the hands in the villain's range, you think about the math in terms of combos?

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Originally Posted by rowhousepd

So once you narrow down the hands in the villain's range, you think about the math in terms of combos?

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Yes, I beleive this is the easiest way to calculate equity without stove. But I also beleive that one would very very rarely need this kind of calculation during the hand. In other words, while it's good for practice/analysis, it's unnecessary during the gameplay.

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Originally Posted by rowhousepd

From what most of you guys said, it sounds like if the villain's range contains hands that, for the most part, the hero is a big favorite over, the equity is high. But when his range consists largely of hands that crush the hero, the equity is probably bad. Is this more or less accurate?

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Correct, but emphasis on for the most part because of drawing hands... Have you read Hand Combinations yet? I think this thread in particular will help out with a lot in understanding the responses about combinations.

No, I hadn't read it ... yet. thanks!

Just use sense and don't worry so much about the numbers. Think of the hands beating you at that point and which hands could draw to beat you. 38 unlikely K8 unlikely. etc.

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Originally Posted by Belt

I want to simplify your example and calculate the equity only against one opponent for you to get a feel of it. Rest is up to you...

Here is how I do it at the table if needed:

First you have to have a range for your opponent. Say you bet the flop and got raised, and you put him on QQ, 88, 33, KQ, K8s.

QQ -> 6 combos (he needs another Q to win, his equity is ~9%, 0.5 combo beat you, you beat 5.5)
88 -> 3 combos (you have almost 0 equity, 3 combos beat you, you beat 0)
33 -> 3 combos (you have almost 0 equity, 3 combos beat you, you beat 0)
KQ -> 8 combos (he needs a Q to win, his equity is ~13%, 1 combo beats you, you beat 7)
K8 -> 1 combo (you need an A to win, your equity is ~13%, given that this is a tiny part of his range, we can ignore this 13%, 1 combo beats you, you beat 0)

So, there are 21 commbos in his range, 8.5 of them beat you and you beat 12.5.
Your equity is 12.5/21 =~ 60%

And if we put it in stove:

Text results appended to pokerstove.txt
20,790 games 0.040 secs 519,750 games/sec
Board: Kd 8c 3s
Dead:
equity win tie pots won pots tied
Hand 0: 60.055% 59.81% 00.24% 12435 50.50 { AhKh }
Hand 1: 39.945% 39.70% 00.24% 8254 50.50 { QQ, 88, 33, KQs, K8s, KQo }

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Can you please tell me how you figured out the equity? I understand how you got the combinations, but not how you figured out equity. Thanks.

With QQ Hero is ahead, so Villain needs to catch 1 of 2 outs. Drawing to 2 outs is ~9% for 2 streets (~4.3% per card). There are 6 ways Villain can have QQ, so 6 combos @ 9% equity each : 6*9% = 45% ~= 0.5
So the combo equity for QQ : 0.5 for Villain, 5.5 for Hero

With 88 Villain is ahead and Hero needs to catch runner-runner Kings, which is a horrible spot to be in and the equity is so small that it's not really worth counting. There are 3 ways villain can have 88, since one 8 is on the board, so 3 combos @ 100% equity each : 3*100% = 300% = 3
So the combo equity for 88 : 3 for Villain, 0 for Hero

Continue this for all pockets in Villain's range and then do the maths.

Add the total number and put that in the denominator.
Add the total number that go to Hero and put that in the numerator.

Nice - Thanks 3M

And Thanks to ryan4h for bumping a useful thread...

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Originally Posted by ryan4h

Can you please tell me how you figured out the equity? I understand how you got the combinations, but not how you figured out equity. Thanks.

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So, there are 21 commbos in his range, 8.5 of them beat you and you beat 12.5.
Your equity is 12.5/21 =~ 60%

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