Equity??? Warning: May Hurt Heads!

[Thunder]

Howdy folks,

So far, you guys have helped clear up many of the fundamentals implied odds, playing for sets, priced in ATC, EV & FE etc and now I am onto my next big hurdle. In fact, I wasn’t even aware of it until I was reading a strategy guide.

It involves maths and this is where I am getting confused. So patience please. And to ensure that we don’t go round in circles, if you can understand where I am coming from, rather than just telling me the correct answer, then that will go a long way to getting me on the right track. Thanks.

I think it’s called equity. I am already familiar with ICM but not what I am about to run through here.


Ok, here is the article in question:
You are playing $1/$2 short handed and have raised pf to $8 with QQ UTG. It folds to the BB who goes all in for $48 and you have a stack of $112. As it stands, you have to call $40 to win $59.

He is a fairly straight forward villain who raises little pf and through history you can assign him a range from JJ – AA, AKo & AKs.

Against this range you have a 45.6% chance of winning if he has JJ - AA and that to call would be +EV. If JJ is not in his range then your equity drops to 40% and is thus an easy fold.

And this is where I get confused.


1) The head hurting bit. I know this is NOT pot odds but the EV aspects should work out the same. Ie: the maths shows that if the pot odds are greater than the odds of winning then that is a winning play whilst calling when the pot odds are lower then that is a losing play – eg: paying 1/2 pot to chase a 1/6 draw is -EV as it will lose you money over time.

So even though this is NOT pot odds, I cannot understand how calling with just a 45.6% chance to win is good as the pot odds on offer (call $40 to win $59) means you need a 67% chance to call.

In this example, the pot is offering 2/3 yet as you stand just 45.6% (barely 1/2) to win then the pot needs to offer in excess of ½ to make such a call profitable – such as 1/3 or1/4.


Now, I was able to email the person who wrote the article and he sent me this reply:

You are a 45% chance to win the pot against his range. In other words you are going to win 9 times out of every 20. For each of the 11 times you lose you lose $40. For the 9 times you win you get $59. So if you ran it 20 times you would lose $440 (11 x 40) and up $531 (9 x 59). So you would end up a long-term winner by making this play.

The maths that he shows does add up to a winning play. But I don’t understand how it adds up to a winning play because from my perspective, this completely undermines the maths of pot odds. As mentioned, if you chase 2/3 bets with just 1/2 chance of success then the maths shows that it is a losing strategy – hence the maths behind pot odds. Yet here, his maths shows that making such calls is profitable.

Also, he just told me the answer but that didn't get through and I felt too embarrrassed to email him again. And that si why I ask that you try and see where I am coming from and then explaining - rather than than just tell me the answer as he did.

2) If 45.6% to win is a profitable call then how can just falling to 40% if he doesn't have JJ be a losing call?


3) As for the equity aspect, I think it's called that as in another thread someone said to call an all in with just a pair of QQ means your equity is only 50% - but how is that figured out?


Once again, help and thanks!

[taipan168]

Don't have a lot of time now for a detailed reply, but I think you're getting mixed up when you're converting percentage odds into fractional odds. For example, if you're 25% to win, this is actually 3 to 1 odds not 4 to 1 (since you win once and lose three times).

[CoccoBill]

1) You're not on a draw here, you have a made hand and you're looking at the odds of it being better than your opponent's. You both have a fairly equal chance of improving, so it can be taken out of the equation.

When chasing draws you have zilch zero nada, and are just hoping you'll hit on later streets. The chance of you hitting your draw needs to be greater than the pot odds.


2)
4*59=236
6*40=240

You lose $4 every 10 games.

3) I'm not sure what this is refering to.

[Warpe]

1) Apples and oranges. You have a strong made hand that you should be happy to get all-in with against a wide enough range.

2) If your equity drops to 40% then you lose one more time out of 20 and win one less time, ie. lose 12 x 40 = $480, win 8 x 59 = $472, so you lose $8 or $0.40 per hand as opposed to the first example where you win $91 or $4.55 per hand. This turns a long-term winning play into a long term losing play, albeit a marginal one.

3.) Download Pokerstove and play around with ranges.

[spoonitnow]

It is pot odds btw.

If your chance of winning > your % put into the pot, etc.

[pgil]

Don't have a lot of time now for a detailed reply, but I think you're getting mixed up when you're converting percentage odds into fractional odds. For example, if you're 25% to win, this is actually 3 to 1 odds not 4 to 1 (since you win once and lose three times).

what he said

[Thunder]

Thx for the replies.

Tai, nowt to do with the ratios. I know 33% is 1 in 3 which is 2:1.

I just don't understand how if you're around 50% to win, it can be profitable to call an all in when the price isn't viable.

Ok, so you're not chasing any outs, but surely the same concept applies: paying over the odds will garner a -ve return? or to use the maths from this example: if you were 45% to hit the card to make your winning draw, calling a 2/3 bet would be bad, long term. So why isn't it here? You're still 45% to win yet are calling 2/3 pot.

Thus the money you win will not make up for the money you lose (which is the principle behind pot odds). Were you to win just 45/100 but win 4 times your investment each time, then I do see how it's a winning strategy. But that's not the case.

But by doing so, I am following the general math behind pot odds where the times you win, even just 33/100 are profitable because the money you win outweighs the money you lose the other 67 times. As said, perhaps that is wrong but that is how I learnt that you need sufficient odds to make a profitable play.

Then spoon says it is pot odds, whch confuses me more.


In short, I assumed the principles would hold true and that you have to have better ROI odds than odds of winning in order for any play to be profitable.

[langaan]

I may be a noob, and am prolly going to learn something here after posting this lol.. but



OP's confusion is comming from the fact that the % of pot to be called is Higher than the % chance to win. I think this would make more sense to OP if the pot odds were calculated correctly ...

the 9 times you lose, you lose $40
but the 11 times you win, you win $59.
this math is correct,,,
but I think OP may be able to make better sense out of this with the below math...

you pay $40 20 times regardless
you win $99 9 times

so i guess the math you are looking for that would make sense is to use the final pot for you pot odds.

IE: $40 to call and win $99 = 40.4%, and you win 45% of the time.

that about right thunder?

anyways, the reason the math in the article doesnt make sense is because the "winning" calculations doesnt include the $40 you win back from your call

[pgil]

you don't win back the $40 you put in the pot.

The confusion seems to stem from op's conversion from % to ratios.

If you are 50% to win a hand, any amount that your opp bets will be a +EV call. If there is $1 in the pot, and your opponent bets $100, you need 1:1 odds to call, and are getting just slightly better than 1:1 (101:100). It is pretty well breakeven, but still just slightly positive.

In this example, you are ~46% to win, which means that you need 1.17:1 odds to make the call. you are getting 1.475:1 odds on your call.

And I just realized where your mistake is. You are putting the pot odds backwards. If you are facing a bet of 10, and there is 50 in the pot, you are getting 5:1 odds, not 1:5. In your example, you are stating that 2:3 odds aren't good enough to make the call, but 3:2 are.

[Warpe]

Don't forget that you have equity in your call as well, $16 at 40% equity and $18 at 45% equity.

Pot is $59 + your call of $40 = $99. Your equity of 45% will be $44.55 in the called pot so $40 is an easy call, but cut your equity to 40% or $39.60 and now it's a really close fold.

Give villain $40 more, make pot $99 + your call of $80 = $179. Equity @ 45% = $80.55, call $80 so it's still a call, but a much closer one. At 40% your equity is $71.60 so a call of $80 is now a clear fold.

This is why a hand that is an easy a/i call against a shortstack can also be an easy fold against a full-buy.

[Pelion]

...means you need a 67% chance to call.

You NEVER need more than a 50% chance to win to make a call correct.

DUCY?

[jyms]

[pankfish]

to make a call getting 50% a bad call you have to be getting worse than 1:1 pot odds. You are never getting worse than 1:1 on any call.

[Thunder]

The lightbulb has finally switched on.
Thx to Warpe, Pgil, Pankfish and co.

I had written a lengthy response (which showed I understood pot odds but was still lost) and also had this feeling that I was on the verge of a revelation. By the time I wrote it, Pankfish had replied, which only added to my sense of "almost getting it."

Basically, I kept thinking that a 2/3 pot bet priced out a 50% shot and that only a 100% certainty could call a pot sized bet and a 50% hand could only call a 50% pot bet. However I eventually realised my flaw: I wasn't adding the bet onto the pot, which increases the odds on offer. D'oh!

The comments that I was getting the odds backwards threw me off as well as I knew that 1 in 5 = 4:1 and knew I was working them out correctly. Yet Warpe's explanation made total sense. And pgils method threw me too. Hence my mass confusion.

Only by breaking down and explaining pot odds to show that I actually understand them did I finally realise that a 2/3 pot bet actually offers odds of 1 in 2.5 or 1.5:1. Eg: a bet of 100 into 150 means you have to call 100 to win 250. The pot is offering higher odds than you need to win and this fully complies with the rules on pot odds, that you can only call if the odds are higher than your odds to win. Ta da! It all tallies up and makes sense! Now all is well with the world.

But it took me a long, long time to get to that point, lol.

Thx for the explanations (which I didn't get due to my glaring blind spot) and thx for making me think and work out where I was going wrong.

[Thunder]

Boy do I feel stupid?

My previous post explaining I “got it” was total BS. The example of calling a 2/3 pot bet was sound in terms of pot odds, if you had a 50% chance to win but the example provided, holding QQ and needing to call $40 to win $69 was an all in and the all in was way more than a pot sized bet. Therefore, you weren’t being asked to call a 2/3 pot bet. Rather you had to call a 2/3 bet.

So I am back to square one

Warpe’s explanation was simple: your equity is $45 and you need to call $40 to win. Is this all I should be looking at when it comes to determining a call – calculate my equity and if the that equity is larger than the required bet, call; if not, fold?

If so, how do I go about working equity on the fly?


If pot odds is still involved, or rather the maths behind it, then I get stuck again. A 50% chance is 1:1 and so I understand how you can call a pot sized bet and break even in the long run. In this example though, villain has jammed the $11 pot with his last $48. In this scenario either you can still call ANY bet at ANY time with a 50% shot or, as I am leaning to, you can only call a 1:1 bet. Raising the pot by 4x negates this option.

Please advise.

Thx

[biondino]

Thunder your second last post was right!!

Here, you are calling $40 to win $99. So if your cards will win MORE than 40 times every 99 hands, the call is right - this equates to 40.4%, so with the villain's initial range it's an easy call and with the villain's revised range (without JJ), it's a marginal fold.

The last para of your last email makes no difference. Because whatever bet the villain makes is added to whatever's in the pot, it's impossible for him to ever make a bet that will require you to be more than 50% to win for your call to be right. If the pot is $5 and he bets $50, then the pot is $55. But you only have to call his bet, i.e. bet $50, which is LESS THAN HALF THE RESULTING POT of $110. Do you see?

This is so simple, so basic and so important I am worried you have over-analysed and are getting confused by numbers which have no place in the calculations. Try and clear your mind and really think about what a call is - you are matching a bet which increases the size of the pot.

The only way you could have a 1:1 situation would be if there were no blinds, i.e., the pot was $0 before the villain's bet. This will never happen, so you will never need as much as 50% to justify a call.

[pankfish]

It doesn't matter if they bet 20x pot. You are still getting better than 1:1.

[Warpe]

If so, how do I go about working equity on the fly?

Seriously, download Pokerstove if you haven't already and start memorizing. There's really not that many you have to keep in your head.

QQ vs ranges in the OP:

297,940,896 games 0.005 secs 59,588,179,200 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 40.207% 38.35% 01.86% 114253440 5540034.00 { QQ }
Hand 1: 59.793% 57.93% 01.86% 172607388 5540034.00 { QQ+, AKs, AKo }

359,583,840 games 0.005 secs 71,916,768,000 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 47.366% 45.79% 01.58% 164644764 5675268.00 { QQ }
Hand 1: 52.634% 51.06% 01.58% 183588540 5675268.00 { JJ+, AKs, AKo }

[pankfish]

poker stove is free btw.

www.pokerstove.com

[langaan]

you don't win back the $40 you put in the pot.
.

huh? you win the $40 back 45% of the time.
if not, I need to go back to grade school.

seriously,

for the sake of "on the fly"math for OP, here is what I do in my head when i am in a hurry, dont know if this will help or not...

if your chance to win is 45%....

vill bets 40 into 59 means you need to call 40 to win a pot of 99.

40 / 99 = 40.4%

you chance of winning (45%) is higher than your call/pot ratio of 40.4%.

it may be a different way of thinking then what most posters are trying to explain, but its still the correct math.

this help at all thunder?

[pgil]

perhaps I misread something, I had thought I had read a post where the call was being included in the pot odds calculations, which is what I was refering to. For the purposes of those calcs, you are not winning the call.

[langaan]

perhaps I misread something, I had thought I had read a post where the call was being included in the pot odds calculations, which is what I was refering to. For the purposes of those calcs, you are not winning the call.

ah ok.

well actually that was the purpose of the post, to explain to the OP that the call isnt included in the pot odds math,,,
and to explain that that may be why it is confusing him more or less.

[Thunder]

Simple things first, I will DL Pokerstove. I hope this be used on the fly when you only have 30 seconds to act in a game or that it's easy to memorise the main numbers as Warpe said.

Pankfish, yup, 1:1 is good for any bet, I see that now. I just ran some basic examples. The bigger the bet, in relation to the pot, the smaller the ROI but as you said, it will always be higher than the amount you risked. So, that explains why I can call any bet with 50% or better. Great. But the maths is still befuddling. So onto Biondino. The good news in all this is that I think I have cracked it.


Biondino, thx for the reply but I don't see how my 2nd to last post was right because I got confused and talked about calling a 2/3 pot bet yet in the example given, there wasn't a bet of 2/3 pot, it was an all in. The pot was $11 and he overbet the pot, hence my revised pot odds was incorrect.

you are calling $40 to win $99

This confuses me as well as the way learnt is that you never add your bet when looking at facing a bet, so it would be call $40 to win $59, not call $40 to win $99. Are you saying I should do this - so when the pot is 100 and it's $20 to call I should see it as $10 to win $120 instead of $20 to win $100"?

As I now understand that any call is viable when you're 50% to win then I don't see the relevance of stating that it's $40 to win $99. Surely it's just a case of "I'm good to call any bet, go go go!"


Here, you are calling $40 to win $99. So if your cards will win MORE than 40 times every 99 hands, the call is right - this equates to 40.4%, so with the villain's initial range it's an easy call and with the villain's revised range (without JJ), it's a marginal fold

Now this is what I think I am beginning to understand. And if I am right, it has nothing to do with pot odds at all. It seems to be just a simple case of "is the equity greater than the cost of the call? If so then call".
On this basis then, the following is true:

$40 to call - $30 equity = fold
$40 to call - $90 equity = call
$100 to call - $45 equity = fold
$50 to call - $47 equity = fold
$65 to call - $70 equity = call

If these examples are correct then by Jove I think I may have cracked it! However, there are a few more questions if this is the case. If it is literally a matter of "is the equity greater than the cost of the call? If so call" then:

1) what about pot odds? If I have 20 outs on the flop and I am put all in, I will call because pot odds say I am a favourite. I am not referring to equity.

2) As I use pot odds when needing to improve, is equity only to be used when you have a made hand and are facing a bet? If so, what about a made hand that may need to improve, like top pair with a flush draw - do i refer to equity or odds of hitting the flush?

3) If the above examples are true, and I wanted to work them out manually, without Pokerstove, would I have to add on my call as you did when you said $40 to win $99? As said, this is not the way I was taught but it does make it easier to work out whether your equity exceeds the bet, making it +EV to call.

4) What about Dan Harrington's methods of evaluating equity? As in my other post he mentions different ways to do this, can I just ignore these long winded routes?

[pankfish]

1) what about pot odds? If I have 20 outs on the flop and I am put all in, I will call because pot odds say I am a favourite. I am not referring to equity.

no, the pot odds don't tell you anything. The odds of you winning the pot at showdown is your equity. Your equity is what you compare to the pot odds when deciding if a call is +ev.

[pgil]

perhaps I misread something, I had thought I had read a post where the call was being included in the pot odds calculations, which is what I was refering to. For the purposes of those calcs, you are not winning the call.

ah ok.

well actually that was the purpose of the post, to explain to the OP that the call isnt included in the pot odds math,,,
and to explain that that may be why it is confusing him more or less.

OK, I just went through and found it. In your equity calculations you said that you win $99 9 times, but you don't. You win $59, here is where you have added your call into your winnings.

[Warpe]

Warning: May Hurt Heads!

[Pelion]

Thunder. Im going to try to explain this slowly. Tell me how far you get.

1) If you want to work with odds you win the pot + your opponents money and you lose your money. If you are thinking of calling a pot sized bet of $100 then you are calling $100 (yours) to win $200 (not yours). Thats 2:1. That means you need to win half as often as you lose so you need to win 33% and lose 66% (or better) to make a profit.

2) If you want to work with percentages and equities then you do it like this.

3) Your bet is the amount you pay to have a chance at winning the total pot. Its like a fee to see the last card. At the end of each hand you will get some amount back. Sometimes that amount will be 0. Sometimes it will be the full pot. On average over millions of hands you will get an average amount back from the pot. Does this make sense so far?

4) Ok lets suppose our call is $100. If we get back $100 on average we have broken even. If we get back $110 on average then we are making an average of $10 per hand. The EV is then +$10. If we get back $90 on average then the EV is -$10. Does this make sense?

5) Ok now lets suppose the pot is $100 on the river and our opponent bets $100. We have to call $100 to see the showdown. That $100 call will make the total pot $300. Sometimes we are going to get back $300 when we call, and sometimes we are going to end up with nothing. But in order to turn a profit we need to get back an average of at least $100 (see 4). Since $100 is 33% of $300 that means we need to have at least 33% equity in this pot to make the call. Does this make sense?

[Thunder]

Thunder. Im going to try to explain this slowly. Tell me how far you get.

1) If you want to work with odds you win the pot + your opponents money and you lose your money. If you are thinking of calling a pot sized bet of $100 then you are calling $100 (yours) to win $200 (not yours). Thats 2:1. That means you need to win half as often as you lose so you need to win 33% and lose 66% (or better) to make a profit.

Gotcha – simple pot odds.

2) If you want to work with percentages and equities then you do it like this.

3) Your bet is the amount you pay to have a chance at winning the total pot. Its like a fee to see the last card. At the end of each hand you will get some amount back. Sometimes that amount will be 0. Sometimes it will be the full pot. On average over millions of hands you will get an average amount back from the pot. Does this make sense so far?

Yes – and still sounds like odds. Is the price to see the last card and try to make your hand EV+ or not? If so – call. If not – fold.

4) Ok lets suppose our call is $100. If we get back $100 on average we have broken even. If we get back $110 on average then we are making an average of $10 per hand. The EV is then +$10. If we get back $90 on average then the EV is -$10. Does this make sense?

This still sounds like odds. Winning $110 is +EV and is the result of not paying over the odds to hit your card to win. Winning $90 can be the results of paying over the odds.

There is no mention of equity in the pot to measure the bet of $100 against so cannot see how this is equity so I stick with it being odds.

5) Ok now lets suppose the pot is $100 on the river and our opponent bets $100. We have to call $100 to see the showdown. That $100 call will make the total pot $300. Sometimes we are going to get back $300 when we call, and sometimes we are going to end up with nothing. But in order to turn a profit we need to get back an average of at least $100 (see 4). Since $100 is 33% of $300 that means we need to have at least 33% equity in this pot to make the call. Does this make sense?

This is equity as you are measuring your equity in the pot against the bet that is to be called.


What I don't understand is
a) the difference between odds and equity and when to use which. for example, in your (5) you mentioned equity when on the river yet the QQ example in my first post used it on the flop.

b) Self computation of equity and whether it's EV to call or not - though think I answered that in my above post: is calling the bet going to return more than that bet?

To go back to odds and equity. I currently make calls based on my pot odds and odds of hitting my cards & winning. This way I know if I am making +/- EV calls and whether I am getting expressed or implied odds.

If I already have a made hand - like AA, a straight or flush - then I will call/push all in as long as I still believe that the hand is good. That's all I do. I am currently not running my made hands through any equity analysis.

It's obv important so at what stage of the hand should I be looking at using it?

Talk of equity and using that to decide whether you call or not has thrown me. Do they do the same job and it's just up to you which method you use? Or do they both have their own situations? Is equity better used for when you have a hand but unsure if it's ahead - like the QQ example I provided?

To be honest, the QQ example I used to kickstart this thread just sounds like odds to me. Eg: QQ is 55% favourite against KA, 82% favourite over JJ and 45.6% favourite against JJ-AA & KA.

[pgil]

equity is basically the % time your hand should win. You use this in conjunction with pot odds to determine whether to call or not. when you are comparing the odds being offered to your chance to win, you are comparing the pot odds vs. your equity.

It sounds like you are just getting confused with terminology, and not the actual concepts.

[Pelion]

the difference between odds and equity and when to use which

There isnt really much of a difference. They both calculate the same number, just in a slightly different order. I tend to think in terms of equity when im considering semibluffing or calling against a fairly wide range, and pot odds when im thinking of calling on a draw or calling with a made hand against a fairly narrow range on the river. Thats not because its the best way to do it. Its just because its what I find easier. As long as you understand how to do both of them I wouldnt wonder about what the "differences" are because there arent any important ones.

[Thunder]

Pelio, Pgil,

Thx for that - seems I was confusing the two.

So, just to confirm, with my 4 to the heart nut flush on the flop and after my opponent showed me he has Ac As before putting me all in, my odds of winning with a flush is approx 36%. Therefore my equity is 36% of whatever the pot is, yes?

Likewise, whatever my odds of winning at any stage of the hand - such as 70/30, 65/35, 90/10 - is a measure of my equity of the pot?

I guess I prefer pot odds but the QQ example in my first thread really showed the benefit of equity - showing how it is mathematical correct to call. Without that example, I would just call or fold depending on whether I think I'm ahead or the state of my tourney stack.

Guess I can use it in decisions like that, rather than my usual "I have QQ, he could have AA but, here goes........"

[Jibalob]

You are playing $1/$2 short handed and have raised pf to $8 with QQ UTG. It folds to the BB who goes all in for $48 and you have a stack of $112. As it stands, you have to call $40 to win $59.

I'm still struggling to understand how the pot is $59

[Pelion]

i assumed he meant $56. if im wrong corredct me. If im rigfht dont pick holes in the least importnant peice f thos

edit: forget that. blinds are $3.

[animal_chin]

You are playing $1/$2 short handed and have raised pf to $8 with QQ UTG. It folds to the BB who goes all in for $48 and you have a stack of $112. As it stands, you have to call $40 to win $59.

I'm still struggling to understand how the pot is $59

Your raise = $8
All-in = $48
Blinds = $3

Total = $59

[Erpel]

This would be true if it wasn't because the raiser was the BB - since he's the BB his $2 part of the blind is part of his $48 all-in bet. The other possible interpretation would be him betting $48 on top of his $2 - which would be raising to $50 and requiring you to call $42 so this interpretation is at odds with most of the data we are given.

The realistic explanation is that the pot contains the following:
SB: $1
BB: $2
UTG (Hero): $8 PFR
BB: $46 3bet (raise TO $48, having already put in $2 as blind)

Thus you need to call $40 (The current $48 bet-size minus your $8 PFR already on the table) to win $57 ($1+$2+$8+$46).

In terms of confusion of terms I'll throw in a perspective of my own (though it may already have been figured out) - it needs to be said that I find Harrington's explanation in Harrington on Cash quite clear.

I think the term equity is just another word for value and is normally applied to a hand, with regards to how often it will win a showdown. The basic equity calculation tends to boil down to a percentage number. If we freeze the betting and progress the hand to river and resolution what is the value (equity) of the hand? How often do we win, lose and split? There is generally only one answer if we know the hand we are up against - when both players go all-in and flip over the cards so they are visible to all before the remaining community cards are dealt - we can conduct purely accurate mathematical equity calculations before community cards are dealt. When the amount of information to determine this exact equity becomes available to us, it is not longer useful to us. In earlier decisions we have an idea what the opponent hand range is most likely to be, as well as things that it is unlikely but still possible to be.

A complete equity calculation would list every single possible hand the villain could hold, consider how many hand combinations are possible for that hand, consider how likely it is that it would have played in exactly the way that it did play and assign a likelihood that it is his current holding - and then calculate the pure accurate mathetical equity against that hand, balance it with the likelihood of that being his exact holding, do this for all possible hands and combine these numbers to give an equity against a range. All pretty basic maths, but oh so many numbers to keep track of. PokerStove does something pretty much like this for us. It doesn't directly allow us to say that our villain would only have played AA this way 20% of the time, but with a bit of fiddling this type of weighing can be faked.

Equity isn't necessarily that complicated, but it's computationally intensive, and therefore poker players have come up with approximations that are good enough for the table or for quick or unaided hand analysis. There's another thread here in the Beginner's Circle titled as a question to a hand analysis in HoH which illustrates one order of approximation - in the book Harrington lists maybe 4-5 types of hands and does rough equity calculations against each - hands like made pair smaller than your pocket pair for example.

When people are talking about pot odds it is usually short-hand for a slightly more complicated calculation - Expected Value. People say "calculate your pot odds", but they MEAN calculate your pot odds, and compare your pot odds to the value (equity - chance of winning at showdown against villain's holdings) of your hand and make the profitable decision. What you're actually doing here is determining the Expected Value of your available plays, but terms are often confused and people are often asking you what your pot odds are implicitly meaning to get you thinking about if it is a play with positive Expected Value - as in they expect you to compare the pot odds with the equity to determine the EV.

That pot odds are often expressed in an odds notation and that equity is often expressed in a percentage chance to win notation is not in itself helpful - but it's not done in this way just to be difficult.

One of the shortcuts, and one of the most used shortcuts, to determining equity is outs. I know I'm up against a made straight, two pair or a set, but not better and my only chance of winning is if my flush comes through - this gives me 9 outs. I could calculate the equity of my hand on this basis, but if I stay with the number of outs I have a shortcut to an odds notation which I can compare immediately to my pot odds which are already in an odds notation. A lot of players find this much easier to work with at the table, and accurate enough to avoid making very -EV plays.