Equity??? Warning: May Hurt Heads!

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!

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).

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.

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.

It is pot odds btw.

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

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.

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

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.

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.

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.

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.

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 Sad

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

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.

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

poker stove is free btw.

www.pokerstove.com

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.

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.

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Equity??? Warning: May Hurt Heads!