The Next Step - Equity? 3 Questions. Warning: May Hurt Heads

[Sentinel]

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.


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 1/2 to make such a call profitable – such as 1/3 or 1/4.


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 pot odds. Yet here, the exact same maths shows that making such calls is profitable.

Help!

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?


Help!

[Jernej Zorec]

pot odds we usually use when we are drawing
EV is slightly different thing the 67% chance u talk i think only assumes u need to hit the hand to win , equity tho also takes in the times ur good

but in this example
your Equity is 45.6%
so look at it this way
54.4% of time u loose 40$ u have to call so u loose 21.76$ on avg

but 45.6% of time u win 59$ and that amounts to a win of 26.9$ on avg
hence call is profitable


with 40% equity it comes to 24$ loss and 23.6$ avg win hence call is bad

[tame_deuces]

Yes, what Zernej said.

Let's imagine an equity of 40% without any pot at all.

You put in 100$.

You win on average: 40$
You lose on average: 60$
Net average loss: 20$

So, it is a bad call.

Now imagine there is already 200$ in the pot and you have to call a 100$ bet with 40% equity:

You win on average: 120$ (40% of 200 and 40% of the other guy's 100)
You lose on average: 60$ (You don't lose what is already in the pot)
Net average profit: 60$.

So, it is a good call.

You can't 'lose' what is already in the pot, so basically you just use equity and pot odds together.

[Sentinel]

The lightbulb has finally switched on.

Even though I knew equity wasn't the same as pot odds (cos you have a made hand) the principle still applied - you needed to have the right price to call.

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 fact that the maths behind the call worked is what added to the confusion.

Only by writing a reply that included 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 with QQ 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.

[Sentinel]

Boy do I feel stupid?

My previous post explaining I “got itâ€