1st post in poker theory forum...I'll try not to sound like a noob but prolly will. Just looking for someone to double check to see if I calculated these odds correctly..assuming I assigned accurate range to this old guy. 1-3 cash game at Caesars palace: Playing with 300 behind. First hand get AK of hearts. Utg limps, I go to 12..Old guy with 400 behind calls and utg calls.

Flop 39$'s: 7h-8h-Ac Utg checks, I bet 22 into 39 and old man goes all in! LOL.
UTG folds and I'm like wtf?

Range I assigned for this I'm old please fold 80yr old Hugh Hefner look alike was 88, 77, A-8, 7-8off, 7-8 suited. He inflates the pot from 61 to 327 ( He puts in more than this, but he has me covered. I have 266 behind flop cbet so 61 + 266= 327) So I need to call 266 to win 327, so our pots odds on a call are 327/266 or 1.22-1

The odds against us making our hand: 47 unknown card in play. Outs include 9 hearts, 2 Aces and 2 Kings (could go 3 Aces and 4 Kings each but we'll balance for the times old man has a set) so thats 13 outs out of 47 or 34/13=2.62 odds against us winning the hand...

So is this really a fold mathematically since the odds against us winning the hand are > the pot odds on a call?

And this is assuming we're never ahead...I mean maybe the old timer will flip over the 9-10hh once in a blue moon or maybe he just wants to bluff the young punks 1 more time before he keels over, but w/out any reads I dont possibly see how we can assign any hands to old mans range here that we have beat on the flop.

You have a few mistakes in here. If you have 13 outs, then your chance of getting there is
1 - (34/47)*(33/46) = 48% or 1.08:1
(This makes the faulty assumption that he won't redraw a boat, though)

Second, if you had calculated your odds right and were 2.62:1 against winning, this is WORSE than your pot odds, not better. If pot odds is X:1 and equity is Y:1 then to call you need X>Y

Also, to make things easier use a tool like pokerstove or propokertools to calculate your equity. I get 43% in propokertools with your range. If you add in 9hTh I get 44% for you. Not much of a difference really.

Thanks for the input. I'm familiar with pokerstove and got the same equity as you did..but I think this was a spot that came down to our pot odds vs the chances against us getting there. I'm confused with your first part and how that factors into the decision though.
Are you saying the 2.62-1 ratio I got for against winning is wrong and 1.08-1 is the right number, or are the chances of us getting there and the odds against us winning not the same thing? If its not then yeh it would be a fold because the odds against us winning are > the pot odds we have in this spot.

This is a spot I would never worry about math and would call VERY fast

this.

I'm fist pump calling. We have 12 outs against A7 and A8, we have 14 outs against 78, we're crushing AK and AQ, etc. If he has a set, so be it.

Your 2.62:1 number is totally wrong, because it's only estimating the chance of you getting there on the next street. But you have 2 streets to get there, right, because you're going to be all in if you call. The easiest way to calculate the chances with 2 streets is like this, assuming your chance to draw in 1 card is X:
2 street chance = 1 - (1-X)(1-X)
this is an approximation but it's really close enough. I gave the exact calculation in my first response.

But my calculation isn't exactly right either because you can get there and still win. It's possible to calculate this exactly but there's hardly any point.

Ok that makes more sense now. Mathmatically speaking it would be a call because our pot odds, 1.22-1 are > the odds against us winning the pot 1.08-1 ..I was a bit surprised when I saw that the math would say to fold..so it makes sense that I was wrong and only accounting for 1 more street instead of 2.
And yeh not mathmatically speaking I agree with you guys that we have to shove it in. We have 43% against his range, and in a tourney, I'm almost never folding if we have > 40% equity in a spot. Had no clue what to do in game though as I havent been playing cash games for too long and his shove is ridiculous.