I've had a crack at an EV calc. Maths doesn't come easy to me as you can problably tell from my calculations. I'm trying to get my head around this EV thing but struggling a little so some advice would be greatly appreciated.

I have included a few scenarios to help grasp the best approach which obvioulsy will help to make the right play!

Blinds 300/600

Stacks
Villain - 14200
Hero - 18500

Cards
Villain - Top 20%
Hero - AQ

Position
Villain - (Mid)
Hero - (BB)

Villain raises top 20% of hands

Equity
Villain 42%
Hero 58%

Villain raises to 2000


1. POT SIZE RAISE

Villain will fold 50% of the time to a pot size raise

0.5(2300) + 0.5 [7400(0.6) – 7400(0.4)] = 2630


2. ALL IN

Villain folds 70% of the time to an all-in raise

0.7(2300) + 0.3[32700(0.6) – 32700(0.4)] = 3572


3. IF STACKS WERE BIGGER

0.9(2300) + 0.1[50000(0.6) – 50000(0.4) = 3070


When I was playing around with these calcs, I noticed that the return changes when the stack sizes change.

Is this the equilibrium that is talked about in “Kill Everyone”

Your equations are ok (ignoring implied odds for the first case) but your win and lose amounts are off if villain calls. You have hero winning and losing the same amount, which is not the case.

For the pot size raise by hero, the pot was 2300, which you have. If hero then raises 2300, he wins 4600 if villain calls and hero wins the pot, or hero loses his 2300 raise. The EV equation with a 50% call probability and equity of 60% is

EV = 0.5(2300) + 0.5 [(2300+2300)(0.6) – 2300(0.4)] = 2070

Similar changes are needed for the other two cases.

the FE(fold equity) part of the equations you seem to have the concept correct but it would seem that 2300 must be the wrong value for the amount you win when he folds.
the part of the equation that represents the EV of when he calls is incorrect also primarily because using the same values for what you win and lose is just wrong.

you are using the wrong values for the amount you win and the amount you lose.
( additionally you are using .6 and .4 when you say 58% and 42% which would be .58 and .42 but i'm guessing you know this)

2. all in for example
if he was the only preflop opener and he limped sb folded and you got a free ride in the bb the pot on the flop is 1500.
for him to raise 2000 you had to bet (which you didn't specify) well use 500 for an example.
so after his raise the pot is $4000 so if he folds to your shove here then you win $4000. the value you have as 2300 should be 4000
having limped preflop for 600 and raised your 500 flop bet 2000 villian has 11100 behind. so your shove is 13100. when he calls your shove you'll win 15100 (4000+11100).

the correct equation then is
0.7(4000) + .3[15100(.58)-11100(.42)]

someone should confirm for OP that this is correct

I had the wrong pot size. Pot size is 900 + 2000 = 2900.

If OP means by pot size raise that hero raises 2900 after calling 2000-600=1400, then hero wins 5800 if villain calls or hero loses 1400+2900 = 4300 The EV equation with a 50% call probability and equity of 60% is

EV = 0.5(2900) + 0.5 [(2900+2900)(0.6) –( 2900+1400)(0.4)] = 2330

I wish simple EV equations weren't so hard (at least for me)

Also, maybe I'm reading this wrong, but it looks like you are using .6(=.58?) for your chance of winning every time, but in scenarios 1 and 2, Villain is calling with a different percentage of his hands, so you are up against different ranges. In other words, in Scenario 1 you say he is calling 50% of the time. You already know he is in the top 20% of his hands, so if he's calling half the time you need to figure your equity against the top 10% of his hands. Likewise in Scenario 2 you need your equity against top 6%.

i misread/misunderstood/something earlier and overcomplicated it.

#2 preflop shoving from the bb over a single raise.

EV= 0.7(2900) + 0.3[.39(15100)-.61(13600)] =+1308

when he folds 70% and calls 30%, which reduces his top 20% to top 6% which has 61% equity vs. AQ.
you win 2900 when he folds (300+600+2000)
you win 15100 when you scoop (2900+12200)
you risk/lose 13600 when you get scooped (14200-600)

Thanks guys, invaluable information, I hope when I get better at this that I can pass some knowledge on some day.

From what you have said, villains calling range effects the equity? Not his raising range.

Conversely, if I was the original raiser once again his calling range is the key.

It seems generally that someones raising range is wider than their calling range a basic understanding of poker but here is the math to prove it.

By the way any comments on what the better play is?

On the face of it, the All-in play seems to be the better play but the pot raise shows a better return.

I believe these calcs are right so is there any reason as to why the raise is the better play?

Pot size raise
0.5(2900)+0.5[(.53)(2900+2900)-(.47)(2900+1400)] = +1976

All in
0.7(2900)+.3[(0.39)(900+14200)-(.61)(12200+1400)] = +1308