remaining stack = 865

Win if he folds = 275+135+35+60=505

Our equity vs his calling range = 30%

EV(folds)= 505

EV(calls)=2095*.3-865= -236.5

EV(shove)=P(folds)*EV(folds) + P(calls)*EV(calls)
= P(folds)(505)+P(calls)*(-236.5)
=P(folds)(505)+ - P(calls)*(236.5)
P(calls)*(236.5) = P(folds)(505)
P(calls)=P(folds)(505)/(236.5)
P(calls)=P(folds)(2.135)

P(calls)+P(folds) = 1
P(folds)(2.135)+P(folds)= 1
P(folds)(3.135)=1
P(folds)=1/3.135= 31.9%

Ex.
(.681)(-236.5)+(31.9)(+505)=0

this is wrong ^ ; sorry I"m not gonna go on about this any further, I don't actually know the formula that splitsuit uses but I know that his algorithim is correct because he doesn't **** around when it comes to math ; all you gotta do is plug in the numbers and if it is confusing then just watch the 5 min video , it is confusing at first so that's understandable

the answer is 31% ( BE %)

Rounding error

sorry not you I meant the guy that said 43% ; we got the same answer lol

Yeah 43% is wrong that’s what I get for trying to skip steps lol

You would think having a math degree I wouldn’t screw it up

haha I'm a math major too , it only takes one tiny mistake and the whole problem is wrong lol unless teacher has mercy and goes partial credit

So firstly, when he makes it 275 here, he's got...710 left? So it's 850 we'd be risking (710 left + his 275 bet - our 135 bet).

So 60 preflop, bet 35, call, 135, 275, there's 540 out there. We risk 850 to win that immediately.

So what fold equity do we need? Like you said, it depends on his range, since only two things can happen:

- He folds (we'll call this P)
- He calls (we'll call this 1-P)

Our EV when he folds is obvious: 540.
Our EV when he calls is not too hard to calculate either: it's our pot share minus our investment. In this case, there would be 2065 in the middle and we'd have equity of X after an 850 investment.

So our EV is: 540*P + (2065*X - 850)*(1-P), and I'll declare this as F

So if F > 0, we have a profitable shove.

Let's construct a call off range, since this is the important part. Let's say he's planning to go with his A hi flush draws (AsKs, AsQs, As3s, As2s) and some overpairs (JJ+ with no spade). Against this range, we have just 27.7% equity.

So F(X=.277) ~ 540P - 278(1-P) = 818P - 278.
818P - 278 > 0
P > 278/818, or approx 34%

So since I listed 16 combos, he needs a little over 8 fold combos in this hypothetical to profit.

Now let's say this guy is loose and a kamikaze pilot and he'll stack off with 88+ (obv A5s, 55, 44) and all broadway and A hi and combo flush draws in his range. So something like 76ss, 87ss get added and he has all the AXss. Against that range we have 31.8%

So F(X = .318) ~ 540P - 193.33(1-P) = 733.33P - 193.33.
P > 26.4%

Generally I think a lot of players will fall into the former, not willing to get in near dead against a 5 in this situation, so plays like this are more likely to resemble the former situation (where it's easy to assume they're folding like 50% when you only need 34% and ram it).

If we want to get back to the actual hand strategy, I seriously doubt this guy is reraising to $275 with a flush draw. He would probably just call with big FDs IP, but if he was going to reraise it would most like be a lot more than $275, so I'm taking those out of his range.

Did V end up having something that crushes you like 44 or maybe even A-5s?
Or were you right in your read of 99-KK?
(No worries if ya don’t wanna reveal yet)

Don’t mean to derail the all the arithmetic going on.

back to the hand strategy , I don't think he is bet/3b'ing any combo that he is going to let go here; maybe a hand like 77-99 but that's a bit of a stretch

I feel like he is folding very close to 0 % of the time in this spot unless he thinks your FOS and has a hand like AKos/AQos ; this is a judgment call that you have to make based off of your image and V's play style

seems like an OP or 5X the majority of the time

EV is calculated as EV of each outcome multiplied by the probability of that outcome. Here, the possible outcomes are:

1. Villain folds at frequency 'f', and our EV is 'W'
2. Villain calls at frequency 1-f, and we have 'e' equity in a final pot of 'P', which we will have payed 'R' to get into. Our EV is e*P-R

Now we can set up the EV equation:

EV = f*W+(1-f)*(e*P-R) >= 0
Solve for 'f':
f >= (e*P-R)/(e*P-R-W)

Now substituting the numbers from OP:

f >= (.3*2095-865)/(.3*2095-865-505) = 31.9%

Seems reasonable, though it could be an attempt to freeze the action and get a "free" card if the turn bricks. More likely it seems like one of two things: either he HAS IT and wants to keep you in, or has an overpair and is giving himself room to fold to a shove. (Could also be an overpair playing like giving room to fold in order to induce a shove, but that's a bit higher level thinking)

^
This is what I was thinking as well.

I have a hard time giving people credit for higher level thinking until they prove themselves capable of such though.

great post, great thread
great math to break down answers thank you to all

I say this as this is a common hand play out ;especially in $2-5 games

on the one hand we have -EV but in live mode are trying to decide if implied FE makes it a good play IE +EV

I think here a read of V and our image play a % as well

Most elegant solution award goes to...

+1

This is clean af

This is basically what I was thinking as well, and I thought there was a pretty decent chance his overpair wasnt that big, which is why I did jam it all in.