Qq Micro Milions

Given your read, this is a math thingie.

Suppose he calls your 4-bet.

There are 6+6=12 (AA/KK) combos you beat with probability X.
There are 16 (AK) combos you beat with probability Y.
You beat 1 combo (QQ) with probability Z=0,5.
Let P be the all in pot size. Let p be the pot before you move in.
Let R be the size of the stack that remains if you fold.

Thus EV_when_he_calls_all_in = 12/(12+16+1)XP + 16/(12+16+1)YP + 1/(12+16+1)ZP.

When you shove, he will fold 6+6+16 (TT + JJ + AQ) = 28 combos.
When you shove, he will call with 1+6+6+16 (QQ+KK+AA+AK) = 29 combos.

EV_before_he_call = 28/(28 + 29)p + 29(28+28)EV_when_he_calls_all_in

Plug i the correct numbers for p,P, X Y, Z (which are all well known).

Please do it, I want to know too.

If EV_before_he_call is bigger than R, then you shove rather than fold. The EV of calling his 3-bet is much harder to calculate. You don't know how much he bluffs of calls down.

(In reality, his range is 49% KK and 49% AA and 2% something weird that beat you. The hand is, after all, posted ♦.)

/Johan =

If those are indeed going to be his ranges, this is going to be a fold. There's approximately 100k in the pot when you shove. If he 3bets TT+, AQs+, AK like you said, he's raising 50 hands, and is calling 34 hands (QQ+, AK). When he calls, you have 40% equity, so you expect to win:

.32 * 100000 + .68 * (.4 * 660000 - 320000) = -6080

The formula here is:

%fold * pot pre + %call * (%equity * pot - amount put in) = cEV

Since you expect to lose chips in this situation, you should fold. Of course, if he 3bets any wider and calls wider as well, it becomes a pretty easy call (even if he just calls JJ as well, you're going to make a substantial profit here), so make sure you put him on a proper range here!

Hey, Tino...

We are both slightly wrong in the exact numbers here.

He is raising pre with 6+6+1+6+6+16+2 = 43 hands. (We block stuff here.)
He is shoving 1+6+6+16 = 29 hands. (We still block stuff here.)
He is folding 6 + 6 + 2 = 14 hands

EV_IF_HE_CALLS_ALL_IN = 12/(12+16+1)XP + 16/(12+16+1)YP + 1/(12+16+1)ZP

FINAL_EV_FOR_PUSH = 14/43p + 29/43*EV_IF_HE_CALLS_ALL_IN

p = pot after his initial 3-bet = 21500 + 55000 + small blind + big blind + 8 antes = 76500 + Something (S).

P = pot if he calls a push = 638024 + same something as above.

X = your chances versus AA/KK = 0.1845
Y = your chances versus AK = 0.5606
Z = your chances versus QQ = 0.500

If S = 23500, then p = 100000, and P = 661500

EV_IF_HE_CALLS_ALL_IN = 12/29*0.1845*661500 + 16/29*0.5606*661500 + 1/29*0.500*661500 = 0.40*661500 = 266506

FINAL_EV_FOR_PUSH = 14/43*100000 + 29/43*266506 = 212294

EV_FOR_FOLDING_TO_PUSH = 319000-55000-ante = 264 000 - ante.

Clear fold. I'm surprised.

Edit:

%fold * pot pre + %call * (%equity * pot - amount put in) = cEV

I don't understand that last term. It should be %call *%equity_vs_QQ/KK/AA/AK_range*size_of_all_in_pot. Then you get chip EV for pushing.

Edit again: To get the NET EV for pushing compared to folding you would subtract from 212294 the remaining (fold) stack (264 000 - ante) , which yields a net loss of about 50 000 chips.

/Johan =

I simplified some numbers to make things a bit easier, but the end result should be essentially the same. Though you are right, that I forgot to account for our blockers, and simply copied the number of hands from the equilab (when you select a range, you can see how many hands this is). Though it doesn't make a difference at all in this case, because he still folds 1/3 of the time and calls 2/3 of the time and we still have 40% equity.

I don't understand that last term. It should be %call *%equity_vs_QQ/KK/AA/AK_range*size_of_all_in_pot. Then you get chip EV for pushing.

Basically, 40% of the time you're going to win. So the 68% of the time he calls, that's what you win. However, you will lose your entire stack of 320k if you lose, so you add -320000 to it. You will win 660k 68% of the time, but you will also lose 320k 68% of the time. By only taking the pot into account, you're not taking your losses into account.

By only taking the pot into account, you're not taking your losses into account.

I do.

Just to be clear, I calculate our expected stack if we push. We get 100% of the small pot (about 100 000) if he folds, and approximately 40% of the size of the all in stack (660000) if he calls. Nothing else can happen.

Edit:
Estimated stack if we push with your estimates and my formula: 0.32*100000 + 0.68*0.4*660000 = 211520.
Estimated stack if we don't push: 319000 - 55 000 = 264 000 .

Difference = -52480 (in favor of folding). Your final result, -6080 (whatever it means) is not even close to my number. We must get this straight, whoever of us is wrong.

/Johan =

With the formula I gave, the outcome means that you expect to lose 6080 chips with this move, meaning it is (in this case) not profitable to shove. That's what it's all about, if you expect to make money/win chips by taking a specific line.

There are multiple outcomes for a specific move. In this case, hero shoves. Three things can happen.

1: Villain folds and we pick up a 100k pot.
2: Villain calls and we win a 660k pot.
3: Villain calls and we lose a 320k pot, meaning we bust.

To calculate the EV of this one move (shoving), all these outcomes have to be considered in one equation.

You are doing essentially the same thing, except in a different, more complicated way, by calculating expected stack sizes, which is imo an unnecessarily complicated route to take. The result is the same, though, but the numbers are different. My formula immediately shows you whether you lose or win money in the long run, whereas your way also requires you to compare multiple numbers

whoever of us is wrong.

So yeah, we are both right

Good! That's what I wanted to hear :).

Then we can argue forever about which formula is simpler (or more pedagogical) ♦. I actually prefer yours in the long term unless the scenarios are more deeply nested. If that is the case, a one line formula is probably incomprehensible.

/Johan =

Originally posted by TinoLaan
.32 * 100000 + .68 * (.4 * 660000 - 320000) = -6080

I'm pretty sure this is a mistake. We already put 21,500 in the pot, so we're only risking ~300k. If you calculate it this way, you get +6k EV as the final result.

@yohan, why on earth are you calculating our equity against the different combos of his range instead of his entire range? (facepalm)

You do raise a good point. This is always how I've calculated it, because the total you're losing is 320k, rather than 320k - ~20k we have already put in.

That indeed would change things quite drastically though. So if someone could confirm this here, that would be great!

Originally posted by meepwn

Originally posted by TinoLaan
.32 * 100000 + .68 * (.4 * 660000 - 320000) = -6080

I'm pretty sure this is a mistake. We already put 21,500 in the pot, so we're only risking ~300k. If you calculate it this way, you get +6k EV as the final result.

@yohan, why on earth are you calculating our equity against the different combos of his range instead of his entire range? (facepalm)

The final result is versus his entire range, as exact as it can be. I do this because it's instructive for anybody not using Equilab and/or not understanding the real underlying math. His entire range is three hands, so it's not like a gigantic effort.

The net result, b t w, is something like -50 000 for a push. Exact numbers require knowledge of blinds and antes. The rest in my calculation is exact.

Edit: @meepwn. Do you mean that do not agree on how to make an EV calculation, or do you mean I go for an overkill by making it exact by considering every combo? If we disagree, the one of us is very wrong and need to get things right. If we do agree, then readers of this thread will be highly confused, an might pick up the wrong ideas.

/Johan =

I just don't see the point in calculating the equity against the three different hands and then multiplying them by their respective probability and adding them to get equity, we can just use equilab ♠_grin:

yeah I might be wrong, but -50k EV looks very wrong to me

Looking at your calculations in the second post, there seem to be two mistakes:

FINAL_EV_FOR_PUSH = 14/43p + 29/43*EV_IF_HE_CALLS_ALL_IN

should be

FINAL_EV_FOR_PUSH = 14/43 (p + 300k, our remaining stack) + 29/43*EV_IF_HE_CALLS_ALL_IN

, since you calculated FINAL_EV_FOR_PUSH and EV_IF_HE_CALLS_ALL_IN as a net amount of chips, and not the difference of chips before and after the hand.

Also, this

EV_FOR_FOLDING_TO_PUSH = 319000-55000-ante = 264 000 - ante.

should look like this

EV_FOR_FOLDING_TO_PUSH = 319000-21500-ante = 297500 - ante.

since when we fold, we are not putting 55k, only our original raise + ante.

Yes, every single remark you have made is entirely correct. Embarrassing for me because I know the math :f_biggrin:. To my defense, I did mention I was mildly shocked over -50 000. I think I'll get drunk!

/Johan =

I think QQ is just to good to consider folding or doing something else with 31bb! I didnt get the part where you say he 3bets TT+ and AQ+ for value but only calls with QQ+ AK, because if he 3bets folds TT-JJ and AQ it´s a 3bet bluff! and i think his calling range is around TT+ AQ+, and even if he is a super NIT it´s like TT+ AQs+! I might consider folding TT but never JJ+ with around 30BB

Hey guys!

Good discussion

Can you please post your final formula! I want to have a look a it!
It seems like a nice shove to me! So please show me what you calculated as you all think this is a fold!

Greets,
Tiltberger

The second one in meepwn's post that should be correct. I'll change names of things to clarify (or confuse even more).

EXPECTED_STACK_IF_WE_PUSH = 14/43 (POT_BEFORE_WE_PUSH + REMAINDER_OF_OUR_STACK_BEFORE_WE_PUSH) + 29/43*EXPECTED_STACK_IF_HE_CALLS_ALL_IN

The factors 14/43 and 29/43 are the probabilities of a fold and a call, respectively, based on combo-counting (earlier post by me) according to the reads.

If REMAINDER_OF_OUR_STACK_BEFORE_WE_PUSH > EXPECTED_STACK_IF_WE_PUSH, then it is a fold, otherwise a push.

EXPECTED_STACK_IF_HE_CALLS_ALL_IN = twice the effective stack times our equity (40% according to both Equilab and an exact calculation in earlier post by me) versus his read based all in calling range.

Whether this means a fold or not, I have no idea. I get different results each time I try to type in the actual numbers.

Guys, I have a neat idea. We should have standardized names for things that are bound to occur in thread after thread in this forum. Not the easiest ting in the world to establish and enforce, but still, think about it...

/Johan =

The correction made in this post by meepwn:

Originally posted by meepwn

Originally posted by TinoLaan
.32 * 100000 + .68 * (.4 * 660000 - 320000) = -6080

I'm pretty sure this is a mistake. We already put 21,500 in the pot, so we're only risking ~300k. If you calculate it this way, you get +6k EV as the final result.

@yohan, why on earth are you calculating our equity against the different combos of his range instead of his entire range? (facepalm)

should indeed give the right solution. You were right, because since we only have 300k left, we can't lose 320k anymore. So that would make the formula basically the same:

%fold * pot pre + %call * (%equity * pot - amount put in) = cEV

I just used one wrong number. And that does change the cEV drastically, like meepwn said.

.32 * 100000 + .68 * (.4 * 660000 - 300000) = +7520

So that would indeed make it a profitable call.

And Yohan, I still don't really see what you're doing. You're just using a lot of huuuuuge variable names that make things pretty unreadable, and it looks to me like you're doing a lot of redundant work, when there is a pretty simple formula you can use in this situation, which is the one I provided here. Of course you will have to use the right numbers, where I made a slight mistake

Aside of that though, in situations like this, this formula is pretty fool-proof.

I can't explain my formula more explicitly than what I've already done. I suggest that you read my last post again. The long variable names are there for a reason.

Also, I'm afraid that you are the one being rather obscure. You don't define the quantities you are using (,which I do by using long descriptive variable names), and, also, you don't derive your results. Having a final single formula is good, but only if it is easy to understand it, and easy to understand how to use it, and possible to see where it comes from.

What is that cEV of yours in words? You are obviously not calculating the expected stack after the decision to push. If you calculate some net number, what is the baseline? What is "pot"? What is "amount put in"? The use of "%" in your variable names is, at best, confusing.

%fold * pot pre + %call * (%equity * pot - amount put in) = %fold * pot pre + %call * %equity * pot - %call *amount put in.

The last term is clearly nonsense, even if you define "amount put in".

/Johan =

If you want a net chip ev type of formula, here is one:

net_chip_ev_push = p_fold*current_pot + p_call*p_we_win*(push_amount + current_pot) - p_call*p_we_lose*push_amount.

In this one, p_we_lose = (1 - p_we_win). The baseline here is our stack before the decision to push.

If he folds (which happens with probability p_fold), we stand to win the current pot (with a probability of 100%). All of this goes to the net by choice of baseline.

If he calls, two things can happen. We win net, with probability p_we_win, the the amount currently in the pot plus the amount we push (more precisely, the amount he is forced to call). The other scenario, with probability p_lose, will cost us the push amount.

If you wish, you can modify the formula by substitution of (1 - p_we_win) for p_we_lose, and by expanding in terms (there will be five in all), and then factorize again. I prefer the above one, because it is straight from the definition of what an expectation value is -and simple enough.

/Johan =

cEV = chip ev. Assuming there's no ICM considerations, I'm simply calculating the amount of chips you expect to win by making a specific move. That's the standard way to calculate EV, afaik. It's basically just EV, except with a c in front of it to denote that we're talking about chips, and not money

I did re-read your post though, and I think I may have misread something when I made my previous post. What you're saying does make sense now.

But I don't see much of a point in having an argument merely over variable names. I'll just clarify what everything means though.

cEV = chip EV. This is a term that should be in any tournament player's dictionary.
%fold = percentage of hands he folds when we raise
pot pre = pot pre flop
%call = percentage of hands he calls when we raise
%equity = equity we have against his calling range
pot = total pot we can win
amount put in = the amount we put in when we raised

Honestly, I think all are fairly easy to understand...

But again, we are arguing over something veeeery small! We're arguing over variable names! I don't think that's something worth arguing over.

I'll try to explain my formula as well as possible, since it's a tried and true formula. I'm not a 100% sure on this, but I think I've seen it pop up in a video here on PS somewhere as well. I just need to convince you that it works

I'll just use the same numerical example from this topic.

When we shove there's two things that can happen.

1: We pick up the pot right away.
2: He calls and we may win the pot by showdown, winning the pot equity we have or the rest of our stack.

Since we have decided that he's going to fold 14/43 hands, we know that he is going to fold 32% of the time, meaning we will be able to pick up the 100k pot 32% of the time.

Obviously we also need to account for the times he calls though. Since he's folding 32% of the time, we know he's calling 100 - 32 = 68% of the time.

Now, two things can happen when he calls. We can win, which is going to happen 40% of the time, which will win us a 660k pot. But we can also lose the remainder of our stack we put in, which is the last 300k we had.

So, putting in the numbers:

We have 0.32 * 100000 = 32000 fold equity.
When he calls, we expect to make 0.4 * 660000 = 264000 from just winning the pot. However, when we lose, lose everything we put in. That's the amount we're going to lose. So, we need to subtract that from the amount we're going to win. The result of this subtraction is therefore the amount we multiply by 0.68 (the % of the time he is going to call our shove). So with the numbers determined, this is what our EV calculation for shoving looks like:

cEV = 0.32 * 100000 + 0.68 * (0.4 * 660000 - 300000)
    = 32000 + 0.68 * (264000 - 300000)
    = 32000 + 0.68 * (-36000)
    = 32000 - 24480 = 7520

Hopefully what I'm doing makes sense now.

Again, I'm not arguing here. I'm just explaining what I'm doing