hi, can anyone tell me if my poker math is correct here?

hand AhKc
headsup 3bet pot


turn - 550
7s Ac 9d 6h
bet 250 and villian shoves. he covers and we have 750 behind.

assuming villian is getting it in with 77,99,A9s,A7s,AJ,AQ
are my calculations correct?

vs 99,77
0% x 1800 - 100% x 750
= -750

vs a9s a7s
10.2% x 1800 - 89.8% x 750
=183.6 - 673.5
=-489.9

vs aj aq
=93.2% x 1800 - 6.8% x 750
=1677.6 - 51
=1626.6

ev(callshove) = 386.7

2ndly, if villian is shoving AQ,AJ 70% of the time, is the following calculation correct?

vs 70%shove AJ AQ
=65% x 1800 - 35% x 750
=1170 - 262.5
=907.5

thanks

There are several things that do not look entirely correct:

(1) You have to be careful how you handle the money that is already in the pot. This is essentially equivalent to saying that you must be careful in constructing EV's of competing options. For example, what are you comparing your "EV(callshove)" to?

(2) You must "weight" villain's possible hands in the EV calculation by the number of combinations possible for each hand. It seems like you simply added the different EV subcases to derive the overall EV. Note that there are many more AJ & AQ than 99 or 77 (and clearly A9s and A7s). You need to count up the number of combinations for each and use them in the EV.

(3) I cannot follow what you are doing in your second "2ndly" calculation. But it does not look correct. You need to be clear what is villain's shoving range (including percents, as applicable). It seems like you multiplied the 70% by the 93.2%, but it is not clear that this is the correct thing to do.

Hope that helps.

hi whosnext,

thanks for your input.

1) in the example, on the turn we are closing the action for the hand either by calling or folding to the shove, so i thought i only had to calculate EV(callshove). what should i compare it to?

2) i get what u mean, so is it like this -
99,77 - 6 combos
AJ&AQ - 16 combos
A9s,A7s - 4 combos

how should i proceed from here?

3) ok let's assume he is shoving 100% of the time with 99,77,A9s,A7s and 70% of the time with AJ,AQ. 30% of the AJ,AQ he calls, how can i calculate my ev on the turn?

4) is the math for calculating ev correct?

If this is the case then you are fine but in other situations there may be other strategic options that you would also need to calculate the EV of.

You can convert this into relative frequencies by adding up all the combos and dividing each number by the total.

99,77 = 6/26 = .23
AJ,AQ = 16/26 = .62
A9s,A7s = 4/26 = .15

Note the above are rounded.

You can just multiple the percentages by the frequencies above.

Shove 99,77 = 1*.23,
Shove AJAQ = .7*.62

Not sure about the 30% call number as I don't remember the scenario from OP and too lazy to look it up :-).

EV is the probability of an event occurring multiplied by the payout when the event occurs. I find it easier to break out the events and then make sure I correctly identify the probabilities and the payout for each event and then adding the seperate events together to get the total EV for a particular line.


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1) Generally speaking, you need to calculate the EV of each of your decision options separately. Here you are deciding between folding and calling. Perhaps you implicitly are calculating the EV of calling relative to that of folding, but care must be taken here. This is equivalent to "setting" the EV of folding equal to zero. The reason I even brought this up is that this issue can be a source of confusion and errors in some EV analyses.

2) Yes, combos are important to consider. I don't think all of your combo counts are correct. Once you have the correct combo counts, you weight each of the respective EV's of that hand combo to derive the overall EV.

For example, if one hand combo represents 20 possible hands and has an EV of 100, and the other possible hand combo represents 5 possible hands and has an EV of 40, the overall EV is [(20)*(100)+(5)*(40)]/[(20)+(5)] = 2200/25 = 88.

The idea, of course, is to give more weight to the EV of the hand combo that villain is more likely to have and less weight to the EV of the hand combo that villain is less likely to have.

3) Allowing the possibility that villain sometimes shoves and sometimes calls on the turn is a different situation. The idea is that the EV is for the different options you can take at a specific point in the hand.

I think you are essentially taking the action back a step before villain shoves. But what decision are you trying to analyze? Your decision to bet the 250? If so, that is an entirely different situation. It can be done, of course.

4) Generally speaking your EV methodology is sound. In addition to taking into account the issues raised above, you must take care in handing pot amounts, including the amount of money already in the pot at the time of your decision.

[Edit: I didn't notice that just_grindin has responded too, so there is a fair amount of overlap in the responses.]

Is there any reason why you're reluctant to use an Equity calculator for something like this? Since counting all the combos or calculating your winning chances invididually is so confusing, I'd just put the hand vs range and board into something like Equilab and get this:

Board: 9d7sAc6h
---- Equity Win Tie
Hero 62.97% 62.97% 0.00% { AhKc }
Vill 37.03% 37.03% 0.00% { 99, 77, AQs-AJs, A9s, A7s, AQo-AJo }

With such a huge equity advantage, you're printing money by calling a shove if you range villain correctly. You're winning the pot 63% of the time.

1)what other options do i need to calculate the ev of?

2)
99,77 = 6/26 = .23
AJ,AQ = 16/26 = .62
A9s,A7s = 4/26 = .15

so after getting this frequencies, how can we use them in the ev formula?

1)yes i am calculating the ev of calling compared to folding. i don't quite understand when you say this is equivalent to "setting" the ev of folding
to zero. isn't the ev of folding always zero? can you also elaborate more on what issue is the source of confusion and errors in the ev analyses?

2) which part of the combo counts ain't correct?
"you weight each of the respective EV's of that hand combo to derive the overall EV." - i think i asked this in my previous reply but it would be great to see an example of how i can calculate the ev in my situation from scratch to end.

3) there are 2 situations which i wanna calculate the ev of. firstly, i wanna calculate the ev of my hand vs his shoving range on the turn (99,77,A9s,A7s,AJ,AQ). secondly, i wanna calculate the ev of my hand vs that same shoving range with the exception that he only shoves (AJ,AQ) 70% of the time instead of 100%.

4) what about the pot amounts that i must pay attention to? at the time of making a decision whether to call the shove, the pot is 550 + 250 + 250 + 750 = 1800. is this what you are referring to?

i have tried to use Pokerstove to calculate the equity for the shoving range and got 63% as well. but i didn't know how to calculate the equity when there are other variables like (70% shoving, 30% calling).

So pot size at our decision point:

550+250+1000 = 1800

750 for us to call.

Range:
77 = 3 combos
99 = 3 combos
A7s = 2 combos
A9s = 2 combos
AQ = 8 combos
AJ = 8 combos
AK = 6 combos
Total combos = 32

Frequencies:
77 = 3/32 = .09375
99 = 3/32 = .09375
A7s = 2/32 = .0625
A9s = 2/32= .0625
AQ = 8/32 = .25
AJ = 8/32 = .25
AK = 6/32 = .1875

About the above. If you are going to assume AQ/AJ shoves here you should also include AK to be thorough.

Now at this point you could calculate the EV using the individual hands, but to make things faster we can lump hands with identical equity together just like you did previously:

77 & 99 = .1875
A7s & A9s = .125
AJ & AQ = .50
AK = .1875

Now we need to determine our equity for each hand grouping. You can either calculate this with outs or the much better solution is to use an equity calculator since it will not miss any outs like you might.

77 & 99 = 0
A7s & A9s = .102
AJ & AQ = .933
AK = .5

Now that we have the equity we can calculate the EV of each scenario.

77 & 99
Since we can never win vs these hands our EV is -750

A7s & A9s
10.2% of the time we hit our K or in the case of A7 the 9 pairs the board and we win and the other 89.8% we lose our 750

.102 * 1800 - .898*750 = -489.90

AQ & AJ
93.3% of the time we win and 6.7% of the time our opponent hits a Q or J and beats us.

.933 * 1800 - .067*750 = 1629.15

AK

We split the whole pot with villain (including our 750 call).

.5*(1800+750) = .5*(2550) =1275

So now to get our total EV we multiply the EV of our individual scenarios by the probability those scenarios occur:

.1875*(-750) + .125*(-489.90) + .5*(1629.15) + .1875*(1275) =

-140.625 + -61.2375 + 814.575 + 239.0625

= 851.775

Hopefully I didn't make any silly math errors in there but that should be the basic process.

Good job j_g of showing all the details of this prototypical EV calculation.

Minor nitpicks.

(1) Unless I am totally wacko, there is only one A9s combo villain can have (not two), and there is only one A7s combo villain can have (not two).

(2) Equity vs A9 is not equal to equity vs A7 (as you rightly mention at the bottom).

I guess I didn' count the combos like I should have, just used OP'S numbers.

Certainly forgot to discount our Ac.

I forgot A7 could be counterfeited until later in the post and I should have gone back to fix it. Thanks for reviewing and providing comments!

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thanks everyone for the input!

1 last thing, so if villian is shoving 70% AJ AQ, it will be 11 combos instead of 16 and the rest of the calculations will be the same?

Yes.

Is it possible to arrive at this same answer using some kind of software (apart from Excel)?