Hey guys,

So I was wondering how to calculate the EV of checking vs. betting against a villain's range, specifically as it pertains to the the hand below. Should we be check/calling the river in order to let him bluff with his missed straight/flush draws, or betting ourselves in order to get value from his weaker Ax/Tx hands? Which of these options would yield a higher EV, and how is this calculated? (Let's assume the two options are check/calling a shove from the villain, or open-shoving ourselves.)

If one of you guys could let me know how this is done, and if there's any software to make the calculation quicker/easier, I'd really appreciate it! (I currently only have Flopzilla.)


Here is a link to the hand replay, in case the description below is confusing:
http://www.pokerhandreplays.com/view.php/id/8423539




Hand Information
$5/$10 (6 handed).
Hand History converter courtesy of pokerhandreplays.com

Table Information
Hero (SB): $1,000 (100 bb)
BB: $1,000 (100 bb)
UTG: $1,000 (100 bb)
MP: $1,000 (100 bb)
CO: $1,000 (100 bb)
BTN: $1,000 (100 bb)

Dealt to hero
**

Preflop (Pot: $15)
UTG****FOLD
MP****CALL
CO****FOLD
BTN****FOLD
Hero (SB)****RAISE $40
BB****FOLD
MP****CALL

Flop(Pot: $90)
***

hero****BET $75
MP****CALL

Turn(Pot: $240)
****

hero****BET $185
MP****CALL

River(Pot: $610)
*****

hero****???
(Both players have $700 behind.)

Someone in position who calls 3 moderate bets on a final unconnected board probably doesn’t have much. In your case I gave villain a river range of {TT+,ATs+,ATo+,KhJh,} not having any prior information such as villain characteristics, your table image, etc. The equity calculator Equilab gives your ace pair an equity of 56%.

If you check and villain shoves, EVcall = 0.56*1310 - 0.44*700 = 425

If you and villain both check, your EV= 0.56*610 = 342

For you shoving OOP, all of the hands in villain’s assigned range are at least a pair except for Kh Jh so he will probably call (he appears to be a calling station). He is hoping you missed a draw, have a small pair or are bluffing. The villain call will result in an EV that is essentially the same as a H.check/V.shove of 425 or so.

If villain folds to your shove, your EV = 610. The bigger the fold equity, the higher is your EV. For example, for fe=50%, EV=518.

Naturally, results depend greatly on the range assigned to villain. Use the free Equilab program and equations shown here to see this.

Would like to also mention assumptions matter a lot, for example in this spot say villain is a nit and will fold a lot of weak Ax and only call AK+ (in order to have a value bet we must get called by worse more then 50%) which do you think is going to have higher EV betting or checking?

Going through the numbers pen & paper style is a bit tricky and very tedious like statmanhal posted above... Understanding the basic concepts of when x decision will be more profitable then the other is good enough.

Definitely, assumptions are very important. As for pen & paper calcs and tedium, true but it doesn't have to be. Many of the calcs I do is through an Excel-VBA program I have. For EV calcs, you simply enter the bet sizes and equities and get an immediate answer. Through Excel's Goal Seek function, you can even get the break-even values for most inputs.

For those who are interested, PM me with your eMail address and I'll send you an image of the module I used for these calcs.

PLEASE! Always wanted to create a simple program like that in excel but never got around to it.

Pmed ya

Statmanhal - Thank you, that is exactly what I was looking for!

I went ahead and downloaded that Equilab program and played around with it a bit. It seems like the looser of a range we assign the villain, the more we should be checking as he will have a ton of missed draws with no showdown value that would likely be bluffing given the stack sizes on the river. Whereas the tighter of a range he has, the more we should be betting as his hands will mostly be made up of weaker pairs and dominated Ax hands that would likely check behind if we checked but might call a river shove given the board runout.

Does that make sense, or did I mess up somewhere?

Evoxgsr96 - Thank you for your response! I agree that assumptions are very important and could definitely make the difference between whether we should be checking or betting.

I guess from a GTO perspective, since we would be shoving a lot of our missed straight/flush draws on the river, we should also be shoving some of our stronger Ax as well, right? Of course this might not be that relevant at the lower stakes but is definitely something we want to keep in mind going forward.

Also, since the river shove would be an overbet ($700 into $610), wouldn't this mean we could add a couple extra bluffs in our shoving range as well? I know this is a bit OT but an interesting concept to think about/discuss as well.

Bump. Could anyone verify whether my logic here was correct?

Your logic seems ok. But I would caution that AQ is strong, but you are not super strong in your range, and villain should think you are about that strong for value range on this runnout, so expecting him to bluff turn/river with his busted draws here is a little bit of a stretch.

I like how you played it, just looks like villain was on a draw, even though you have one heart blocker.


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Sounds like a huge time saver, PM sent.

He should only sell it to a few people

Even though i'm sure someone could make it themselves in excel using the said equations having made sure they are correct, though it sounds tedious lol