maths check

Mr.Plough

This is a fairly standard scenario, but im really just looking to make sure my maths is accurate here. Just trying to brush up i suppose.



1/2 live
villain is fairly loose like much of the value on the dublin cash scene.
Hero utg and covers the villain in bb
I'm dealt AK no clubs and raise to 8. co and bb call

flop is 6c 6s kc (pot 25)

bb donk bets, you raise, co folds, bb shoves.
after the flop there is 197 in the pot and its 87 to call.

(its obviously a call but just testing my math on it).

the only hands i see a player like him having in this spot are:

6x (he loves to see flops with any two) with which i win ~8%
two clubs i win ~62%
kx i win 88%

im pretty sure he either has a 6 or the flush draw so ive decided he has a weaker king 20% of the time.

x = % of times he has a 6

so EV of calling if he has a 6 = x[(-87)(0.92) + (0.08)(197)] = (-64.28)x

if he has the fd = (0.8-x)[(-87)(0.38) + (197)(0.62)] = (0.8-x)89.08

weaker king = 0.2[(-87)(0.12) + (197)(0.88)] = +32.584

so total EV of calling = x(-64.28) x(-89.08) + 71.264 +32.584

= - x*153.08 + 103.848

therefore for neutral EV -> x = 103.848/153.08 = 0.68

so he has to have a 6 less than 68% of the time for this call to be profitable?

sorry for making your eyes bleed, just making sure i have the maths down, any mistakes can someone point them out.



thanks

5starpool

Are all the blank lines necessary? Easy call at this point.

Mr.Plough

I said in the post i know its an easy call. its the ev calculation + hand range utilisation etc I'm interested in.

Chucky the tree

pokerstove?

ozpoker

Chucky the tree wrote:

pokerstove?

http://pokerstove.com/

Hitman Actual

Why are people saying pokerstove? That just gives you your equity against a hand range; it won't tell you exactly what OP is looking for. He already knows his (approximate) equity against the possible hands.

Mr Plough, to check your maths I think you can just rework the equations and plug in the percentages and see if you get zero i.e. something like this:

0.2(EV against Kx) + 0.68(EV against 6x) + 0.12(EV against FD) = 0?

I haven't really time to look through your maths though, but it looks reasonable.

Mr.Plough

alright thanks lenny. was what i was looking for