Question on basic probability and Ev

[SimaoMacaco]

Could somebody please comment on validity of the following analysis of EV for me please:
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Game is NL holdem
Villain range is {55, 22, KQs, KQo}
Hero has 8c7c
Board is Qc2c5cKd

Hero equity at Turn = 0.82273
Villain equity at Turn = 0.17727[/i]

Turn (Qc2c5cKd)
Villain bets $8 into $14 pot, Hero to act
Effective remaining stacks after bet is $32.7
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Option 1:
..Hero calls and pushes river (Hero folds perfectly when beaten)
..villain folds river 0.4, calls 0.6

(0.82*22)-(0.18*8) = 16.6 << Value at turn
(16.6*0.4)+(32.7*0.6) = <font color="red">36.22</font> &lt;&lt; includes river push &amp; fold %


Option 2:
..Hero pushes turn
..villain folds 0.5, calls 0.5

(0.82*54.7)-(0.18*40.7) = 37.5 &lt;&lt; value of push
(37.5*0.5)+ (0.5*22) = <font color="red">29.75</font> &lt;&lt; includes fold %

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So it appears Option 1 is more EV.. however.. this assumes that Hero can fold perfectly when beaten..

If villain folded the best hand 20% of the time on the river his EV would be 0.8*36.22 = 28.97

[SimaoMacaco]

Anyone agree with my Math..

[raistlinx]

I have some different numbers.

For option 1 you are always seeing the river and will be beat (but fold 100% correctly) 18% of the time. There for our calculations are:

($30 * .33) + ($46.7 * .49) + ($-8 * .18) = $31.34

That is, 18% we lose our $8 turn call when we fold correctly, now of the remaining 82%, villain folds 40% and calls 60% meaning we win $30 33% and $46.7 (his stack plus what was in the pot before we called the turn) 49% of the time for a profit of $31.34

If we just push the turn we get:

($22 * .5) + ($54.7 * .41) + ($-32.7 * .09) = $30.48

We win the $22 in the pot 1/2 the time when he folds on the turn, $54.70 (the rest of his stack + what's in the pot already) 41% of the time and we lose $32.70 the few times he both calls AND we lose for a total profit of $30.48

So calling an evaluating the river is better in theory, however, since you will not make the right play 100% of the time in practice pushing is better.

I may have estimated the pot sizes wrong though, I did this quickly at work this morning.