Seemingly easy EV calculation I can't figure out

[swede554]

(This requires doing some math, so if no one feels like doing it, I understand. However, it's good practice if you're not that familiar how to calculate Expected Value)

So for some reason when I run these numbers through pokerstove they don't match up. Please tell me why.

This is the situation. It's somewhat hypothetic.

CO raises, Hero re-raises allin from SB w/ 44. CO's raising range is 77+, ATs+, AJo+, KQs+ and he'll call the re-raise 100% of the time.

If Hero wins the hand he'll win 160,000.
If Hero losses, he'll lose 131,000.

According to pokerstove Hero has 37% equity vs. villains range.
equity win tie pots won pots tied
Hand 0: 62.943% 62.65% 00.29% 669397500 3137016.00 { 77+, ATs+, KQs, AJo+ }
Hand 1: 37.057% 36.76% 00.29% 392806164 3137016.00 { 44 }

So,

+160,000 x 37%= +59,200
-131,000 x 63%= -82,530

59,200-82,530= -23,330

So Hero's play has a EV of -23,330 right?


BUT when I calculate my EV by separately adding my EV vs. the overpairs (77+) and my EV vs. the overcards I get a different number.

There are 48 combos of overpairs he'll call with. 77-AA(8x6) There are 80 combos of overcards he'll call with. AT+, KQ(5x16). So when he calls, 37.5% of the time it's 77+, 62.5% it's AK-AT, KQ. Given that:

77+
.19x +160,000= +30,400
.81x -131,000= -106,110
= -75,710 x 37.5%
= -28,391

AT+, KQ
.53x +160,000= +84,800
.47x -131,000= -61,570
= +23,230x 62.5%
= +14,519

-28,391+14,519
= -13,872

So doing it that way my EV is -13,872, different from the initial calculation.

What am I doing wrong?

[illini43]

[ QUOTE ]
If Hero wins the hand he'll win 160,000.
If Hero losses, he'll lose 131,000.

[/ QUOTE ]

This might be your problem.

What are the beginning stack sizes?

[illini43]

What I'm thinking you are doing wrong is calculating the amount of chips hero loses if he loses the pot.

Hero can't lose more chips than are in his stack - even if CO had a tiny stack, Hero wouldn't lose more than the amount of CO's stack.

[swede554]

Villain got Hero covered. Hero's stacksize after posting the SB is 131,000. Hence if Hero losses the hand he'll lose 131,000 right?

If Hero wins the hand he'll win 136,000 (Villain's call)+10,000(BB)+5,000(SB)+9,000(antes)= 160,000

Hero wins 136,000 from Villain because he has to call the 131,000+the 5,000 SB.

[Tackleberry]

I think its a matter of rounding. You can simplify your question by just taking the flat percentages:

If you calculate your EV against the whole range you get a winrate of roughly 37%. If you calculate the winrates separately and combine them afterwards(!!) you get roughly 40%:

(Rate[OP] x Chance[OP]) + (Rate[OC] x Chance[OP]):
=> (37,5% x 19%) + (62,5% x 53%) = ~40%

The difference of 3% sounds small but makes the big difference in the calculation of your final EV:

EV(40) = (0,4 * 160000) + (0,6 x -131000) = -13782,5
EV(37) = (0,37 * 160000) + (0,63 x -131000) = -23330

[Tackleberry]

After the explanation of a rounding error did not satisfy me I thought it over again. [img]/images/graemlins/smile.gif[/img]

The real problem is, that you counted 5*16 combos for the overcards. This is not correct, as there are only four (!) combos of ATs and KQs. So the correct amount of OC-combos is (3*16) + (1*4) + (1*4) = 56 (instead of 80).

In this case the distribution is 46.15% for OP and 53.85% for OC. When you take this figures, the EV comes out identical, no matter which way you take.