Hi,

I've started reading Jonathan Little on Live No Limit Cash Games Vol 1 and one of the EV calculations is confusing me (p19 - kindle). Shouldn't the EV calculation be:

EV = (0.174)($114) - (0.826)($32) = -$6.60



If my solution isn't correct I'd be grateful if someone could explain why?

Thanks in advance,

Snook

No, because when you win, you just get your $32 back. I prefer the more explicit form, which is to say
when you win, you win $32 + 50
when you lose, you lose $32
EV = .174*82 - .826*32 = -12.16

You can actually from here to his by saying
EV = .174*82 - .826*32 + .174*32 - .174*32
you see what I mean? I added 2 terms to the end, but they cancel each other out so the value is still the same. Now I can move them around and say
EV = .174*82 + .174*32 - .826*32 - .174*32
EV = .174*114 - 32

Nope looks correct. You pay those 32$ into the pot 100% of the time. You win the pot (including these 32$) in 17.4% of the time.

You can do it your way too, but then you can't include your 32$ in the pot:
EV = (0.174)($82) - (0.826)($32) = -$12.16

For the complete EV calculation with money in the pot, terms I will be using are:

$pot = money in the pot ($50)
$bet = money bet ($32)
Pwin = chance of winning (0,174)

So you add up the money you win * frequency - money you lose * frequency.

With $50 in the pot, when you win you get the $pot plus the $bet that your opponent has put in. This happens Pwin of the time. When you lose you only lose the $bet times (Pwin-1).

EV = ($pot+$bet)*Pwin - $bet*(1-Pwin)

We can expand this and get:

EV = $pot*Pwin + $bet*Pwin + $bet*Pwin - $bet

Pwin is the common factor so you get

EV = Pwin($pot + 2*$bet) - $bet

In this case EV = 0,174*114 - 32

Edit; I'm slow as ***.

Yes,

this is best imo as it makes more sense intuitively. If you're in an all in spot don't include the money your putting in as money you can win.

Thanks all, much appreciated. I think I'm beginning to get my head around it a bit better now.

Curios as to why he expressed it in a different way although both methods reach the same conclusion? I think most websites and books use EV = (%W X $W) - (%L X $L) instead he chose EV = (%W X $POT + $CALL) - $CALL . Sorry it just so happens that ive been looking into EV and Semi bluff shoving calculations and am basically trying to reaffirm what I think I know so far.

These are two slightly different concepts:
1) As described in the book, you calculate the $EV (e.g. $POT*%WIN) in the pot after taking a certain action and subtract the immediate cost of choosing that action ($CALL).
2) The alternative is to calculate the various $ outcomes ($WIN, $LOSE) and weight them by their probability (%WIN, %LOSE).

Both methods are perfectly fine, it's a matter of preference and context. If you are doing complex calculations it makes sense to use the way he described it in the book, because you can intuitively break up the calculation over multiple decisions. For simple EV calculations the second calculation by outcome is probably slightly easier to understand.