formula 2 calculate EV?

[Altreg]

Hey all
My question is-what is right formula for calculating EV on my play?

lets say pot is 20bb HU,my opponent have 30% fold equity,when he calls i bet 10 bb and i will win pot 20% of the time is this correct formula?-

EV=0.3x20+0.7x((20+10)x0.2-0.8x10))

thank you

[sixhigh]

<font color="#FF4444">[*] </font> I'm not sure I understand you correctly, I'll give you a general formula. Say the size of the pot is p, your fold equity is f, your equity against his calling range is e, the size of your bet is b and there wont be any more betting after he calls your bet.

Then the EV on your bet will be as follows:

EV = f*p +(1-f)*(e*(p+b) + (1-e)*(-b))

with the numbers you gave:

30%*20 + 70% * (20%*(30) + 80%*(-10))

which is exactly what you got there.

[Altreg]

ok,thank you

now another one,this is 50bb in the pot on the 4rth street -he raises17bb, i re-raise all-in(another 53bb),hes fold equity is 35%,and when he calls my all-in he wins 70% of the time ,check my math is this correct or not?--

EV=0.35*50+0.65*((50+17+53+70)*0.30-0.70*70

thank you for reply

[sixhigh]

<font color="#FF4444">[*] </font>In case he folds you gain the pot and his bet (+50 +17)

In case he calls two there are two possibilities:
30% of the time, you will win the pot, his bet and his call of your raise (+50 +17 +53)
70% of the time you lose your raise (-70)

-&gt; 35%*(67) + 65%*(30%*(120) - 70%*(70)) = 15

[Altreg]

oh,ok
this is what i meant

thank you very much 4 your reply

[Altreg]

here is another one

pot is 80bb after the turn,i check-call river bet 30bb and have 25% chaince to win. Is this correct calculation of my EV-

EV=(80+30+30)*0.25-0.75*30

or i dont need 2 include my bet-call in this and it will be like that-

EV=(80+30)*0.25-0.75*30

thank you

[Altreg]

and another one
after the turn pot is 40bb,i bet 15bb and got re-raised to 40bb(15bb+25bb more),if i call i win the pot 25% of the time,is this correct calculation on my river call?
EV=(40+15+25)*0.25-0.75*25

[sixhigh]

<font color="#FF4444">[*] </font> You don't include the amount you have to call because that's no money you can win. It's the money you pay for the chance to win. So the 2nd formula is correct.

2nd Problem: don't bet 15BB into a 40BB pot [img]/images/graemlins/smile.gif[/img]. You have to call 25 BB to win 40+15+40 (the original pot + the amount you put in the pot already + the money he put in the pot).

--&gt; EV = (40+15+40)*25% - 25*75%

[R Gibert]

[ QUOTE ]
<font color="#FF4444">[*] </font> You don't include the amount you have to call because that's no money you can win. It's the money you pay for the chance to win. So the 2nd formula is correct.


[/ QUOTE ]

The 1st formula is incorrect, but not for the reason stated. Here is the corrected version:

EV=(80+30+30)*0.25 - 30

This version illustrates a nice trick that saves a multiplication. Here is the algebra that justifies it:

<font class="small">Code:</font><hr /><pre>
EV = (pot + bet)*P(win) - P(loss)*call
= (pot + bet)*P(win) - (1 - P(win))*call
= pot*P(win) + bet*P(win) - call + call*P(win)
= pot*P(win) + bet*P(win) + call*P(win) - call
= (pot + bet + call)*P(win) - call</pre><hr />

[Altreg]

thank you all
it was little confusing for me,because for flop or turn EV calculation i include my bet,so i thought on river calculation i should do the same 2.But now ,i think ,i get it.

By the way any one know any good method to calculate EV during the hand or this is 2 hard 2 do and ppl just remember hands EV versus ranges?