ridiculously easy ev calculation

[mr pink]

someone do this for my friend because he thinks i'm full of [censored].

Party Poker 5/10 Hold'em (8 handed) converter (http://www.selachian.com/tools/bisonconverter/hhconverter.cgi)

Preflop: Hero is MP2 with 8/images/graemlins/heart.gif, 7/images/graemlins/heart.gif.
<font color="#666666">2 folds</font>, MP1 calls, Hero calls, CO calls, <font color="#666666">1 fold</font>, SB completes, BB checks.

Flop: (5 SB) 9/images/graemlins/club.gif, T/images/graemlins/diamond.gif, A/images/graemlins/diamond.gif <font color="#0000FF">(5 players)</font>
SB checks, <font color="#CC3333">BB bets</font>, MP1 calls, Hero calls, <font color="#CC3333">CO raises</font>, <font color="#CC3333">SB 3-bets</font>, BB calls, MP1 folds, Hero calls, CO calls.

Turn: (9 BB) 2/images/graemlins/spade.gif <font color="#0000FF">(4 players)</font>
<font color="#CC3333">SB bets</font>, BB calls, Hero FOLDS, <font color="#CC3333">CO raises</font>, SB calls, BB calls.

please explain how calling the turn here is +EV and work out the calculations for me, i'm kind retarded when it comes to it. for simplicity, just give him the 8 full outs for his OESD even though they're slightly discounted due to the 2 toned board.

thanks in advance.

[AaronBrown]

If I count this right, there's $85 in the pot and it's $10 to Hero when he folds. If this were a bet paying $85 if he makes his straight against $10 if he doesn't, that has an EV of +$6.52. But you have to figure on at least one raise, which makes it $20 against $125, which reduces the EV to +$5.22. If Hero gets two raises, it's $30 against $155, and his EV is down to +$2.17.

Now, what happens on the river? If Hero doesn't get a 6 or J, he folds. If he gets a 6 or J of diamonds, he's probably going to lose to BB, but with these pot odds, he'll call the bet. There's some positive EV here. With any other J, he's got nuts, barring some crazy in the pot with Q 8. Any other 6 and he has at least tie. He's going to get at least a call, and I wouldn't rule out a raise, from the high trips/high two pair SB and CO are representing. If one or both of them are bluffing, they are also going to raise.

So Hero has positive EV even in the worst case before the river card. 38 river cards don't change that, because he folds. 2 river cards add a little to the EV, 6 add a lot. That's an easy bet.

I'd also consider raising after the flop. It might have saved some money, and since it misrepresents the hand, increased the winnings if Hero does make the straight.