Quote:
Originally Posted by scylla
There's really only one way to calculate EV, and that's the first one. That's simply because that's how EV is defined. If I correctly understand you the second way would mean setting the pot to 0 at every decision? This would ignore the fact that often the pot offers an overlay, which justifies playing an inferior hand. For example, flushdraws are usually a "worse hand", but can be played due to the pot offering additional odds.
Actually there are two ways.
For example,
Board: 2 2 2 3 3 rainbow
Villain check on the river
assume Villain hold AA or QQ
Hero hold KK
Pot: 100
Bet:50
Assume if Hero bet 50, Villain will call with all the AA, and fold all the QQ.
Hero is considering between checking down/betting half pot
calculate using 1st way:
<HERO CHECK> = 0.5*100 = 50
<HERO BET> = 0.5*-50 + 0.5*100 = 25
calculate using 2nd way:
<HERO CHECK> = 0
<HERO BET> = 0.5*-50 = -25
Another example:
Villain check on the turn, Hero considering checking/betting
Assume Hero hold a draw which has 20% equity all the time no matter what Villain hold
Assume Villain has 80% equity all the time
Pot:100
Bet:50
Assume if Hero bet, Villain will fold 50% of time, and if Villain call, Hero simply lost the whole pot
Assume Hero will get 100% of equity if he check
(in the reality Hero will not lose the whole pot when Villain call, and will usually get more than 100% equity when Hero check down, but I will just simplify it for the sake of this discussion)
calculate using 1st way:
<HERO CHECK> = 100*02 = 20
<HERO BET> = 0.5*100 + 0.5*-50 = 25
calculate using 2nd way:
<HERO CHECK> = 0
<HERO BET> = 0.5*80(when villain fold I win those 80% equity I don't have) + 0.5*-70 (when villain call, I lost the bet 50 plus my 20% equity 20) = 40 - 35 = 5
To transfer the ev between 1st & 2nd ways is easy though, for example in a 800 pot CREV show the ev of AKs is 836, and it's equity is 86%. 836 is the ev calculated by using the 1st way. Then it's ev of the 2nd way is 836 - 800*0.86 = 148
Cheers,
Pokoteng
Last edited by pokoteng; 12-05-2015 at 11:33 PM.