A question about equity

[cartman]

I have been thinking lately about the situation in which I open-raise preflop, flop a quality draw and get led into on the flop heads up. I typically autoraise the flop in this spot, but I never really know what to do when checked to on the turn at which time the pot contains 4.25 big bets.

<font color="blue"> Before I go on, do you guys usually bet or check behind here if your draw has showdown value?

What if your draw has no showdown value?</font>

Lets assume that I have a J high four-flush and get checked to on the turn after my autoraise on the flop. Lets also assume for simplicity sake that the board is big and I value my pair outs at zero so I will fold on the river unless I make the flush. So I have 9 outs (only the flush cards).

Check my methodology here:

I have 9/46 or about 20% equity. My opponent has 37/46 or about 80% equity (assuming that he will autobet any river and I will fold if I don't make my flush). Now when deciding whether to bet the turn, I must evaluate the 3 possible results of my turn bet.

1) He folds and I win 4.25 big bets.

2) He calls and I lose .6 big bets <font color="blue"> which is the difference in our respective equities multiplied by the amount that I put in on the turn. (80%-20%)*(1BB) = .6 BB LOSS. </font>

3) He checkraises and I lose 1.2 big bets. (80%-20%)*(2BB) = 1.2 BB LOSS.


So now I just estimate the percentage of time I think he will take each of actions 1), 2) and 3) and multiply them by the resulting gain or loss of each and add the terms up to find the EV of a turn bet.


EV OF A TURN BET =
(% HE FOLDS)*(4.25) + (% HE CALLS)*(-.6) + (% HE CRs)*(-1.2)


<font color="blue">Is this methodology correct?</font>


Thanks,
Cartman