I raise pre flop with 65suited. Someone 3 bets with AA and I call. I figure I need 33% equity or more on the flop to call a cbet (lets assume villain always c bets). So my question is: whats my average equity on the flop when I continue with hands that have 33% eq or more. I think I need the average of a continuous probability distribution. If someone could help I would be very grateful.

Poker equities are chunky so I don't think there is an easy answer to your question. Assuming a continuous probability distribution may allow you to approximate an answer, but I cannot think of anything better than simply calculating the conditional expected equity directly by programming a computer to deal out every flop and calculating your equity. You proceed in the hand if your equity is at least 33% and otherwise fold to a c-bet. By keeping careful track you can calculate your conditional expected equity.

Ok thank you.

why 33%? pot sized bets are very rare nowadays.

It's just a weighted average, but if you want to know these things often, I agree that writing a simple piece of software would be the way to go.

The following calculation should be close:

P(flop straight flush) +
.999 * P(flop quads) +
.97 * P(straight & Villain no 4-flush) +
.915 * P(boat) +
.91 * P(trips) +
.83 * P(flush only) +
.74 * P(two-pair & V no 4-flush) +
.61 * P(monotone straight of V's suit) +
.54 * P(open-ender + flush draw)
.5 * P(monotone two-pair of V's suit) +
.45 * P(gutshot + flush draw) +
.36 * P(pair + gutshot) +
.35 * P(flush draw only) +
.33 * P(open-ender or double-gutter only)

All that remains is to calculate the P's. The total flop combos is C(48,3). There's a 50% chance of Villain having a specific suit (given that they have AA). So now we just count the flop combos of interest. I'll do a few now:

N(flop SF) = 4
N(quads) = 2
N(boat) = 2*3*3 = 18
N(trips) = 2*3*42 = 252
N(flush only) = C(11,3) - 4 = 161

I think odds oracle does these calcs but I can´t download it. Thanks for the input.

If I have time tonight, I'll kick off an exhaustive calculation dealing out every possible flop. The program will likely take forever, so I don't want to promise when it might be done, but if it finishes in our lifetime, I will report the result.

Ok. I have come up with a rudimentar method to find the average equity when it's above 33%, So im eager to know if it's correct or not and compare results.

I kicked off my program last night. This morning I find that it is only about 20% complete. So that means it will literally take days to finish. I will let it keep running but don't hold your breath.

Ok. Ty

I lost electricity temporarily this afternoon so my computer shut down unceremoniously. I think the program was somewhere near completing so this is either terribly sad or terribly funny (or both). I re-kicked off the program tonight for what it is worth.

I imagine the next thing that will happen is that just before finishing a couple of days from now, my computer will do a hard re-boot due to an unneeded and undesirable forced Windows update.

haha ok. Im waiting.

Stuff like this is why I'm sticking with Win7 as long as possible. When Win7 becomes obsolete, I'll quit Windows for good on personal pc's.

And your quote is incomplete. You forgot to mention that the "upgrade" may break various functionality of the OS until MS releases the next upgrade to repair the previous upgrade.

If anybody is still interested, my program finally finished. Hurray!

I ran the case in which the two aces are both of different suits than the suited 65.

If I have 65s vs AA heads-up and I only continue on flops on which I have at least 1/3 equity, my average equity at that point is:

53.22839%.

I downloaded Odds Oracle from PPT and I also got to that number (53.459%, close enough). Thanks anyway