Quote:
Originally Posted by ronrabbit
Being pretty confident villan has qq,KK,aa here l, if we do flop an ace can we not take it away on a later Street and make up for some lost equity?
I have always worked off 10:1 generally but I am usually deep enough for it to be pretty trivial, this was very marginal which is why I checked it out....
Is there a standard number to work off in these sort of spots, we are at 11:1.... Is 12:1 better? 13:1?
Here's my take on the math.
We're about 7.5:1 against flopping a set. When we don't flop a set, let's assume we always fold, so we lose $30. When we do flop a set, against a range of AA-QQ, let's assume we always get it in on the flop no matter what the other cards are on the flop. If we're up against a range of AA-QQ, and all we know is that 1 of the cards on the flop is a T, we have 80.7% equity, which I'm going to round down to 80% to make my life a bit easier. So when we flop a set, 80% of the time we win $336 and 20% of the time we lose the $30 we're putting in pre + $270 more. So our EV when we flop a set is .8*$336-.2*300=$208.8. 7.5 times we lose $30, so that's -$225, and we don't win enough when we bink to make up for it.
Now, let's assume we had $432 back to start the hand, or $120 more, which would give us 15:1 implied give or take. We still lose the same $30 when we whiff. When we flop a set, 80% of the time we win $456, and 20% of the time lose $420, so our EV when we flop a set is $280. That's well bigger than our risk adjusted -$225 when we miss, and pretty clearly shows 15:1 is good enough IO.
Basically, I'd never go less than 12:1, and really want 15:1. While you're right that sometimes we can take it away on ace-high flops, that by definition means we don't have the same implied odds on those flops. Similarly, you may also say that we can sometimes get away from set over set, but that again cuts into our implied odds. What this really shows is that it's hard to set-mine in 3-bet pots.