Quote:
Originally Posted by TheDarkKnight
Here’s what that distribution looks like:
AA (6)
Sets (6)
AK (12)
Suited Kings (9)
Flushes (7)
That’s 7 of 40 combos that have flushes on the river. That’s 17.5% of my combos beating 43dd.
Even if you add KQo into that mix, which is reasonable, we are still at 13.4% of my river betting combos that beat 43dd.
...
However, it’s also worth noting that, given this distribution, I will have three nut flushes in my range, which means I will be 4-betting the river almost 6% of the time...
Quote:
Originally Posted by TheDarkKnight
Let's say I'm calling with all my two pair or better hands... which I'm not. That means I'm calling his 3-bet 25% of the time, but almost 31% of the time I call, I have a bigger flush than him.
These statements seem to contain the necessary information.
Quote:
Originally Posted by TheDarkKnight
EV(call) = (85% * 17) + (15% * -2) = 14.15
EV(3-bet) = (5.7% * -4) + (7.7% * -3) + (17.3% * 19) + (69.3% * 18) = 15.3
1) It looks like you're using 15% as an estimate for the probability that you have a flush. I think that's an estimate based on the 17.5% and the 13.4% numbers.
2) You're 4-betting the nuts (3 hands), which you're saying is 5.7% of your range. This seems to be calculated based off of the 40 hands you listed plus 12 KQo combos for a total of 52 hands.
3) You're calling with your non-nut flushes, which is 4 hands out of 52, which is about 7.7%.
4) The 17.3% number is from your calls with two pair or better, but not flush hands. I think that's your 6 sets plus 3 suited KJ (which should probably only be 2 suited KJ since the K and J on the board are different suits).
5) 69.3% is the remaining times you don't call.
6) You didn't calculate the 3-bet correctly when considering the times you fold. The last number in that line should be 17 and not 18. That's where the inflation came from.
I will reproduce the calculation more equitably. You're going to raise the nuts. You're going to only call with sets and not two pair.
0) I think your hand count is wrong. I can't reconcile the "suited kings" number. There are 2 KJs hands and 3 KTs. There's also 3 KQs, but if you count those in there, then you only have 9 KQo hands. So something is wonky. Your AKs hands are in your AK listing. So I'm going to use the following hand count:
KTs (3)
KQs/KQo (12)
AK (12)
AA (6)
KJ (2)
Sets (6)
Flushes (7 -- 3 nut flushes + 4 non-nut flushes)
TOTAL == 48 hands
Calling:
An estimate is not good for a direct comparison. So this will be done with the exact values in the 48 hand count.
* You will 3-bet with the nuts, which is 3 hands.
* You will call with with non-nut flushes, which is 4 hands.
* You will call with everything else.
* BB will lose with everything.
EV[Call] = 6.3% * (-3) + 8.3% * (-2) + 85.4% * (17) = 14.16
3-Betting:
* You will 4-bet with the nuts, which is 3 hands.
* You will call with non-nut flushes, which is 4 hands.
* You will call with sets, which is 6 hands.
* You will fold everything else.
* BB will call with everything and lose with everything.
EV[3-bet] = 6.3% * (-4) + 8.3% * (-3) + 12.5% * (19) + 72.9% * (17) = 14.27
Miscellaneous Comments:
* I don't know that you call with top pair for one more bet. If you fold that, the EV of calling goes down and makes 3-betting more profitable.
* If BB wins, it should hit both scenarios in basically the same way. The total EV will go down, but I don't expect that the difference to change much.
* At the end of the day, the question is still basic: He is wagering 1 BB to win 2 BB. If that ratio holds in the hands you call with, it's a win for him. You have 7 hands that beat him. If he gets a call out of 3.5 hands of your remaining range, it's +EV to 3-bet. That's about half the time you hold a set.