08-28-2001, 04:04 PM
This is my first foray into figuring out EV mathmatically.
Mason's last 'hand to talk about' was great and brought up some very interesting and subtle aspects of the game.
He cleared up a lot of things in his responses but his explanation of why he didn't cap the flop didn't seem right to me. I did a little EV calc based on a couple assumptions and I want to run it by you all, see what you think, especially Mason. This might be a little dry and long, so those who are bored by EV discussions will want to move on.
I'm taking the scenario presented by Mason's Hand to Talk About from a few days ago on the Medium Stakes Forum. Basically, in a three handed flop jam, Mason slowed down with KK against a possible flush draw and a likely top pair. He chose to only call the fourth bet instead of cap it.
Ok here we go. Let's assume you're facing 14 outs. The button has top pair for 5 outs against you and the small blind has a non-nut flush draw for 9 outs (not counting running trips and two pairs). With two cards to come, you'll win slightly better than 50% of the time.
If you cap it on the flop, you'll win 6 chips half the time and lose 3 chips half the time. So you are sacrificing three chips by not raising.
Those times when the turn comes a blank, you become the favorite to win the pot and you get about 70% of the money put in on the turn. The turn comes a blank about 70% of the time. So the question is, will not capping the flop get you enough extra chips on the non-scare-card turns to make up for the guaranteed 3 chip profit on the flop?
About 30% of the time you'll make nothing because the turn card will kill you. Assume that means either an ace or a club or another jack. 14 out of 46 = 30.4%
So about 70% of the time you'll have an opportunity for more chips. At this point, you've got a slightly better than 70% chance at the pot, so you're winning about 2/3 of the chips that go in. You win 8 chips on the turn every time there's no scare card and there's no raise (2 opponents put in 6 chips each x 2/3). This means you win those 8 chips that 70% of the time the river doesn't kill you. In other words, once you see the flop, you have a guaranteed profit of roughly 5.5 chips on the turn (70% of 8, which is 70% of 12, assuming both opponents will stay for a single bet when the turn is a blank).
When there IS a raise, you win 11 chips instead of 5.5. What are the odds that foregoing the guaranteed profit of 3 chips on the flop will increase your chance of winning 11 instead of 5.5 on the turn for a net gain of 2.5 chips? Obviously, it better happen more than 1/2 the time to break about even. Even MORE importantly, it had better be the CAUSE of the turn raise. If the turn raise was going to happen anyway, you've thrown away 3 chips. That's where it gets fuzzy because it's impossible to exactly determine the chance of getting raised anyway and the affect that not-capping the flop will have on that.
I believe the chance of the flush draw folding on the turn to a raise is close to zero, in fact with 30 small bets in the pot (see below for how I got that number), he SHOULD call. So calculating the EV of getting him to fold and thus increasing your odds of winning the pot is negligible. This guy is here for the ride, he's going to see the river.
So your EV on not capping the flop is not positive unless the chance of getting raised on the turn is higher than 50%.
I just thought of a couple more minor points. Those rare times when you get raised on the turn after capping the flop AND the flush draw folds, your EV is astronomical. But again, I think this is extremely unlikely. Also, if you have even ONE more guy along for the ride on the flop your EV goes through the roof. Say he's holding a pair with a counterfeited overcard. You now make tons of money with each flop raise.
Ok, everyone, tell me if and how I got it wrong.
natedogg
PS: the 30 bets: The 30 bets are there in the non-capped flop scenario.
10 preflop (five players called 2 bets), 12 on the flop (3 players call 4 bets each), 6 more when the small blind faces a turn raise (mason bets, button raises, that's six small), and the EXTREMELY likely call behind him from Mason. That totals 30. If Mason caps the flop, the small blind is facing a pot with 33 bets.
Mason's last 'hand to talk about' was great and brought up some very interesting and subtle aspects of the game.
He cleared up a lot of things in his responses but his explanation of why he didn't cap the flop didn't seem right to me. I did a little EV calc based on a couple assumptions and I want to run it by you all, see what you think, especially Mason. This might be a little dry and long, so those who are bored by EV discussions will want to move on.
I'm taking the scenario presented by Mason's Hand to Talk About from a few days ago on the Medium Stakes Forum. Basically, in a three handed flop jam, Mason slowed down with KK against a possible flush draw and a likely top pair. He chose to only call the fourth bet instead of cap it.
Ok here we go. Let's assume you're facing 14 outs. The button has top pair for 5 outs against you and the small blind has a non-nut flush draw for 9 outs (not counting running trips and two pairs). With two cards to come, you'll win slightly better than 50% of the time.
If you cap it on the flop, you'll win 6 chips half the time and lose 3 chips half the time. So you are sacrificing three chips by not raising.
Those times when the turn comes a blank, you become the favorite to win the pot and you get about 70% of the money put in on the turn. The turn comes a blank about 70% of the time. So the question is, will not capping the flop get you enough extra chips on the non-scare-card turns to make up for the guaranteed 3 chip profit on the flop?
About 30% of the time you'll make nothing because the turn card will kill you. Assume that means either an ace or a club or another jack. 14 out of 46 = 30.4%
So about 70% of the time you'll have an opportunity for more chips. At this point, you've got a slightly better than 70% chance at the pot, so you're winning about 2/3 of the chips that go in. You win 8 chips on the turn every time there's no scare card and there's no raise (2 opponents put in 6 chips each x 2/3). This means you win those 8 chips that 70% of the time the river doesn't kill you. In other words, once you see the flop, you have a guaranteed profit of roughly 5.5 chips on the turn (70% of 8, which is 70% of 12, assuming both opponents will stay for a single bet when the turn is a blank).
When there IS a raise, you win 11 chips instead of 5.5. What are the odds that foregoing the guaranteed profit of 3 chips on the flop will increase your chance of winning 11 instead of 5.5 on the turn for a net gain of 2.5 chips? Obviously, it better happen more than 1/2 the time to break about even. Even MORE importantly, it had better be the CAUSE of the turn raise. If the turn raise was going to happen anyway, you've thrown away 3 chips. That's where it gets fuzzy because it's impossible to exactly determine the chance of getting raised anyway and the affect that not-capping the flop will have on that.
I believe the chance of the flush draw folding on the turn to a raise is close to zero, in fact with 30 small bets in the pot (see below for how I got that number), he SHOULD call. So calculating the EV of getting him to fold and thus increasing your odds of winning the pot is negligible. This guy is here for the ride, he's going to see the river.
So your EV on not capping the flop is not positive unless the chance of getting raised on the turn is higher than 50%.
I just thought of a couple more minor points. Those rare times when you get raised on the turn after capping the flop AND the flush draw folds, your EV is astronomical. But again, I think this is extremely unlikely. Also, if you have even ONE more guy along for the ride on the flop your EV goes through the roof. Say he's holding a pair with a counterfeited overcard. You now make tons of money with each flop raise.
Ok, everyone, tell me if and how I got it wrong.
natedogg
PS: the 30 bets: The 30 bets are there in the non-capped flop scenario.
10 preflop (five players called 2 bets), 12 on the flop (3 players call 4 bets each), 6 more when the small blind faces a turn raise (mason bets, button raises, that's six small), and the EXTREMELY likely call behind him from Mason. That totals 30. If Mason caps the flop, the small blind is facing a pot with 33 bets.