wtfsvi
08-18-2005, 06:56 PM
I'll go through the math more thorougly than needed in this thread, just because it's good for me to do some thorough poker math.
This post will deal with a statement I see around here that makes no sense to me: "We have to get it all in on the flop while we have correct odds, or else he can prize us out on the turn."
When we get it all in on the flop, we buy both the turn and the river card for one prize. When this prize gives us correct odds, that's fine. But it will always be better to buy the turn card for even more correct odds, and then get prized out before we see the river, than to get it all in on the flop. That should be obvious without doing lots of math imo, but here's an example anyway:
Decent LAG opens in the CO for 3bb. I (100BB) hold 7 /images/graemlins/heart.gif8 /images/graemlins/heart.gif on the button and raise it up to 10bb. Loose-passive villain (100BB) min-reraises in SB. BB and CO folds, I call.
Flop (43BB) comes 4 /images/graemlins/club.gif5 /images/graemlins/heart.gifJ /images/graemlins/heart.gif. Villain leads into me for 20BB. Now, tell me pushing isn't totally retarded? It seems to me it is.
EV of pushing:
This guy, as most LPs, can be put on an overpair with near 100% accuracy after this manuever, so I think it's safe to operate with no folding equity. According to twodimes, we have 45,3% equity against an overpair with half a heart.
EV push = (0.453 * 203BB)-80BB = 12BB
EV of calling:
Lets assume he will push any turn. That is the worst case scenario(, except if he check folds when I hit of course, but that isn't going to happen given his above mentioned characteristics).
I have 12 outs against an overpair. 9/12 = 3/4 of my outs are hearts. He'll have a heart 50% of the time, and that means 4.5 of the hearts will give him a flush redraw and 0.5 of them will give him a full house redraw. That means I'll own 83.4% of the pot 5/9 of the time and 100% of the pot 4/9 of the time when a heart hits. In conclusion, when my heart hits I have (5/9 * 0.834) + 4/9 = 90.8% pot equity. This is desregarding that the 4 /images/graemlins/heart.gif gives him two outs to the boat, so lets say 90% for simplicity. Furthermore, when a non-heart 6 hits I have 100% equity, so that doesn't require much attention.
Now lets look at what happens when I don't hit my outs. Three different scenarios are possible: My hand improves without hitting an out (a seven, an eight, a nine or a ten), a brick falls, or he hits his set and I lose 1.25 outs (I lose the 4 /images/graemlins/heart.gif, and I lose the quad-making card the 1/4 times it's a heart). The latter will have fairly little impact, and I've conviently set up the math so I won't have to calculate it.
A seven or eight gives me 5 extra outs. A nine or ten gives me 3 extra outs. With a brick I still have my old 12 outs. The turn push is for 60BB to play a 203BB pot, so I need 30% equity to call. When the turn is a brick I have 9/46 + 3/44 = 26,4% equity, so I fold. (And when the turn is an A-Q it is a tiny bit worse since there's a chance he hit a set, so I obviously fold then as well.) When the turn is a seven or eight I have 26,4% + 5/44 = 37,7%. Great, I call. When the turn is a nine or ten I have 26,4% + 3/44 = 33,2%. I call.
The turn will be a heart 9/47 times, a six 3/45 times, a seven or eight 6/45 times and a nine or ten 6/45 times. The rest of the time it will be a brick or an overcard, both which I fold to.
EV call = (1-9/47-15/45)*(-20BB) + 9/47((0.9*203BB)-80BB) + 3/45(203BB-80BB) + 6/45((0.332*203BB)-80BB) + 6/45((0.377*103BB)-80BB) = 14BB
This doesn't seem like a huge difference, but remember I'm using the worst case scenario as to his play. He will probably be scared of not get payed off on his aces and bet 30BB or something like that on the turn. It will at least happen some of the time, enough to make quite the difference.
Now if you add in some folding equity (in this scenario the only folding equity we have is misclick equity /images/graemlins/smile.gif), it's a completely different story. But in conclusion: Villain leaving himself with enough behind to prize you out on the turn is a good thing for you, and when you're the one with the made hand, you should not worry about having enough left to prize his draw out on a later street.
This post will deal with a statement I see around here that makes no sense to me: "We have to get it all in on the flop while we have correct odds, or else he can prize us out on the turn."
When we get it all in on the flop, we buy both the turn and the river card for one prize. When this prize gives us correct odds, that's fine. But it will always be better to buy the turn card for even more correct odds, and then get prized out before we see the river, than to get it all in on the flop. That should be obvious without doing lots of math imo, but here's an example anyway:
Decent LAG opens in the CO for 3bb. I (100BB) hold 7 /images/graemlins/heart.gif8 /images/graemlins/heart.gif on the button and raise it up to 10bb. Loose-passive villain (100BB) min-reraises in SB. BB and CO folds, I call.
Flop (43BB) comes 4 /images/graemlins/club.gif5 /images/graemlins/heart.gifJ /images/graemlins/heart.gif. Villain leads into me for 20BB. Now, tell me pushing isn't totally retarded? It seems to me it is.
EV of pushing:
This guy, as most LPs, can be put on an overpair with near 100% accuracy after this manuever, so I think it's safe to operate with no folding equity. According to twodimes, we have 45,3% equity against an overpair with half a heart.
EV push = (0.453 * 203BB)-80BB = 12BB
EV of calling:
Lets assume he will push any turn. That is the worst case scenario(, except if he check folds when I hit of course, but that isn't going to happen given his above mentioned characteristics).
I have 12 outs against an overpair. 9/12 = 3/4 of my outs are hearts. He'll have a heart 50% of the time, and that means 4.5 of the hearts will give him a flush redraw and 0.5 of them will give him a full house redraw. That means I'll own 83.4% of the pot 5/9 of the time and 100% of the pot 4/9 of the time when a heart hits. In conclusion, when my heart hits I have (5/9 * 0.834) + 4/9 = 90.8% pot equity. This is desregarding that the 4 /images/graemlins/heart.gif gives him two outs to the boat, so lets say 90% for simplicity. Furthermore, when a non-heart 6 hits I have 100% equity, so that doesn't require much attention.
Now lets look at what happens when I don't hit my outs. Three different scenarios are possible: My hand improves without hitting an out (a seven, an eight, a nine or a ten), a brick falls, or he hits his set and I lose 1.25 outs (I lose the 4 /images/graemlins/heart.gif, and I lose the quad-making card the 1/4 times it's a heart). The latter will have fairly little impact, and I've conviently set up the math so I won't have to calculate it.
A seven or eight gives me 5 extra outs. A nine or ten gives me 3 extra outs. With a brick I still have my old 12 outs. The turn push is for 60BB to play a 203BB pot, so I need 30% equity to call. When the turn is a brick I have 9/46 + 3/44 = 26,4% equity, so I fold. (And when the turn is an A-Q it is a tiny bit worse since there's a chance he hit a set, so I obviously fold then as well.) When the turn is a seven or eight I have 26,4% + 5/44 = 37,7%. Great, I call. When the turn is a nine or ten I have 26,4% + 3/44 = 33,2%. I call.
The turn will be a heart 9/47 times, a six 3/45 times, a seven or eight 6/45 times and a nine or ten 6/45 times. The rest of the time it will be a brick or an overcard, both which I fold to.
EV call = (1-9/47-15/45)*(-20BB) + 9/47((0.9*203BB)-80BB) + 3/45(203BB-80BB) + 6/45((0.332*203BB)-80BB) + 6/45((0.377*103BB)-80BB) = 14BB
This doesn't seem like a huge difference, but remember I'm using the worst case scenario as to his play. He will probably be scared of not get payed off on his aces and bet 30BB or something like that on the turn. It will at least happen some of the time, enough to make quite the difference.
Now if you add in some folding equity (in this scenario the only folding equity we have is misclick equity /images/graemlins/smile.gif), it's a completely different story. But in conclusion: Villain leaving himself with enough behind to prize you out on the turn is a good thing for you, and when you're the one with the made hand, you should not worry about having enough left to prize his draw out on a later street.