fimbulwinter
08-06-2005, 09:18 AM
Previously, in this thread (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=ssplnlpoker&Number=2997442 &Forum=,,,,,,,,,,,All_Forums,,,,,,,,,,,&Words=&Sea rchpage=10&Limit=25&Main=2997442&Search=true&where =&Name=11964&daterange=&newerval=&newertype=&older val=&oldertype=&bodyprev=#Post2997442), I went over the easier EV calculations that go on when facing an all-in bet. This post will deal with (in much shorter order) the math behind making big all-in "bluffs" with drawing hands. These can be very profitable plays, but they are very easy to do poorly.
This post will assume you've read the previous one. If you haven't, then go read it first, then read this one. Although it is shorter, it is also more complex and will probably be hard to read if you don't read the other one first.
Here's a general framework on how to think about this: in general when we were discussing calling, we were getting odds like 2:1 on our draw. now that we're betting and raising, we'll be doing thing things like betting 4 to win 2 etc. Since we often have hands with less pot equity than that (50%, 35% etc) these plays are almost never profitable if the opponent will call every time. Thankfully this is not the case.
Part II: Calculating EV of All-In Semibluffs
First let's look at the PSR (pot sized raise). this is generally more than we will raise most often (if the pot is 100 and he bets 100 then a PSR is a raise to 400), but it makes the math easier. then we'll go back and look at smaller raises (like say 3/4 or 2/3 pot) like those we typically make.
A PSR has us betting 4 to win 2 (we offer our opponents 2:1 on their call. if our all-in is roughly a PSR (say moving 200 into a PSB of 50) then we can use the equities of various draws to calculate folding equity we need to make them neutral EV.
1/3 equity draw (standard flush draw vs TPTK/overpair)
EV = 2x + (1-x)((1/3)(10)-4)
EV = 2x + (1-x)(-2/3) [you can think of -2/3 as the long term "cost" we pay every time we get called]
0 = 2x + 2/3x -2/3
2/3 = 8/3x
x = 2/8 = 25% of the time they must fold in order for this to be profitable.
@ a more standard 2/3PSR (pot = 1, his bet = 1, your raise = 3)
EV = 2x + (1-x)((1/3)(8)-3)
EV = 2x + (1-x)(-1/3) [our "cost" is now half the above, though our raise is 3/4 the size of the above raise]
0 = 2x + 1/3x - 1/3
1/3 = 7/3x
1/7th of the time he needs to fold to make the raise profitable
this result is encouraging (we don't need a fold even half the time) however, looking at the equation, there is room for improvement. since we really cannot change the raise size (say making a smaller or larger all-in raise) we instead look to increase our pot equity on this move by picking stronger draws with which to do it.
Notice something interesting: once we set our pot equity at 40%, our all-in PSR is a freeroll. namely, if we had an exactly 40.01% draw, we should call an all-in PSR, so making one ourselve just lines our pockets with free sklanskybucks every time we get someone to fold.
Now, onto the hands:
Ex1: Simple
you end up in a raised pot of 20BB on the button with a flush draw on a raggy flop and maybe clean overcard worth ~1 out. your opponents cover you and you have 100BB in your stack.
opponent 1 bets pot, opponent 2 calls.
assuming opponent 2 will always fold if opponent 1 does (as opponent 2 is smart enough to raise his monsters on drawing boards), and that if called, only one will call, how often must they fold?
well, here we're making a PSR (60BB in pot, 20 to you, PSR = your stack) with ~4*10 = 40% equity.
EV = 60x + (1-x)((.4)(240) - 100)
EV = 60x + 4x - 4 [the "cost" of getting caught here is a mere 4BB...]
x = 4/64 = 6.25% they must fold.
Ex2: Intermediate
My buddy, we'll call him L, wishes to not be outplayed by DW on his right, and so he wants general neutrality in his bet/3bets ST DW cannot make the right decision against him.
assuming L will always have ~10 outs on his draws and will always be facing 2/3 PSR's from DW and will always have another PSR to that PSR in his stack for the 3bet, how often should he be doing this with a set vs draw in order to make DW's calling EV neutral?
assume the pot is 10, we'll bet 10 and get raised to 30, when we'll shove 100 total in over the top. DW will be facing 70 more to play a 210 pot or getting 2:1 on his call.
DW sees it like this:
need 1/3 pot equity to make the call. when he has draw, have 60% PE. when he has set, have 5% PE.
.33 = .05x + (1-x).6
.27 = .55x
x = 49% of the time he should have a set when he bet/3bets to make DW unable to play profitably without reads
Ex3: Advanced
Our hero, from time to time, really likes to speed. on certain turns that a pro player would feel scared getting raised on (say 89 on 4587r) he will do things like put in big raises with a pair and a gutshot because he feels his fold equity is so good. when he does this, he has 9 outs (3 twopair, 2trips and 4 gutshot) and makes PSR's. how much folding equity needed?
EV = 2x + (1-x)((1/5)(10) - 4)
EV = 2x + 2x - 2
x = 50%
Problems:
All these are hands against DW, so you can assume the player is smart.
1. L has 99 and leads into DW on a board of J96 with two clubs, DW raises and L pushes. I say ni han. why?
2. L has JT and leads into DW on a board of Q93r, DW raises, L moves in for a 2x PSR. I say ni han. why?
3. A LP player makes a CB after a PFR. board QT8 w flush draw. DW has 96 with the flush draw and C/R PSB the flop which takes 1/4 of his chips (he is covered). I don't like it. why?
This post will assume you've read the previous one. If you haven't, then go read it first, then read this one. Although it is shorter, it is also more complex and will probably be hard to read if you don't read the other one first.
Here's a general framework on how to think about this: in general when we were discussing calling, we were getting odds like 2:1 on our draw. now that we're betting and raising, we'll be doing thing things like betting 4 to win 2 etc. Since we often have hands with less pot equity than that (50%, 35% etc) these plays are almost never profitable if the opponent will call every time. Thankfully this is not the case.
Part II: Calculating EV of All-In Semibluffs
First let's look at the PSR (pot sized raise). this is generally more than we will raise most often (if the pot is 100 and he bets 100 then a PSR is a raise to 400), but it makes the math easier. then we'll go back and look at smaller raises (like say 3/4 or 2/3 pot) like those we typically make.
A PSR has us betting 4 to win 2 (we offer our opponents 2:1 on their call. if our all-in is roughly a PSR (say moving 200 into a PSB of 50) then we can use the equities of various draws to calculate folding equity we need to make them neutral EV.
1/3 equity draw (standard flush draw vs TPTK/overpair)
EV = 2x + (1-x)((1/3)(10)-4)
EV = 2x + (1-x)(-2/3) [you can think of -2/3 as the long term "cost" we pay every time we get called]
0 = 2x + 2/3x -2/3
2/3 = 8/3x
x = 2/8 = 25% of the time they must fold in order for this to be profitable.
@ a more standard 2/3PSR (pot = 1, his bet = 1, your raise = 3)
EV = 2x + (1-x)((1/3)(8)-3)
EV = 2x + (1-x)(-1/3) [our "cost" is now half the above, though our raise is 3/4 the size of the above raise]
0 = 2x + 1/3x - 1/3
1/3 = 7/3x
1/7th of the time he needs to fold to make the raise profitable
this result is encouraging (we don't need a fold even half the time) however, looking at the equation, there is room for improvement. since we really cannot change the raise size (say making a smaller or larger all-in raise) we instead look to increase our pot equity on this move by picking stronger draws with which to do it.
Notice something interesting: once we set our pot equity at 40%, our all-in PSR is a freeroll. namely, if we had an exactly 40.01% draw, we should call an all-in PSR, so making one ourselve just lines our pockets with free sklanskybucks every time we get someone to fold.
Now, onto the hands:
Ex1: Simple
you end up in a raised pot of 20BB on the button with a flush draw on a raggy flop and maybe clean overcard worth ~1 out. your opponents cover you and you have 100BB in your stack.
opponent 1 bets pot, opponent 2 calls.
assuming opponent 2 will always fold if opponent 1 does (as opponent 2 is smart enough to raise his monsters on drawing boards), and that if called, only one will call, how often must they fold?
well, here we're making a PSR (60BB in pot, 20 to you, PSR = your stack) with ~4*10 = 40% equity.
EV = 60x + (1-x)((.4)(240) - 100)
EV = 60x + 4x - 4 [the "cost" of getting caught here is a mere 4BB...]
x = 4/64 = 6.25% they must fold.
Ex2: Intermediate
My buddy, we'll call him L, wishes to not be outplayed by DW on his right, and so he wants general neutrality in his bet/3bets ST DW cannot make the right decision against him.
assuming L will always have ~10 outs on his draws and will always be facing 2/3 PSR's from DW and will always have another PSR to that PSR in his stack for the 3bet, how often should he be doing this with a set vs draw in order to make DW's calling EV neutral?
assume the pot is 10, we'll bet 10 and get raised to 30, when we'll shove 100 total in over the top. DW will be facing 70 more to play a 210 pot or getting 2:1 on his call.
DW sees it like this:
need 1/3 pot equity to make the call. when he has draw, have 60% PE. when he has set, have 5% PE.
.33 = .05x + (1-x).6
.27 = .55x
x = 49% of the time he should have a set when he bet/3bets to make DW unable to play profitably without reads
Ex3: Advanced
Our hero, from time to time, really likes to speed. on certain turns that a pro player would feel scared getting raised on (say 89 on 4587r) he will do things like put in big raises with a pair and a gutshot because he feels his fold equity is so good. when he does this, he has 9 outs (3 twopair, 2trips and 4 gutshot) and makes PSR's. how much folding equity needed?
EV = 2x + (1-x)((1/5)(10) - 4)
EV = 2x + 2x - 2
x = 50%
Problems:
All these are hands against DW, so you can assume the player is smart.
1. L has 99 and leads into DW on a board of J96 with two clubs, DW raises and L pushes. I say ni han. why?
2. L has JT and leads into DW on a board of Q93r, DW raises, L moves in for a 2x PSR. I say ni han. why?
3. A LP player makes a CB after a PFR. board QT8 w flush draw. DW has 96 with the flush draw and C/R PSB the flop which takes 1/4 of his chips (he is covered). I don't like it. why?