schwza
12-22-2005, 01:29 PM
i put answers in quotes because everyone seems to have a different answer from me for number 3. it looks like it's because people underestimated the equity of K2 vs a hand like K6 (as i did until i pokerstoved) but i'm not ready to present this as the definitive correct answer.
check out aplus's post here (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=4257990&an=0&page=0#Post 4257990) for a nice answer to number 1.
also, the original quiz is here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=0&Number=4243377&an=0&page=8# Post4243377) .
[ QUOTE ]
question 1
hero has 8 /images/graemlins/heart.gif6 /images/graemlins/heart.gif. pot is 2k. villain has 4k, hero covers easily.
board is 7 /images/graemlins/spade.gif 9 /images/graemlins/heart.gif 2 /images/graemlins/club.gif 3 /images/graemlins/diamond.gif
villain bets 2k. hero can only push or fold. what percentage of the time must villain fold to make pushing better than folding? villain only calls with 9x or better.
[/ QUOTE ]
approach 1
if villain calls, pot is 10k, hero has 1/6 equity = 1.7k. hero paid 4k for 1.7k, so being called is -2.3k. stealing the pot is +4k, so hero has to steal a little over 1/3, so call it around 36%. (lmn calculated it exactly; it's 36.5%)
approach 2
i think this way is worse, but i'm not sure. villain has 1/6 equity, so he could call a 1/4-pot bet with 0 EV. here that is 500. so hero is putting in 3500 at 1/6 equity. to figure out the (negative) value of doing that, double 1/6 to 1/3, subtract from one and multiply by 3500 to get 2/3*3500 = 2.3k.
-2.3k when called, +4k when not, so around 36%.
[ QUOTE ]
question 2
blinds are 150/300. it's folded to the SB (2k, hero covers) who pushes. what is hero's calling range if SB's pushing range is
a) KJ+ A8+ 66+
b) JT+ Q9+ K7+ A4+ 22+ (take 45 sec's each)
[/ QUOTE ]
600 in dead money, 1400 to call. to call a 2x pot, hero needs 40%, so call it 42%.
using pokerstove these hands are 42% vs the range in a) KJ+ A8+ 66+:
KQs, A9s, AT, 33
these hands are 42% against the hands in the range for b) JT+ Q9+ K7+ A4+ 22+
22, QJ, QTs, KT, K8s, A2o,
[ QUOTE ]
question 3
you hold K /images/graemlins/spade.gif 2 /images/graemlins/heart.gif. villain has 4k, you cover. pot is 3k. villain pushes. the board is:
K /images/graemlins/diamond.gif 7 /images/graemlins/club.gif 3 /images/graemlins/heart.gif
a) villain has 1 pair. 67% of the time he has Kx, and 33% he has 7x. should you call?
[/ QUOTE ]
i totally blew this one when i did it in my head. i said "ok, K2 has 3 outs against Kx, multiply by 4 and K2 has about 12% equity." this works find if Kx is KQ or AK, but when it's K6, it's not close because of the chops.
K2 v Kx (where Kx is one pair) is 27%.
K2 v 7x is 81%. (this is more straight-forward: 7x has 5 outs, 5*4 = 20, so 7x has around 20%).
next we need to do (27*2+81)/3. i don't really have a good way to do that in my head cause we need to be fairly accurate. i'm going to start keeping a calculator by computer. for now i'll cheat, it's 45.
to call a 4/3 pot bet, we need to be between 33% (full pot) and 40% (2x pot), so call it 35%. (it's actually 4/11 = 36.4%)
45 is bigger than 36, so it's a call.
[ QUOTE ]
b) what % of the time must villain have 7x to make the call barely profitable for hero?
[/ QUOTE ]
again, not sure how to do this quickly with no calculator. we only need to get from 27% to 36%, so we don't need a lot of 81%'s thrown in. i'll guess 20%. then by calculator, if villain has 7x 20% then we are 37.8%. so he probably needs to have 7x around 18%.
check out aplus's post here (http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=4257990&an=0&page=0#Post 4257990) for a nice answer to number 1.
also, the original quiz is here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=0&Number=4243377&an=0&page=8# Post4243377) .
[ QUOTE ]
question 1
hero has 8 /images/graemlins/heart.gif6 /images/graemlins/heart.gif. pot is 2k. villain has 4k, hero covers easily.
board is 7 /images/graemlins/spade.gif 9 /images/graemlins/heart.gif 2 /images/graemlins/club.gif 3 /images/graemlins/diamond.gif
villain bets 2k. hero can only push or fold. what percentage of the time must villain fold to make pushing better than folding? villain only calls with 9x or better.
[/ QUOTE ]
approach 1
if villain calls, pot is 10k, hero has 1/6 equity = 1.7k. hero paid 4k for 1.7k, so being called is -2.3k. stealing the pot is +4k, so hero has to steal a little over 1/3, so call it around 36%. (lmn calculated it exactly; it's 36.5%)
approach 2
i think this way is worse, but i'm not sure. villain has 1/6 equity, so he could call a 1/4-pot bet with 0 EV. here that is 500. so hero is putting in 3500 at 1/6 equity. to figure out the (negative) value of doing that, double 1/6 to 1/3, subtract from one and multiply by 3500 to get 2/3*3500 = 2.3k.
-2.3k when called, +4k when not, so around 36%.
[ QUOTE ]
question 2
blinds are 150/300. it's folded to the SB (2k, hero covers) who pushes. what is hero's calling range if SB's pushing range is
a) KJ+ A8+ 66+
b) JT+ Q9+ K7+ A4+ 22+ (take 45 sec's each)
[/ QUOTE ]
600 in dead money, 1400 to call. to call a 2x pot, hero needs 40%, so call it 42%.
using pokerstove these hands are 42% vs the range in a) KJ+ A8+ 66+:
KQs, A9s, AT, 33
these hands are 42% against the hands in the range for b) JT+ Q9+ K7+ A4+ 22+
22, QJ, QTs, KT, K8s, A2o,
[ QUOTE ]
question 3
you hold K /images/graemlins/spade.gif 2 /images/graemlins/heart.gif. villain has 4k, you cover. pot is 3k. villain pushes. the board is:
K /images/graemlins/diamond.gif 7 /images/graemlins/club.gif 3 /images/graemlins/heart.gif
a) villain has 1 pair. 67% of the time he has Kx, and 33% he has 7x. should you call?
[/ QUOTE ]
i totally blew this one when i did it in my head. i said "ok, K2 has 3 outs against Kx, multiply by 4 and K2 has about 12% equity." this works find if Kx is KQ or AK, but when it's K6, it's not close because of the chops.
K2 v Kx (where Kx is one pair) is 27%.
K2 v 7x is 81%. (this is more straight-forward: 7x has 5 outs, 5*4 = 20, so 7x has around 20%).
next we need to do (27*2+81)/3. i don't really have a good way to do that in my head cause we need to be fairly accurate. i'm going to start keeping a calculator by computer. for now i'll cheat, it's 45.
to call a 4/3 pot bet, we need to be between 33% (full pot) and 40% (2x pot), so call it 35%. (it's actually 4/11 = 36.4%)
45 is bigger than 36, so it's a call.
[ QUOTE ]
b) what % of the time must villain have 7x to make the call barely profitable for hero?
[/ QUOTE ]
again, not sure how to do this quickly with no calculator. we only need to get from 27% to 36%, so we don't need a lot of 81%'s thrown in. i'll guess 20%. then by calculator, if villain has 7x 20% then we are 37.8%. so he probably needs to have 7x around 18%.