math quiz

[schwza]

MLG wrote this in his "evolving" post.

[ QUOTE ]
Step 4: Poker Players
If you make it here, the math has become 2nd nature (even the most complicated of it).

[/ QUOTE ]

so i put together a little math quiz. it's only 3 questions, and if people are interested i'll do more. here are the rules:

- read the question, then start the clock. within 45 seconds, write down your answer. after that, you can write some explanation if you want, but you can't change the answer.

- assume we're early in the tournament and decisions will not cripple hero (so chipEV is around $EV), and villain just moved to table.

- use only what you normally use during poker. if that includes pokerstove / calculator / etc, then that's ok.

question 1

hero has 8 [img]/images/graemlins/heart.gif[/img]6 [img]/images/graemlins/heart.gif[/img]. pot is 2k. villain has 4k, hero covers easily.

board is 7 [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/heart.gif[/img] 2 [img]/images/graemlins/club.gif[/img] 3 [img]/images/graemlins/diamond.gif[/img]

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.

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)

question 3

you hold K [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/heart.gif[/img]. villain has 4k, you cover. pot is 3k. villain pushes. the board is:

K [img]/images/graemlins/diamond.gif[/img] 7 [img]/images/graemlins/club.gif[/img] 3 [img]/images/graemlins/heart.gif[/img]

a) villain has 1 pair. 67% of the time he has Kx, and 33% he has 7x. should you call?

b) what % of the time must villain have 7x to make the call barely profitable for hero?