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 /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.

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 /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?

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

[KingDan]

1) EDIT: [censored] me misread action
2) 99+ AJ+ .
2b)KJ+, 77+, A5s+, a7o?
3) Muck.
b) ran out of time but for solid guess but i imagine around 40%

[Pat Southern]

Question 1: EV(pushing)= EV(win/opp call)+ EV(lose/opp call)+ EV(win/opp fold)

EV= .18(1-x)6k-.82(1-x)4k+xx*4k

x=30.5%

2. I'm home for the holidays so no pokerstove, if I had to guess:
a) AT+, 88+, maybe KQ
b) KJ+, A6+, 22+

3. Pot Odds: 7/4= 1.75
So we have to be good 1 out of 2.75 times to make calling correct. We have to be good 36.36% of the time to make calling correct. We are 10%(2/3) +81%(1/3)= 33% so calling is incorrect. To find out how often he needs to have 7x substitute x for 1/3 and 1-x for 2/3 and set equation equal to 36.36 and solve for x, I'm too lazy to do that right now, probably is going to be about 2/5 7x to make calling right.

[A_PLUS]

#1
60%, thought went like this
hit my straight about 16% of the time, so if he calls, I win
10K x 16% = 1,600

I'm missing 2,400 in equity, 4,000 in the pot, if he folds 60%, I should be even

2.) Dont use pokerstove when I play, so this is off the top of my head. I know I need about 40% equity, which will be hands like 2OCs vs a PP, SC vs. AXo (we are higher than X), KJo vs lower SC.
22+ (b/c the unpaired hands are way more likelY
suited connectors T9s+
KQo
A7+

b) SC (76s+)
AX
K5+
22+

3.) 11K total, pot, I need to get 4 (in expectation) to make the call. About 36% of the time. If he has a King 33% of the time, I have 3 outs twice (unless he has 2p, or turns 2p, or resucks 2p), but he has more than that when he has 7X, so we may need a higher % than 33%. I say around 40%, to account for the fact that when he is behind, he is drawing liver than us.

I like this idea a lot. I need practice making decisions quickly

[A_PLUS]

Screwed up #1

I included my 4K in the 1st part, but not the 2nd. So, cut the 60% in half, around 30%.

But, at least I didnt cheat

[Sam T.]

Great googley moogely, I have no idea. I feel like Number Two.

Does this mean I need to get pokerstove?

[Exitonly]

Awesome idea, here goes nothing.

1. er. 50%+. 8 outs, so like 15% equity,
2. a) KQs, AT+, 77+
b) KJs+,KQo+, A6s+, A8o+, 55+
3. a) less than 2:1 odds, so 67% shouldn't be good enough. so.. no.
b) between 63 and 64% (i'm an idiot, thats the % he has a K. So... between 36 and 37%)



well that was humbling. great idea.

[locutus2002]

1. Villain folds hero wins 4K.
Villain calls hero hits str8 15% of the time and wins 10K and 85% of the time loses 4K. Net -2K.
villain folds 33% of the time to break even.

2a. Who knows. hero calls 6XBB to win 7XBB and has to be 46.5% in the hand. roughly a big hand like KQ. (tight range)
2b. Not so tight a range ~QT
3a. Hero calls 4K to win 7K and must be 36% in the hand or have an avg of 17 outs against entire range.
2/3 of the time we have 3 outs and 1/3 of the time we have 43 outs, don't call. ~15 outs. Don't call but its close.
3b. Hero needs 17 outs. 1 out ~2% (1/50) so add 4%. Villain must have middle pair 37% of the time and top pair 63%.

this is of course way too complicated for at the table calculations, you would have to have a great read on villain to even consider him having top pair more frequently than middle pair when you hold a king.

the table dynamics counts for much more than than a few percent, so I wouldn't waste my time on these details. It's close enough to be a call in the first case inspite of the unlikely circumstances.

[gobboboy]

I don't think this quiz is very indicative of what you use for poker. No one will ever calculate this much at the poker table and if they are, I don't suspect they are close to expert players. Despite what we say, math is not nearly as important as experience and good instincts in NL tournament play. There are too many factors which we can't account for, which is one reason why there aren't any computers which can play NL Holdem efficiently.

I looked at the questions and thought about my answers, but there were too many variables which you can't account for in numbers. Especially since most of us never think about the answers to questions like this in the heat of the moment (prove me wrong, please, but I've NEVER run the numbers in depth during a decision).

Don't take this the wrong way, but this thread is just going to be us patting ourselves on the back but at the table you'll get a completely different answer from 95% of us.

[Exitonly]

Er. I think i completely disagree with you. This isn't serious math, and i doubt these problems were meant for you to get a pen and paper and figure them out... you have to practice doing the math so you know it quickly when you ahve to apply it at the tables.

You're right that when you're at the table you're not going to break down his hand range, and solve for how often he has to fold for you to breakeven. But how else are you supposed to practice? If you can solve these problems quickly, then you'll sure as hell be able to have a 'feel' at the table for what you should be doing.

And, if you suck at doing these problems, then you're going to suck going with your gut at the heat of the moment.

[gobboboy]

Yes, we do use the basic outline of it, and I do think about their hand range and I do use the simple calculations which you think about. But at the same time we usually have guidelines based on math that allow us to take shortcuts.

If we're getting 2 to 1 on a push with a hand like 66, we automatically assume we're getting close to the correct odds. Maybe in my post it comes off as if I'm saying we never use math, but all I'm saying is that we almost never think about it indepth at the table. Even our discussion of it here is tainted because we don't have the adrenaline rush that we have at the table.

[Exitonly]

And the more math you do like this, the more practice you get, the more decisions become automatic, like the 66 w/ 2:1 odds.

i forgot where iw as going with this, because i got distracted. But anyway. Yea.. practice makes the harder decisions more automatic.

[gergery]

Very interesting. Trying to answer these as I would at the table, taking <15seconds

1. He must fold >64%
2a KQ, AT, 88
2b KJ, A6, 55
3 yes, 30%

-g

[Lmn55d]

I just want to say that for number 1, answers above 50% make no sense at all. If he goes all in, hero risks 4k to win 4k in the pot. If hero has no equity at all, villain needs to fold 50% of the time for moving all in to have a positive expectation. Since hero has equity, villain needs to fold less than 50% of the time.

If hero is a 4.9:1 dog, he has about 17% equity. So of the times that he is called, he will win 6k 17% of the time.

EV(calling) = EV(folding) where x equals the percentage of time villain folds and 1-x equals the percentage of time he calls

x (4000) + (1-x)(.17)(6000) + (1-x)(.83)(-4000) = 0
4000x + 1020 - 1020x - 3320 + 3320x = 0

6300x = 2300

x = 36.5%

You definitely don't need to do this calculation at the table, but if you're guessing like 70% that might be a leak. My first guess was 40% (a bit below 50).

[bmxreed36]

For the first two, I made my initial guestimate, checked it out and was surprisingly close (I think). #3 I'm having a problem with though. My intial thought it that it's very close, but as I'm doing the math, I'm havin problems coming to an answer. The times that he has something like K5, there's a good chance of a split pot which is screwin me up. I'd like to know how to go about this one.