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 04-05-2012, 11:21 AM #1 newbie   Join Date: Feb 2012 Posts: 16 Variance question This one is for the math/probability inclined: How likely (or well unlikely) is it for me to be down 700BB after 30K hands if I am a 2BB/100 winner? how about a 1BB winner? How likely am I to be down (any amount) after 30K hands when I am a 2BB winner, how about a 1BB winner? How many hands would a 2BB winner need to play before he is 99% certain he is not down? How about a 1BB winner (IE will u be 99% certain to be winning after 10K hands, 20K hands, or maybe 50K hands?)? Please also explain how to do these calculations if possible. Thanks a lot!
 04-05-2012, 11:40 AM #2 adept     Join Date: Oct 2006 Posts: 774 Re: Variance question Do you know your standard deviation? Look up 'normal distribution', standard deviation, and confidence intervals on Wikipedia. I'm far from an expert on this stuff but can probably help you out if you can't figure it out.
 04-05-2012, 01:18 PM #3 newbie   Join Date: Feb 2012 Posts: 16 Re: Variance question I know what standard deviation and confidence intervals are but I dont know how to calculate the things I want to find out. IE for the last question I set the confidence interval at 99% (0,99 thats close to 3 std deviations right?). Basically I dont know how to go about figuring this out.
 04-05-2012, 01:19 PM #4 newbie   Join Date: Feb 2012 Posts: 16 Re: Variance question The questions are hypothetical btw, so I dont know the standard deviation.
04-05-2012, 04:47 PM   #5
veteran

Join Date: Sep 2006
Posts: 3,226
Re: Variance question

Quote:
 Originally Posted by Wildspeaker How likely (or well unlikely) is it for me to be down 700BB after 30K hands if I am a 2BB/100 winner?
ok, lets assume a 20BB/100 SD (standard deviation).

2BB winner for 30k hands should on avg be up 300x2 = 600BB.

For 30k hands 1SD = 20 x root(300) = 340BB

So to be down 700BB or worse is a (600+700)/340 = 3.82SD occurance

~0.007% probability

Borderline impossible in other words

Quote:
 Originally Posted by Wildspeaker how about a 1BB winner?
same equations yield it to be a 2.94SD ocurance

~0.16%

to be down any amount after 30k hands as 1BB winner should be 600/340 = 1.76SD

~ 3.9%

does this look right to anyone else?

your last question i think i would need a little bit more than a calculator to figure out

 04-06-2012, 12:16 AM #6 East Coast Elephant     Join Date: Dec 2005 Location: CHASE QP, PAYPAL, AMAZON = UNSAFE! Posts: 18,391 Re: Variance question
 04-06-2012, 04:10 AM #7 newbie   Join Date: Feb 2012 Posts: 16 Re: Variance question First of all thanks a lot for the comments, very helpful! Hm that would mean that variance is not nearly as big as I thought. Even a 1BB winner would be very reasonable to expect to be winning after 30K hands. I used to play a lot of 6max and always thought variance in HU was larger than in 6max. But if these calculations are correct (and I dont see why they wouldnt be), then 6max would have much larger variance. That surprises me. Does HM calculate SD? And if so where can I find it?
 04-06-2012, 04:14 AM #8 newbie   Join Date: Feb 2012 Posts: 16 Re: Variance question Never mind about the last question. BBB's link already explained that
 04-06-2012, 04:20 AM #9 newbie   Join Date: Feb 2012 Posts: 16 Re: Variance question Ok so it gives me a std dev of 5,33 bb (blinds not bets) this is per hand I assume? How do I get to the SD for 100 hands? Or is this the stat I need (seems way too low)?
 04-12-2012, 05:19 PM #10 Minbet Millionaire     Join Date: May 2005 Location: Un-official Internet Poker Support Posts: 4,378 Re: Variance question Yea, that Stdev is low and those numbers above were very bogus. evplus is the ticket and will blow your mind as to the true level of variance in any game.
04-13-2012, 05:19 AM   #11
grinder

Join Date: Jul 2006
Location: Portland
Posts: 458
Re: Variance question

Quote:
 Originally Posted by Wildspeaker Ok so it gives me a std dev of 5,33 bb (blinds not bets) this is per hand I assume? How do I get to the SD for 100 hands? Or is this the stat I need (seems way too low)?

A 5.33 big blind per hand standard deviation implies a 26.65 big bets per 100 hands, which is relatively normal.

 04-13-2012, 09:34 AM #12 Carpal \'Tunnel     Join Date: May 2005 Location: Toronto Posts: 23,479 Re: Variance question I don't think you will find a single long-term winner at this game who hasn't had a 700bb downswing. I've had one or two that big in about 600k hands of headsup. That being said, the best way to deal with this is to stop focusing on the variance numbers, which can drive good men to a life of murder, and focus on ways to improve your game. There is no way to know your true winrate anyways, since the games are constantly shifting and adapting and results from two years ago mean nothing.
04-13-2012, 03:16 PM   #13
grinder

Join Date: Jul 2006
Location: Portland
Posts: 458
Re: Variance question

Quote:
 Originally Posted by Gildwulf I don't think you will find a single long-term winner at this game who hasn't had a 700bb downswing. I've had one or two that big in about 600k hands of headsup. That being said, the best way to deal with this is to stop focusing on the variance numbers, which can drive good men to a life of murder, and focus on ways to improve your game. There is no way to know your true winrate anyways, since the games are constantly shifting and adapting and results from two years ago mean nothing.
I have played ~500k hands and my largest downswing was ~350 BB, but I was pretty good at bum hunting.

Totally agree with the bolded tho. Still didn't stop me from doing it all the time for fun, but what can I say i'm a math nerd.

04-13-2012, 05:36 PM   #14
Carpal \'Tunnel

Join Date: May 2005
Location: Toronto
Posts: 23,479
Re: Variance question

Quote:
 Originally Posted by DVDA4life I have played ~500k hands and my largest downswing was ~350 BB, but I was pretty good at bum hunting. Totally agree with the bolded tho. Still didn't stop me from doing it all the time for fun, but what can I say i'm a math nerd.
nice. you probably play well, run well and game select.

Just checked to be sure and on this computer I have 530k hands at 2.5bb/100 from 3/6-300/600 with no game selection below 50/100 and including some six-max. I am roughly ballparking in PT3 but it looks like one 600bb, two 350bbs and one sonofabitch 1000bb in that time. A lot of that is probably playing tough guys at high stakes I shouldn't have. Other than that it is pretty damn sexy and still looks like a straight line.

IN SUM, VARIANCE IS A CRAZY WOMAN WHO WE HAVE TO CUDDLE AT NIGHT AND ASK ABOUT HER DAY EVEN THOUGH WE JUST WANT TO TURN OVER AND FALL ASLEEP AFTERWARDS.

04-13-2012, 06:57 PM   #15
grinder

Join Date: Nov 2010
Location: State of Denial
Posts: 528
Re: Variance question

Quote:
 Originally Posted by Gildwulf IN SUM, VARIANCE IS A CRAZY WOMAN WHO WE HAVE TO CUDDLE AT NIGHT AND ASK ABOUT HER DAY EVEN THOUGH WE JUST WANT TO TURN OVER AND FALL ASLEEP AFTERWARDS.
And if there weren't any variance - you (and I) wouldn't be getting any!

Last edited by beeker; 04-13-2012 at 06:57 PM. Reason: fish, that is.

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