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Standard Deviation - "normal" range?

  
 
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RiverMonkey
Old 09-14-2005, 06:11 PM     Post subject: Standard Deviation - "normal" range? #1 (permalink)  
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PokerTracker calculates two different standard devation numbers for you:

SD=xBB/100 hands, and
SD=xBB/hour

I've yet to see a really good introductory discussion of std. deviation and its utility to analyzing your game. I'm aware that people use it for determing confidence intevals etc, but I haven't done this myself nor have I really thought through how this would be of use to me. Anyhow, I digress ......Anyone care to summarize the meaning/relevance and utility of these numbers in simple terms? (I do have a math background, but my statistics are a little rusty). Also if you can direct me to a good source of info I'd appreciate that as well. (I've poked around on 2+2, but it frikin' hard to find useful info by wading through all the condecensions and insults. Do you see why? If not, you obviously have a low IQ, rank below me and others in all respects, and you're a damn foo )

I've calculated a SD # from my brick and mortar records to try and get a feel for how much variance there is my playing style. I used Mason's approximation formula that Pat also used in PokerTracker's calcs. (As an aside, I find it curious that Mason says you only need a sample size of about 30 sessions to get a decent approximation for your SD). I regularly play in a $10/20 kill game, so I've calculated my win-rate in $$/hour played and likewise, my SD in units of $$/hour.

I have a few questions:

[1] Using a 60 session sample size, my calcs put me at a winrate of just over $29/hour and a SD of $301/hour, or about 10.3 times my win-rate. Assuming a regular LHE game without kill what is an acceptable range for your SD compared to your win-rate? i.e. When can you clearly say that there is too much variance in your game?

[2] Would having a kill in your game add additional variance to your results and therefore affect/widen that acceptable range for SD?
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euphoricism
Old 09-14-2005, 06:35 PM #2 (permalink)  
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Your Standard Dev. is really, really inconsequential, and really doesn't tell you very much about your poker game. Especially with a small sample such as 60 sessions.

the standard deviation is simply the "expected" variation around an average. As you can tell with your $29/hour and SD of $300/hour -- you need a LARGE sample size for this to be even remotely accurate. Its basically telling you, that in your 60 sessions your average (mean) is $29/hour -- but it wouldn't be unexpected for on any given hour to discover that you were up or down $300.

Really, your standard dev is most aptly used when you don't KNOW the value for something. Thats what confidence intervals are for. PT Already tells us these values (mean, median, mode) -- so its kind of a confusing non-issue. Say I had a sample size of 800 people, and I wanted to know what the average height of the group was. Well, it would be easy. Add the heights of everyone and devide by 800.

But now what if I want to take that 800 people's average (say 5'11 for example), and make a conclusion on the entirety of america. I can't, based on an 800 person sample, make a conclusion about some hundreds of millions of people. This is where a confidence interval and a standard deviation comes in. "I am x% confident that the average height of an American is 5'11..."

The same applies to your poker game. 60 sessions, obviously, isn't enough to tell you about your lifetime with any degree of certainty.
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stevedonel
Old 09-14-2005, 06:58 PM #3 (permalink)  
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Well if the goal of poker is to win the most on your winning hands, and lose the least on your losing hands, wouldnt the better player be the one with the highest winrate, and lowest SD? Granted SD requires a much larger sample size, 100,000 hands is a normal number I hear.
Is that guy still part of the forum??
 
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Fnord
Old 09-14-2005, 07:01 PM #4 (permalink)  
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Quote:
Originally Posted by stevedonel
Well if the goal of poker is to win the most on your winning hands, and lose the least on your losing hands, wouldnt the better player be the one with the highest winrate, and lowest SD? Granted SD requires a much larger sample size, 100,000 hands is a normal number I hear.
Consider that it is possible to have a larger win rate and higher SD but a lower chance of a 100BB downswing. I find that my new style generates a lot of small downswings and break even stretches when my cards go to crap. When the cards are comming... aye carumba!
http://www.youtube.com/watch?v=EBvge-c2_Xg
http://www.youtube.com/watch?v=w-Xz8aLuD7Y
 
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RiverMonkey
Old 09-14-2005, 08:41 PM #5 (permalink)  
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Quote:
Originally Posted by stevedonel
Well if the goal of poker is to win the most on your winning hands, and lose the least on your losing hands, wouldnt the better player be the one with the highest winrate, and lowest SD? Granted SD requires a much larger sample size, 100,000 hands is a normal number I hear.
That's why I found it curious that Mason's article on calculating SD clearly states that 30 sessional results is a large enough sample to get a good estimate of your SD.

Fnord, by "new stye" I assume you are referring to SELECTIVELY lagging it up in situations where you've already made good table and seat selection decisions.
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Fnord
Old 09-14-2005, 09:00 PM #6 (permalink)  
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Quote:
Originally Posted by RiverMonkey
Fnord, by "new stye" I assume you are referring to SELECTIVELY lagging it up in situations where you've already made good table and seat selection decisions.
Yup, although you are probably one of the only posters that can make me look downright tight/passive.
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stevedonel
Old 09-15-2005, 03:31 AM #7 (permalink)  
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Quote:
Originally Posted by Fnord
Quote:
Originally Posted by stevedonel
Well if the goal of poker is to win the most on your winning hands, and lose the least on your losing hands, wouldnt the better player be the one with the highest winrate, and lowest SD? Granted SD requires a much larger sample size, 100,000 hands is a normal number I hear.
Consider that it is possible to have a larger win rate and higher SD but a lower chance of a 100BB downswing. I find that my new style generates a lot of small downswings and break even stretches when my cards go to crap. When the cards are comming... aye carumba!
Basically I'm saying that perfect play would result in the winrate being equal to the SD, with the exception of the blinds. I do see your point of short run results screwing with your numbers.

Perhaps, if SD were calculated over a larger number of hands, it would be more useful. Of course it would approach the winrate, as the length of calculation approached the total number of hands included in the winrate calculations.

But then maybe I should just worry about my play and let the stats say what they want.......
Is that guy still part of the forum??
 
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Demiparadigm
Old 09-15-2005, 04:13 AM #8 (permalink)  
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Quote:
Basically I'm saying that perfect play would result in the winrate being equal to the SD,
This is absolutely untrue.

For example: In Blackjack with a high low count and a 6 deck shoe and 80% penetration, using basic strategy, varying bets from $10-$50, you should have a winrate of approximately $20/hr with a SD of $400/hr.

The point is, perfect play will result in a standard deviation much higher than you winrate. This is because despite the fact that a play is +EV (or less -EV, another important concept from blackjack that most poker players discount) There is still probabilities to contend with.
Accepted "ideal" values for poker are 3BB/100 with a SD of 15BB/100
I run about 4BB/100 with a SD of 20BB/100

A point that Fnord made is very important: with a higher winrate, you are less likely to have an extended downswing despite your short term standard deviation.
With a high winrate AND high standard deviation, you will actually reach your expected rate after a downswing faster.
To win in poker you only need to be one step ahead of your opponents. Two steps may be detrimental.
 
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salsa4ever
Old 09-19-2005, 04:20 AM #9 (permalink)  
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An unrelated aside:

How can you say that in a 6 deck game (i'll take classic las vegas rules) with 80% penetration with $10-$50 bets you'll make an average of $20?

Are you making an estimate of the number of hands per hour, the average bet size, and the expected player advantage?

In any case, how do you calculate the house/player advantage in a blackjack game using a hi-low count?

Thanks!
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well courtie, since we're both clear, would you accept an invitation for some unprotected sex?
 
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pokerfanatic
Old 09-19-2005, 04:26 AM #10 (permalink)  
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Quote:
Originally Posted by salsa4ever
An unrelated aside:

How can you say that in a 6 deck game (i'll take classic las vegas rules) with 80% penetration with $10-$50 bets you'll make an average of $20?

Are you making an estimate of the number of hands per hour, the average bet size, and the expected player advantage?

In any case, how do you calculate the house/player advantage in a blackjack game using a hi-low count?

Thanks!
last time i checked they didn't play poker with a 6 deck shoe...
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Demiparadigm
Old 09-19-2005, 05:13 AM #11 (permalink)  
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Hm...
I may make a blackjack post to explain a lot soon.
Not sure where I'd put it though.

As a quick answer:

I was a little off...

6 decks,
one deck cut (5 dealt out)
dealer stands on soft 17,
double down any 2 cards, not after split
split up to 4 times
only 1 card for splittling aces
insurance
no surrender
blackjack pays 3:2
high/low count, with strategy changes based on count
true count = total count/ #decks remaining
bet the following:
$100 if (true)count is +4 or greater
$75 if count is +3
$50 if +2
$25 if +1 or 0
$10 if negative

win rate based on MonteCarlo simulation of 600 million hands
$16 / 100 hands
average bet size: $26.54
Standard deviation $415/ 100 hands

Double after split changes this to:
$26/100
StdDev $424/100

If dealer hits soft 17:
$11/ 100
StdDev $416/100

Varying bets with count, but sticking to basic strategy:
$12/ 100
StdDev $401/ 100
To win in poker you only need to be one step ahead of your opponents. Two steps may be detrimental.
 
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