Whats your standard deviation?

[ranka]

47.4116

[Sandviper23]

i've looked through my different months in PT and took my worst losing month and my standard dev was exactly the same number.
11k hands -6bb/100 standard dev 34
91k hands, +1.25bb/100 standard dev 35
and another month with
41k hands +3.97bb/100 standard dev 32
18k hands +3bb/100 standard dev 30

i'm just alittle confused about what the numbers mean
doesn't really show anything about a winning or losing player ... i'm assuming its more of just a player's particular style

those above were all FR
i looked at a month of 6 max
75k hands, 2.5bb/100 standard dev 42

So i guess the tighter you are the lower your standard dev, the looser the higher but doesn't have anything to do with whether you are winning or losing.

[CalledDownLight]

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This will prove the point.

<u>From January 1, 2007 through July 1, 2007:</u>
Total hands: ~158,000 at NL100
Running at 14.5/6/2.4 winning at 3.24 ptbb/100
33.37 std. dev./100

<u>From July 1, 2007 through current:</u>
Total hands: ~146,000 at NL100
Running at 13.5/7/2.3 winning at 2.85 ptbb/100
50.17 std. dev./100

Especially when you play ~400,000+ per year, 100,000 hands is nothing.

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i'm not sure what this proves....

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less std dev=more profits.

im at 36.5

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not true at all. You could have a very low SD if you folded every hand and you'd be a loser.

[CalledDownLight]

mine is 33.3%

[HonestRyan]

105K hands of NL100 is..... 34.3

[AlexB182]

37.9 over 44000 hands in the last two months, since I use PT.

Really, it would be great if at the end of this thread, somebody could give a brief explanation about what this is really telling us about our game.

[Kornspitz]

SD is just how your winrates deviate from your true winrate (to the positive AND negative). It doesn't tell anything directly about your true winrate itself.

[Sandviper23]

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SD is just how your winrates vary around your true winrate. It doesn't tell anything directly about your true winrate itself.

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So if after you've played 1,000 sessions, and 100k+ hands
your win rate is say 3bb/100

SD is figured out by using your variance in your winrates throughout each session.

So for your SD to be 0, you would have to have an exact same win rate at each individual table during the sessions you played.

And the bigger the swings you take from each table will make a higher SD

[RiverMustelid]

Cliff Notes: A 3PTBB winner with Standard deviation of 30PTBB will win between 1.10 and 4.90PTBB over 100,000 hands 95% of the time. So we do need an f of a lot of hands to determine true win rates, but can get helpful pointers from less.

30.82 PTBB over 125,000 hands in my database.

I'm no stato, but I'll have a go at telling people what it means.

Lets say I have a win rate of 3 PTBB at 100NL. However, I have a standard deviation of 30PTBB per 100 hands. Standard deviation measures how individual sets of 100 hands vary from this average result.

95% of all 100 hand samples will lie within 2 standard deviations (http://www.statsoft.com/textbook/sttable.html). This means that 95% of the time if I sit down and play a hundred hands I'll earn between -57PTBB(my 3PTBB average - 2*30 my standard deviation) and +63PTBB (3 +2*30). So if you play short sessions, get psychologically primed to lose some of them. Quite a lot of them in fact!

In fact you are only 1/10 of a standard deviation away from a breakeven result (3 winrate/30 STDev). Using the table above this means I am going to win 54% or so of my sessions and lose the rest. These feels about right - look at your individual table results, which are based on small samples, and I bet there aren't many of us that have more than 60% winning table sessions.

Luckily for us, by playing more hands the standard deviation converges, making our results bunch within a tighter range. The relationship is the square root of the number of samples. So if I play 100,000 hands, I've played 1000 100 hand samples. The sqrt is 31.6 so I've now got a standard deviation of 948PTBB per 100,000 hands. And my average win rate is 3000 (3 * 1000 samples). For me to be a breakeven player I would need to be around 3stdeviations from the mean. From the tables, only 0.1% of samples lie here. I am prepared to take that risk. I declare myself a winning player, at a level that scientists are happy with!!!

Using the 95% confidence level, which is commonly taken for statistical results where people don't die if you get it wrong (amongst which poker is probably one, unless you play DLM live with his new gun and 2 outer him), I can calculate my win rate.

3000-948*2 = 1104PTBB won in 100,000 hands, or 1.10 PTBB per 100 is the bottom.

3000=948*2 = 4896PTBB won in 100,000 hands, or 4.90 PTBB per 100 is the top.

So even after 100,000 hands, its pretty hard to see whether we're on a big roll or not. But it gives you a much better idea, especially if you combine it with other luck tools like pokerev or flopaset to estimate where you might sit in terms of the luck of your sample.

My results over the last year have been as follows.
Sep 2006 2.57
Oct 2006 0.29
Nov 2006 -0.59
Dec 2006 4.34
Jan 2007 2.11
Feb 2007 Holiday!
Mar 2007 2.41
Apr 2007 4.07
May 2007 2.42
Jun 2007 Holiday!
Jul 2007 3.81
Aug 2007 2.89
Sep 2007 4.97 Booya!

Thats about 500k hands - I'm pretty sure I'm a winner now, but have no idea if I'm a 2 or 4PTBBer which makes a big difference to my life.

You can use this for the number of hands you have played to get an idea of the range of your true win rate. But a word of caution - don't use this without commonsense. Win rates are affected by:

Time of Day
Changes in Your Skill
Changes in Oppponents Skills (e.g. new Poker HUD)
Changes in Player Pool (e.g. Legislation)
and any number of other factors.

Face it kids - we're still gambling! But you can use this to work out your risk of ruin too and work out what chance of going bust you are happy with.

Happy analysing! [img]/images/graemlins/smile.gif[/img]

[guaranteedBluff]

good post river, thx!