Standard Deviation

[ActionMatt]

ive seen the term standard deviation used several times on the forum. I am 14 years old and obviously havent come upon that term in my math classes yet. can someone explain standard deviation to me and its relation to poker. thanx

[AaronBrown]

Standard deviation is a measure of spread. In Poker context, it is usually applied to the spread of outcomes after a set amount of play. For example, a player might say his average win rate is $50/hour with a standard deviation of $600/hour. The $600 tells you something about how likely he is to deviate from the average. A standard deviation of zero means he wins exactly $50 every hour. A standard deviation of $1 would mean almost all the hours were within a few dollars of $50.

If he won $650 one hour and lost $550 another, that would give him a standard deviation of $600 for the two hours. Since every deviation is $600, one up and one down, the standard deviation is $600. With more than two hours, he could have a range of wins and losses.

Assuming one hour's play does not affect the next, his standard deviation goes up with the square root of the number of hours. If he plays 100 hours his average winning will be $50 x 100 = $5,000, his standard deviation will be $600 x SQRT(100) = $6,000. The longer he plays, the more likely his average win rate will be near $50/hour.

[sammy1]

To add, one +/- std dev is approx (assuming normal distrib) 68% (empirical rule). So, for the original poster, in Aaron's example, 68% of time your range will be between +$650 and -$650.

[TomBrooks]

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To add, one +/- std dev is approx (assuming normal distrib) 68% (empirical rule). So, for the original poster, in Aaron's example, 68% of time your range will be between +$650 and -$650.

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Hi,

What percentage of the time will your range be within 2 std devs? 3? And is the second and subsequent std devs the same size as the first one? i.e. $600 in the above example.

[TurtlePiss]

It will be within 2 STD 95% of the time and within 3 STD 99.7% of the time, assuming normality. Yes, each subsequent STD is the same size as the last one.

[uDevil]

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I am 14 years old and obviously havent come upon that term in my math classes yet. can someone explain standard deviation to me and its relation to poker.

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Tsk. Tsk. What would your parents say if they knew you were posting statistics questions on an internet forum?