Standard Deviations, what are they good for?

[donkeyradish]

Not strictly a probability question but I don't know where else to put it.

My question is:

If I know the standard deviation (of my winnings over a time period or number of hands), what actual use is that to me?

I'd like a practical example, please

thanks

[AleoMagus]

You can use your standard deviation to predict the range and probability of future results.

I am a sng player and for each 30+3 sng that I play, I have a mean expectation of about $12 with a SD of about $56.

Given my mean $/tourney, I could state that my expectation over my next 100 tourneys (about a month's play) is $1200, but that isn't actually realistic. This is where standard deviation becomes useful.

My standard deviation over n tourneys will equal SD*SQRT(n)
Over 100 then, it will equal $56*10 or $560

I can now say that about 65% (1 standard deviation) of the time, I can expect $1200 +/- $560.

Another way of putting this is to say that 65% of the time I will make between $640 and $1760 in a given month (100 sngs).

Similarly, about 95% of the time (2 standard deviations) I can expect $1200 +/- $1120.

Standard deviation is also necessary for calculating % confidence levels in your actual mean $/session. Most players do not realize it, but they do not actually know for sure that they make (for example) 1BB/hr. In truth, they make 1BB/hr plus or minus an amout to a % confidence.

This confidence level will rise as two things happen.
-Play lot and lots of hours to increase the sample
-Increase the range of error (1BB/hr + or - XBB)

I'm sure there are lots of other great uses for SD, but these are just a few that spring to mind

Regards
Brad S