Calculating standard deviation of X hands

[LordMushroom2]

If I know the standard deviation of 1 tournament/hand, how do I calculate the standard deviation of X tournaments/hands?

[tame_deuces]

SD is the square root of the average squared difference between data and the mean.

So if you got {8,16,4,20}, the mean is 12. The deviations are {-4,4,-8,8} which squared are {16,16,64,64} and the square root of that is {4,4,8,8} and the average of that is 6. So your SD is 6.

I just usually think of it as the average of all the (absolute) distances to the mean - in your case for all X hands. Since I haven't done proper numbers in years and I probably even botched this minimal thing up.

[LordMushroom2]

I play HU STTs and using my winrate I have calculated that the standard deviation for an STT is almost 1 buy-in.

What I wanna know is how do I then calculate how big the standard deviation is over a set of say 10 STTs using the knowledge of what the standard deviation is for 1 STT.

I am pretty sure there is a simple formula for this, but a quick google didn´t help me.

[jay_shark]

Sample standard deviation for n unknown is :

s.d /sqrtn

So ~ 1/sqrt(10)

Since we use the fact that the standard deviation for 1 heads up sng is ~ 1 . This should make a lot of sense since as n approaches infinity , the standard deviation approaches 0 .

[LordMushroom2]

Thanks.

[LordMushroom2]

[ QUOTE ]
Sample standard deviation for n unknown is :

s.d /sqrtn

So ~ 1/sqrt(10)

[/ QUOTE ]

Am I supposed to multiply the answer with the number of STTs as well? Like this:

ns.d /sqrtn

So (10*~1)/sqrt(10)

[jay_shark]

No just the s.d for one buy-in divided by the square root of n .

For heads up it's ~ 1/sqrtn . For a 9 player sng , it's ~ 1.7/sqrtn , etc .

[LordMushroom2]

[ QUOTE ]
No just the s.d for one buy-in divided by the square root of n .

[/ QUOTE ]

But if I do the calculations to find the standard deviation of a high number of STTs (say 900), the answer seems wrong:

1/sqrt(900) = 0,033 buy-ins

Say the buy-in is $105 and my long run ROI is 10%. I then read the answer as "it is 68,3% certain (within 1 standard deviation) I will end up with a profit of $105*900*0,1=$9450 +/- $105*0,033=$3,47. That can´t be right.

$9450 +/- $3,47*900=$3123 on the other hand looks more realistic.