Standard Deviation

Can someone please explain how the standard deviation of 1.1418 is calculated from the payoff table?

Quote: aviator99

Can someone please explain how the standard deviation of 1.1418 is calculated from the payoff table?

https://wizardofodds.com/blackjack/appendix4.html

For each of the net win lines:
(p-e)^2*c where p is pays, e is player ev , and c is the total. Example using 8
(8- -0.00291455) = 8.00291455
8.00291455*8.00291455 = 64.04664129
64.04664129 * 1079 = 69106.32596
The add up all of those values: 2222190225
Then divide by the total number of ways: 1704507420
2222190225 / 1704507420 = 1.303714022
The standard deviation is the square root if that number 1.14180297
Hope that helps.

Quote: aviator99

Can someone please explain how the standard deviation of 1.1418 is calculated from the payoff table?
https://wizardofodds.com/blackjack/appendix4.html

Since miplet showed you one way how it can be done from the table,
Excel does it real fast with the "sumproduct function" and it is a great work double-check. And you could just use the first 2 columns (Net win and Total) of the table.

3 quick steps:
First to get the weighted average (the mean) =SUMPRODUCT(A3:A21,B3:B21)/SUM(B3:B21)
Then the variance =SUMPRODUCT(B3:B21,(A3:A21-B24)^2)/SUM(B3:B21)
Then the st dev =SQRT(B25)
Here is a snap shot of what I am trying to describe.

Good Luck!

Quote: miplet

For each of the net win lines:
(p-e)^2*c where p is pays, e is player ev , and c is the total.

An estimate of the ensemble variance from the observed data is much more complicated than this.

Thanks guys!

I was trying to use Excel's STDEVP but I guess I'd have had to expand the table to way bigger to use that function lol...

Guido,

Which simulator do you use to get that figures?
Is it your own code?




grettings from Argentina.
Alvaro

Quote: alvaro

Guido,
Which simulator do you use to get that figures?
Is it your own code?
grettings from Argentina.
Alvaro

Good Day to you.

Never been to your country. Only to Santiago, Chile.

The BJ data is from the Wizard of Odds site HERE

I just showed a snapshot of my Excel worksheet on how to calculate variance from a data table..

I am sure he uses his own code. Maybe one day he will share some of his code with the world.

I use Blackjack PowersSim HERE
for some of my Blackjack simulations because it is open source code, free and is easy to code IMO.
But you have to do your own coding for BJ stats and it does take some time.

If you are looking for some code, I am sure you could ask the Wizard if he would share his. Worse case is he says "no"

Thanks for reply.

I also use PowerSim, I handle statst with Excel and Matlab.

I didnt realize those figures were from the Wizard site, thank point it out.

Is interested to view the {-8 to 8} colum.