Very Quick Standard Deviation Thing

Sorry, I haven't taken stat yet, and don't know how to properly interpret standard deviation (I'm also aware that there are a few different definitions, so I'm getting myself confused).

Anyway, I want to have a good error on my earnings/game on heads up SnGs, so I calculated the standard deviation as sqrt(p(W-E)^2 + q(L+E)^2), where p is my win % in decimal form, q = 1-p, W is amount won when I win, L is amount lost when I lose, and E is my earnings/game. This was nice, except that I don't know if it's the standard deviation per game or standard deviation of total profits or just not what I'm looking for.

First answer gets a cookie; sorry for wasting your time.

[BruceZ]

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Sorry, I haven't taken stat yet, and don't know how to properly interpret standard deviation (I'm also aware that there are a few different definitions, so I'm getting myself confused).

Anyway, I want to have a good error on my earnings/game on heads up SnGs, so I calculated the standard deviation as sqrt(p(W-E)^2 + q(L+E)^2), where p is my win % in decimal form, q = 1-p, W is amount won when I win, L is amount lost when I lose, and E is my earnings/game. This was nice, except that I don't know if it's the standard deviation per game or standard deviation of total profits or just not what I'm looking for.

First answer gets a cookie; sorry for wasting your time.

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That's correct, and it is the standard deviation of your winnings for 1 game. Not to be confused with the standard error of your win rate. For that, you would divide this by the square root of the number of games played.

This is an important and potentially confusing distinction. If you take the number you computed and multiply it by sqrt(N), you will get the standard deviation of total winnings for N games. If you divide the number you computed by sqrt(N), that will give you the standard error (SE) of your win rate for N games, which tells you the accuracy of your win rate to a certain degree of confidence after playing N games.

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Sorry, I haven't taken stat yet, and don't know how to properly interpret standard deviation (I'm also aware that there are a few different definitions, so I'm getting myself confused).

Anyway, I want to have a good error on my earnings/game on heads up SnGs, so I calculated the standard deviation as sqrt(p(W-E)^2 + q(L+E)^2), where p is my win % in decimal form, q = 1-p, W is amount won when I win, L is amount lost when I lose, and E is my earnings/game. This was nice, except that I don't know if it's the standard deviation per game or standard deviation of total profits or just not what I'm looking for.

First answer gets a cookie; sorry for wasting your time.

[/ QUOTE ]

That's correct, and it is the standard deviation of your winnings for 1 game. Not to be confused with the standard error of your win rate. For that, you would divide this by the square root of the number of games played.

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Is the standard error the value that I'd use for calculating confidence intervals?

[BruceZ]

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Sorry, I haven't taken stat yet, and don't know how to properly interpret standard deviation (I'm also aware that there are a few different definitions, so I'm getting myself confused).

Anyway, I want to have a good error on my earnings/game on heads up SnGs, so I calculated the standard deviation as sqrt(p(W-E)^2 + q(L+E)^2), where p is my win % in decimal form, q = 1-p, W is amount won when I win, L is amount lost when I lose, and E is my earnings/game. This was nice, except that I don't know if it's the standard deviation per game or standard deviation of total profits or just not what I'm looking for.

First answer gets a cookie; sorry for wasting your time.

[/ QUOTE ]

That's correct, and it is the standard deviation of your winnings for 1 game. Not to be confused with the standard error of your win rate. For that, you would divide this by the square root of the number of games played.

[/ QUOTE ]

Is the standard error the value that I'd use for calculating confidence intervals?

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Yes. Go back and read the second paragraph that I just added to my original post.

Thank you very much. Feel free to delete thread if you don't think others need it.