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Variance in betting
torsdag 11. mai 2017

21.00

Assume that we place bets.
Let be our payout from the th game.
Let be our probability of winning bet .
Let be our stake at bet
For simplicity, assume that

, where

is the bookmaker odds (implying no edge)

Then, according to the definition of expected value,

This was to be expected, as we have no edge due to my assumption above. We simply expect to get our stake in return.

Then we calculate the variance of

Then we introduce a new variable,

:

, which is the sum of all returns divided by the sum of all stakes.

We expect intuitively that the expected

is , which also holds mathematically true because

What is more interesting is the variance of

.

The standard deviation is calculated as follows

This expression gets simplified if we assume that every stake

Side 1 for Teori

If we assume equal (constant) odds for every bet such that

, we have that

Assume that you are placing 20 bets all with an odds of .

This confirms that

obtained from

bets is not a statistically significant result.

Side 2 for Teori  