In a box, there are 51 red balls & 49 black balls.
You pick randomly.
Pick the red ball, you win.
There are four payout options:
games.png
Intuitively, the 4 games are the same, but game 4 has the highest EV. Also, game 4 has the highest variance.
My second question is, how to calculate the standard deviation of game 1?
It should be close to 1, but what exactly is it? What's the formula for the calculation?
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