[calahad]

"Expected Value is complicated because a 50% chance for $100 is the same as a 10% chance at $1000"

Is it though?

[nightpool]

OP messed up their numbers—they probably meant 5% chance for $1000 ($50 EV to match .5*$100) or similar. But I think their point is still clear

[jdmoreira]

The payout is exactly the same but what op means is that you need less "50% of 100%" bets than "10% chance at $1000" to reach the same payout.

1 in 2 for the first one will pay out. and 1 in 10 for the second one will pay out.

Variance is higher for second than for first.

[westward]

I think the questioner is asking if

"50% chance for $100 is the same as a 10% chance at $1000"

should be

"50% chance for $100 is the same as a 10% chance at $500"

[jdmoreira]

ah yes, of course. You are correct

[kqr]

At first I was confused because of my mental rule of thumb that in a Bernoulli choice, p=0.5 is highest variance.

But that is when the payoff is 1, of course!

When it's not, we're really looking at payoff² * p * (1-p) and indeed the second situation has much higher variance.

[calahad]

"The payout is exactly the same"

Again I ask, is it really?