[ QUOTE ]
Are you agreeing that the variance differs for each situation? If so, can you explain why if the EV is the same and the risk is the same that the variance is different?

[/ QUOTE ]

The risk and EV are clearly the same, as my example shows (risk = $2500, average return = $5000).

The variances do differ. To get an idea of why this is, start by considering the distributions of outcomes in each scenario.

In the draw-to-a-low scenario, if you hit your low all 100 times, you will end up with $10k. If you hit your low zero times, you will end up with $0. The distribution is symmetric around the $5k mark.

In the draw-to-a-scoop scenario, if you win every time, you will come away with $20k; if you lose every time, you come away with $0. The distribution is asymmetric, with a fatter edge near the lower end in exchange for a long skinny tail to the upper end. It's intuitive to see that these two distributions will have different variances... it may not be intuitive, but the variance of the scoop distribution is actually higher.

To see this mathematically, model each scenario with the binomial distribution (which captures the sum of n random draws of probability p). The variance, by definition, is n*p*(1-p). So, for the low-only situation, the variance is:

1/2*100*0.5*0.5 = 12.5 pots

where we throw in the extra factor of 1/2 because we only get half of the pot with a success, which is our unit of measure.

For the scoop situation, the variance is:

100*.25*.75 = 18.75 pots

So, drawing to a low here is the better option for the risk-averse. On the other hand, if you want to win $20k one in 4^100 times, you should prefer drawing to the scoop.