[socketnaut]

It's not that simple because taxes modify gains but not losses.

Imagine we bet $1 on a coin toss. The expected value for either of us is $0. Now imagine the winner is required to pay 10% tax on his proceeds. The expected value becomes (-$1.00 + $.90)/2 = -$0.05.

[perfunctory]

Very good example. Let's look at it. Note that the new expected value will be negative regardless of the tax rate. No matter how low it is. Even if the tax is 0%, the expected value is still, as you pointed out, $0. So a rational investor would not bet on this coin toss regardless.

Also, as brorfred pointed out, capital losses are deductible, afaik.

[brorfred]

But aren't business losses tax deductible?