This is wrong and misses the point of the post.
The median outcome is indeed negative, for the reason you give. But the mean outcome is positive, because some players become exceedingly rich.
You can try it at home, here's some Julia which runs it over 1M people, each with 1K flips:
using Distributions
n = 1000
d = Binomial(n, 0.5)
to_wealth(heads) = 1.5^heads * 0.6^(n - heads)
rand(d, 1_000_000) .|> to_wealth |> mean
You can keep running that, it's above 1 almost all the time.
To look at this another way — would you take the other side of the bet? Someone on average has to be making money, and the other side is clearly losing money.
The median outcome is indeed negative, for the reason you give. But the mean outcome is positive, because some players become exceedingly rich.
You can try it at home, here's some Julia which runs it over 1M people, each with 1K flips:
You can keep running that, it's above 1 almost all the time.To look at this another way — would you take the other side of the bet? Someone on average has to be making money, and the other side is clearly losing money.