[beanlog]

What an interesting trick. A starting point to intuit a resolution: yes you have a 50% chance of doubling and a 50% of halving. But the doubling only happens if you have x dollars, and the halving only happens if you have 2x. So you can see you either gain x or lose x, so your expected return is 0.

When the amount you multiply your money by depends on the amount of money you currently have, you have to factor in your initial money to each case to compute expected return.

[cyborgx7]

Oh, that actually really helped me getting a grasp on the problem. I feel like other comments and sections of the article were trying to get at that idea, but your phrasing of it made it finally click for me. Thanks.

[IshKebab]

This is a far better explanation than the confused hand waving in the Wikipedia article.