It's probably an excess of analytic mentality, but I reached exactly the same conclusion. Because the game imposes no limits on the number of bets, the only way

It's probably an excess of analytic mentality, but I reached exactly the same conclusion. Because the game imposes no limits on the number of bets, the only way I lose is if I go bankrupt. Because a random walk will visit every point with probability 1, if I don't lose then I almost certainly win. Hence the only rational bet is the lowest nonzero amount. The way they compare strategies (i.e. which is more likely to "be ahead" after N rounds) is more interesting, but it feels like they flipped the script on me :)