[hari_seldon_]

That's a fair point for some games, but even in games where the gambler has a positive expected value would have him/her go bust eventually when playing against someone with much, much more wealth (ignoring the fact that you can walk away):

https://en.wikipedia.org/wiki/Gambler%27s_ruin

[Zanni]

This actually should not happen if you adjust your bet size to match your bankroll (with the caveat that your bankroll is sufficiently large to be unaffected by the minimum bet). The article you link to actually suggests that, in the first bullet point, though it's expressed in the negative.

[milesvp]

For those interested, look up The Kelly Criterion.

https://en.m.wikipedia.org/wiki/Kelly_criterion

This is why poker players who are good enough to play at a certain table level can't maintain it if their bankroll falls too low. At each stakes level the game not only gets harder, but the minimum bet can eat up your bankroll if you get large string of unplayable hands (let alone bad beats or bad plays). What ends up happening a lot is that players will win a significant amount of money at say the $5 table, then try to play the $10 table, and lose enough money they find themselves back at the $5 table. The really unlucky ones may end up back at the $2 table because they may not have moved back to $5 early enough to be able to bankroll that level properly.

I find the economics of poker to be completely fascinating, and when I found out about kelly betting from a HFT friend if mine, it really changed how I looked at the topic.