It's not a lottery game, it's a poker game (and in reality, it's much easier than poker because the economy is positive sum and poker is zero sum). If you only consider "wealthy" to be people who have made billions or hundreds of millions then it's a lottery. But someone that consistently makes decisions that maximize expected monetary gain can consistently become a "rich" person if our definition of rich is have more than $10million.
(Poker is negative sum if you are playing in a raked game)