Lets suppose that the gambler is a genus, a group of 10 species, one for each dollar. Eventual extinction is a certainty, although having a bigger stake will prolong the game. One problem that you may see with this is that it relies on randomness, and that randomness may not occur. In fact the logic is sound for any odds, although the graphs change a little. But all genera must start out with one species, and we said that increasing the stake money gave us a better chance.
Many more genera are short than long lived.
This is due to a number of factors number of species in a genus life span of species numbers of individuals per species geographic range of species. Most genera have few species Most species occupy small geographic areas. A useful model of this sort of thing is the surname. They start with small numbers, and die out if no sons are born. Malthus, as part of his famous Essay on the Principle of Population looked at surnames in Bern from 1583-1783.