If you want some math that employs raw chance and has at least some relevance, take a look at the cash flow at a casino. Every wager is stochastic, and yet the trend is inexorable.
Ironically, your example of casino math only conveys a single trend (i.e. the house eventually wins), failing to yield enough properly sequenced data to code a life form (e.g. red casino chips being DNA A, green casino chips being DNA G, black casino chips being DNA T, blue casino chips being DNA C) or otherwise convey any meaningful amount of information.
In fact, the sum of all casinos playing colored chips over all of history will not, statistically, properly sequence (by chance) the DNA of even the most simple life form.
Not even once.