There are currently 855 Coins in CoinMarketCap
That means coins that actually have some volume and are present in some markets.
Even if you could only invest in one of those you would odds of 1 in 855 incredibly higher than the
1 in 13,983,816 of lotto
If you take the time to research, study the markets and read the whitepapers you probably could drop most of those having a short list of projects of 100.
That means 1 in 100.
~
You are trying to compare incomparable things here. Winning a lottery jackpot means getting millionfold more of that what you spent on one ticket. Investing in the right crypto can give you, in most cases, not more than hundredfold increase of your investment. I'm not saying that one shouldn't try to invest in a good crypto(Bitcoin for instance) after doing some proper research, but, as Lucius said above, you can do both since lottery doesn't require big investments.
Also, there are 2,000+ coins/tokens on CoinMarketCap, not 855.