Wow, I absolutely love the math breakdown, 
@Elanor! 
This kind of stuff totally brings back the old college discrete math days.
If we want to turn the nerd dial up just a little, since slot spins are discrete events, the exact model for the chance of hitting at least once by spin x is:
1 - (1 - p)^x where p = 1 / 1,000,000,000 (assuming the jackpot odds really are that).
This comes from the Binomial distribution for repeated Bernoulli trials, where we calculate the probability of at least one success in x spins. Reference: Bernoulli Trials and Binomial Distribution - GeeksforGeeks
I suppose you can also think about the waiting time to the first jackpot as a Geometric distribution. But because the numbers are so huge, it ends up being really well approximated by the Exponential distribution you used to get that 63.21% figure. It’s basically math magic. 
Another fun way to look at it is the median wait time vs the average. The expected wait is a billion spins, but the point where I have a 50/50 chance of hitting it is around 693 million spins (since ln(2) × 1 billion ≈ 693 million). That lines up nicely with the ~700 million row in your table where the probability is about 50%.
So looking on the bright side, I only need about 100 “Night Guy Years” to reach coin-flip territory! 
I might have to pass this jackpot quest down a few generations lol.
The memoryless property you mentioned is definitely the most brutal part though. My previous millions of spins don’t improve my future odds at all. Ouch. The only thing they really mean is that I had about a 0.77% chance of having already hit it by now so not literally zero… but still very tiny.
And that exponential waiting time is exactly why casinos love these ultra-rare jackpots the math basically guarantees most players spend a very long time in the “not yet” part of the curve.
Thanks again for crunching the numbers and bringing some awesome science to my billion-spin quest! 
