You've got a 1/20-1/40 chance per river. I apply for about 10 or so. That makes me likely to draw out every 2-4 years. But my wife is also applying. So now I'm likely to draw out on something every 1-2 years. And I've got 5-10 friends putting in too that are likely to invite me along. So that means every year I probably get to do a couple of trips. Which is precisely what I did last year (Deso and the Main) and about as many weeks as I have to dedicate to river trips.

I'm familiar with the four rivers lottery. Here is the most recent data that is made available by the forest service adjusting for the COVID rollovers that impacted 2021. These are averages of the whole lottery season. If you pick more popular times, your odds are much less.

Odds of getting at least one winning application:

Middle Fork: 1/60 for one application, 1/12 for a five applications

Main Salmon: 1/60 for one application, 1/12 for a five applications

Selway: 1/150 for one application, 1/30 for a five applications

Snake: 1/20 for one application, 1/4 for a five applications

All Four Rivers: 1/10 for one application, 1/3 for five applications (and you are most likely winning the Snake)

Let me know if there is interest. I can also check your estimated probability of winning a lottery by dates for 2023.