Pinball and Probability

When I was in middle school, I used to play a lot of pinball-- I was pretty good at it, but not so good at math. Anyway, after I had racked up a couple of credits, I’d play several games at once, because I thought I was increasing my chance of getting a free game by way of a match.

It’s occurred to me today (I just bought my own pinball machine) that my math was way off-- if I used eight games to match two numbers, instead or eight different numbers, I increased the chance of one of the target numbers getting a match, (2/5, instead of 1/10) but that had nothing to do with winning a free game. Played one at a time, or four at a time, each game had just a 1/10 chance of matching-- assuming that the match numbers really are random. I don’t know enough about pinball to say that they are.

So: eight numbers with a 1/10 chance each is the same as two numbers with a 2/5 chance each, right? (It’s been ten years since the one math class college required of me.) 2 x 2/5 = 4/5, and 8 x 1/10 = 4/5 also. Did I set that up right? Can someone who’s better at math confirm my current thinking?

Also, anyone out there know for sure if the match numbers in pinball are really random?

Shopping is still cheaper than therapy. --my Aunt Franny