In functional safety, probabilities are usually clamped to an hour of use.

> I hate “one in a million” because its meaning depends on how many times you’re rolling the die!

I'd argue that it doesn't depend on that at all. That is, its meaning is the same whether you're performing the trial once, a million times, ten million times, or whatever. It's rather whether the implication is "the possibility may be disregarded" or "this should be expected to happen occasionally" that depends on how many times you're performing the trial.

One in a million is more than rolling 4 doubles in a row in backgammon (it's played with two 6 sided dice.) So if a backgammon app or server starts having about 10 thousands players it's not uncommon that every single month (or day) there is such a sequence. Some players will eventually write in a review or in a support forum that the server, the bot, the app cheats against them because of the impossible odds of what just happened. The support staff have to explain the math with dubious results, which is ironic because every single decision in backgammon should be made with probabilities in mind.