Just a further observation about probability and luck, and why therefore the machine as explained doesn't make sense. Let's take a simple, quintessential game of chance: The coin-toss.
Every time you toss a coin, there's a fifty percent chance it will land heads, and a fifty percent chance it will land tails. If you have tossed the coin forty times already and every time it has landed heads, the chances of it landing heads again are still equal to it landing tails as it was the first time. But it's improbable that you will get this exact string of heads. For that matter, any specific combination of heads and tails for those forty coin tosses are equally improbable. The more complex any hypothetical situation is, the automatically more improbable it becomes. The specific fact of me having my name, wearing clothes, speaking English, in the room I am, using the kind of computer I am, posting where I am, and so on, all put together is a very improbable outcome.
The episode of "Rivals" only works if you assume things that happen tend to be probable, and rare occurences are improbable, and this is therefore reversed.