Can a random action be replicated?

Thanks to Tony Padilla for the answer!

Will - On the show Tipping Point. Often at the end they play out the final three counters as what would've happened. Would the result actually be what would've happened? I argue that such a random action could never be replicated. Good question, David. For those unfamiliar with Tipping Point, it's a game show based around the penny pushing machine in arcades, you chuck a coin in, it drops into an oscillating flat surface and pushes a huge pile of coins ever so slightly further towards dropping off. Even though they never seem to do that. If a contestant decides not to risk the bank, they often run through what would've happened if they had been able to drop another three counters. But would this have actually happened given the sheer number of variables involved? Alan on the forum seems to think so, saying this question concerns a finite number of choices starting from a known assembly. Therefore there is only a finite, albeit very large, number of possible outcomes. A sentiment echoed by theoretical physicist at the University of Nottingham, and author of fantastic numbers and where to find them, Tony Padilla.

Tony - So I think the listener makes a good point, but there are a few things we need to consider. The first is that the descent of the coin is not governed by fundamentally random physics in any kind of quantum mechanical sense, but by classical physics, which is entirely deterministic. So in other words, if you make sure that you drop the coin in the same way from exactly the same position with the same velocity, with the same orientation, the air flow in the room is exactly the same, then indeed the coin will drop exactly as it would've done. Of course, the reality is that you can never guarantee that level of precision. So the coin drop does become a kind of random event. So does that mean we really can't learn anything from Ben Shephard saying, 'well, let's see what would've happened'? Well, not quite, because the most important thing is not the coin drop, but the distribution of the large body of coins at the bottom. Inevitably, the larger it is, the more important it is. So if that body of coins really is piling up close to the edge, then that's what really matters. It's the big body. This is like a game of David versus Goliath, only now Goliath nearly always wins. Of course, what happens to that pile of coins is also a question of probability. It's not that a single coin drop is guaranteed to knock them over, it's just that it becomes more and more probable as things pile up close to the edge. And it's the distribution of that pile of coins that really matters. Incidentally, this pile of coins that you get in arcade games, it does actually behave very much like a fluid with the coins being like the molecules of the fluid and the friction between them giving them a sort of surface tension. And you could do like a cool little experiment where you test some of these ideas. And so what you do is you take a large coin and you drop droplets of water onto the coin one by one. Now, if you've got a pipette, then great use that. If not, just squeeze a wet sponge onto the coin. Now, count how many drops it takes before the tipping point where the water starts to flow off the edge of the coin, and then repeat the experiment multiple times. Now what you'll find is that it's not that the water's going to start to overflow at the same point every time, but it will be more or less the same point. There will be a distribution, and it's kind of the same physics that's governing the penny pusher machine. So by the way, did you know how the arcades make their money with this game? What happens is that at the tipping points, a bunch of coins fall off to the side away from your stash, and this is something that I never knew.

Will - So mechanical probability and arcade advice, we really do it all here. Thank you to David for the question and to Tony Padilla for the answer.