why do (most) dice have the same face placements? As in, why is the 6 usually opposite to the 1, likewise with the 3 and 4? Does this affect the “fairness” of a dice roll, making it a 1/6 chance every roll as opposed to a different value?
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Here’s the ELI5 I haven’t seen yet: let’s assume the dice are fair and perfectly made. Now, imagine one with no numbers at all. Mentally label one face. When you roll, there will be exactly 1/6 of a chance it’ll land on that face. So in terms of strict probability, there’s no difference created by rearrangement. As others have pointed out, you can use sleight of hand to manipulate the outcome, but that’s not really about the arrangement, either, just about *knowing* the arrangement and physically influencing the result. You could not use sleight of hand with a pair of dice whose numerical arrangement is unknown to you. So, especially if the dice are properly crafted, and preferably do not have divots, there’s literally no difference where the numbers go unless you’re playing a game that hinges on what number is on the opposite side, like “when you roll a six that’s a perfect outcome but you suffer a penalty of one next round because that’s the number facing down” kind of thing. But that’s not statistics in action, that’s just the game rules making that important. No idea if there’s a game like that, but I’m sure you can picture the rough concept. To prove this at home, take a few dice, roll them a hundred and twenty times (this gives you a good amateur sample size) and see what happens. Then do an analysis for the spread at 20, 40, 60, 80, 100, and 120. You should see that as the rolls increased, the value for each face closer approaches 16.6…%. Mystery managed! Oh, and you’ll also see “streaks”, but as you increase the rolls, you’ll realise that those are evened out later by other “streaks” or “droughts.”
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