Three Dice Trick - Numberphile

So dice tricks; again, this is from Martin Gardner's book. This is an absolute classic I think; three dice, d6s, and I've got my little blindfold because I'm going to pretend I can't see - I actually can't see. Now I could cheat, I could look through this thing, but I'm not right; and the point I'm going to show you is that I don't need to cheat, there's a way through. So I'm going to ask you to roll the dice, I'm going to blindfold myself from now on. Can you grab those three d6s and roll them for me- so I'm going to ask you to do some adding up, I know that's pressure but-. - (Brady: Okay I can) (do that. I can do that. Okay,) (I've rolled them.). - Can you add up the three numbers you can see - keep this total running in your head; obviously I can't see them. Now choose one of the dice and check the number on, the bottom - show the camera - and add that on. That make sense? Okay can you re-roll that one? And add the one, on top of that one, that you just re-rolled. onto your total as well. And now if you want to, leave the totals pointing up, but like put the dice together so I can't tell which one got re-rolled or anything; the point is that I can't see anything about which dice you re-rolled and I missed the re-rolling business., - (Yep.) All done? I'm gonna take my blindfold off now, but I've missed the crucial stages. And you're thinking of a number in your head there's no way I can know that the number is 16., - Except I do, because it's amazing.. - (Wow,) (that's pretty cool.), - I'm impressed that you're impressed. Let's try it again, I mean like like all magic tricks, as we will say, if you want to know how a trick works you try and repeat the trick. I'm just going to cover my eyes this time, are you happy to re-roll again?. - (Yep.) You can be thinking about. how it's possible for me to know this and I'll show my answer. (All right, here we go. Okay.) (Add them up?), - Yep, get it right, pick a dice - you don't have to pick the same one as you picked last time. And check the number on the bottom and add that onto your total. (Yep.).

- And re-roll that one; and then group them so I can't really tell which one got re-rolled, there's no way I can see it and I'm going to look at these now. So you have a number in your head? - (Yep.) And that number is definitely 12., - (Yep.) Good. I mean the audience can't see Brady's brain whirring, like hmm-. - (It somehow involves the) (number seven?) Go on- wait - good conjecture! I need a bell to. ring - conjecture - is the number seven involved? Why do you say seven? I know that some people will be shouting that a bit.. - (Because opposite) (sides of a dice add up to seven.). - Does it help? (Well the fact you made me turn one of) (them the other way around makes me think) (it must.) Let's use your conjecture - we're kind of working backwards here, like, check these three dice again. (There is a difference of seven there.) Between what? - (Between the number) (you said and what they add up to.), - Do you remember what happened the first time? (No.). - Should we do it again? (Oh yeh alright, yeah all right, one more.) I'm going to watch this time., - (All right,) (here we go, here we go.) (So that adds up to 12.). - I agree. (If I take this one and add two) (that comes to fourteen.) Yeah and then you re-roll.

- (17.) And at this point I take my blindfold off and I've missed all the crucial-, - (Ooh) (look and that's ten, so you add seven!) (You add seven!) - If I tell you your conjecture is correct, now you need to tell me why. And like all magic tricks when you spot this, I guarantee you'd be like ah seriously why did I not see that a million miles off. (Oh let's let's- all right let's let's let's-) (Okay, so there we go, that. adds up to ten.) I agree. (Adds up to ten. That's unchanged.) (Add three, takes it to thirteen,) (plus six - nineteen.) And I can see- just that., - (Twelve- and that) (twelve add seven gets you) (up to nineteen. What-) (what happened?, I don't know what happened!) It's- like all magic tricks, again it's misdirection right? You're at the heart of the problem, you've got the key but the the way the trick is presented directs your attention away from the crucial thing. I will make this really obvious to you now I think; when I take my blindfold off this is all I can see. So what have I missed? I've missed this one having its first roll - what was it I can't remember? Yeah, it doesn't actually matter does it? Because whatever it was you add the bottom number to it. (So the first roll was irrelevant?) Well it's not irrelevant. What matters is the dice are set up in the way that you know dice are set up - and this is the key - opposite numbers, of a die, d6, add to seven. But that means the first roll is that and that, and that's always seven. It was always going to be whatever the sum of those two is plus seven plus that. You can't see the seven anymore- No, I know it's seven. - (Yeah, that's seven's gone.) In the pub when you're doing this, when we're allowed back in pubs, so you do that, you glance and you look away and then basically you're panicking about trying to add seven to the number you've just seen on the table. It can be done, it sounds difficult I know, genuinely it's difficult under pressure, but all you've got to do is add seven to that because you know that the roll and the bottom - before the re-roll - is gonna be seven. That's it, like it's just seven. But the obfuscation, technical word for the misdirection, is is neat enough; and a lot of people know a lot of dice tricks that use the property of the seven but this is one of the neatest ones because it's right there in front of you,, if you break it down, but the way the re-roll and the performer claiming they didn't see the re-roll is the misdirection that you need to make the seven obvious. But it doesn't need a lot of practice to learn and you can adjust it, you can do it with with four dice you just gotta adjust what you expect to happen. You could ask them to re-roll two of them; hey the world's your oyster, and the nice thing about magic in maths is that once you've got the maths taped you've got the sort of creativity of the performance of the magic and the misdirection and the story to be creative about. So my advice is to do it with four dice, do it with different dice - although there's a problem with this one, octahedral dice? Five on that side, on the opposite side has a six, that's to eleven. One on that side, opposite side is a two, that adds to three. This die does not have a consistent sum on opposite faces, and I don't know why. They could have made it so it so it did, but for whatever reason the factory producing these is not doing it when they are doing with the the other die. And I was checking some other dice, they seem to do it for the dodecahedron dice, that does seem to have a consistent sum, and the icosahedron, but not the octahedron. And we could find a tetrahedron as well but then we have a problem; that doesn't have. opposite sides. So my advice is don't use that one; you can get away with those if you figure out what the opposite sum is, it's not hard, but watch out for octahedral dice - they seem to be made in two versions and this version is one that won't work for our little trick. There you go, that's the three dice trick. ..This one- like it feels like it's rigged against you, I did it right and that's the luck of a dice roll, that's why games with randomness are interesting. - ..be the second state. Okay, this flap is below what he's holding. Now you cannot go from the first state to the second state, because he's in the way. - If it wasn't true there would be only finitely many exceptions. Did we do it? Am I- did I not make it? You got it. I got it? Oh thank God.