MATT: This is brilliant. OK, so can I have some of your famous brown paper?
OK, excellent. Now let's look at why this trick works. Now you're going to have to bear with me here. I'm going to set up a slightly unusual way to look at the cards. Because when you get the 27 cards, the very last step-- if we go from the end of the trick-- I pick them up into three piles of nine cards. From now on I'm going to call the top one the 0th pile, and then the first pile, and the second pile. And there's a reason for that in a moment, but just bear with me while I set up some notation https://oncasinogames.com/keno/. So when the cards go back together there are nine cards in the top pile one, two, three, four, five, six, seven, eight, nine. So that was why I called the 0th pile on top. Then there was one, two, three, four, five, six, seven, eight, nine in the first pile. And the bottom one-- one, two, three, four, five, six, seven, eight, nine, that was the second pile. And as it turns out your one was the king of hearts. That ended up being the 10th card down. Because you said at the very beginning your favorite number is 10, and your king of hearts ended up there. And so now when you think about it these top three from the final pile-- because this is the very last top, middle, and bottom pile-- that top one came from the previous top pile. That was the previous 0th pile, that was the previous middle pile, that was the previous bottom pile. That was the previous top, middle, bottom. Top, middle, bottom. And so actually if you watch it you can see how that happens. Because I've picked them up from the second time. I've got the top, the middle, and the bottom packets. Each are nine cards, I've put them together. I deal out the next three piles, and the first three come from that top pack of nine. And then the next three come from that top pack of nine, and then the next three from the same top pack of nine. So that's why over here the top three come from the previous top 0th pile. The next three of each one come from the middle pile. So that's the first three off the middle, next three off the middle, next three off the middle. And I've got nine left, that was the previous bottom pile. That's why now I get three from the bottom, three from the bottom, three from the bottom. So they end up going down like that. And if you get some cards and you start playing around with this, within the final ordering it turns out from the very, very first time you put them together this is the top, the middle, the bottom. The top, the middle, the bottom. The top, the middle, the bottom. And don't lose too much sleep over exactly why this happens. If you get a pack of cards and deal it, you'll start to see why. And what you end up here is this is the ordering from the first time we dealt the cards out. That's the ordering from the second time we dealt the cards out, and that's the ordering from the third time we dealt the cards out. And to get it here at 10th, I can see that to get this position here it's the 0th 0 first. Or top, top, middle. And so each time Brady pointed to where his card was the first time I put that pile back on top, the second time I put that pile back on top, The third time I put that pile in the middle. The first time I put that pile back on top. The second time I put that pile back on top. The third time I put that pile in the middle. In fact, Brady, do you want to pick a different number? BRADY: So say I told you my favorite number was 13, what would you have done? MATT: OK so 13, I need to put 12 cards on top of that, and 12 is one 9, one 3, and no units. So I'm going to put that on the top, the middle, the middle. 13 is, nine, 10, 11, 12, 13. Yeah see? 0, top, middle, middle. But the way I work it out is I'm actually working it out in base-3. Because this whole trick uses base-3 ternary numbers, which I think are absolutely amazing. And the first time you put the piles back together you're doing the units column of your base-3 number. The next time you put them back together you doing 3's column, and then the last time you're doing the 9's column. And so when you give me your number I work out that number in base-3, and then that tells me how to put the piles back together.
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