I’M gon na show you a game which seems difficult, But I’f. You learn one simple trick and i’m serious it’s genuinely this one simple trick: The game becomes so easy. Most people can be beaten by a piece of plastic From the sixties. -Music-. Here’S the game of Dr.Nim, I managed to find and buy online. It came in a fantastic original 1960s box check that out.
You can tell us nineteen sixties, America, because there’s a wholesome family having fun with guns. In the background, The game starts with the row Marbles along the top of the board there, and the goal is to take the last marble. Whoever gets that one, there wins the game and each time you have a go, you can choose to take one two or three marbles, but who am I going to play against? Well for dr.Nim, you play the piece of plastic itself.
There are levers and things that toggle and bars underneath it will make its own moves and in theory it will always beat me as the human i get. The luxury of going first there’s a little toggle down here. It is on the left and means it’s Dr.Nim’s. Go if it’s on the right, it’s my go as a human and whenever I want to release a ball, i just hit the button on the side there.
There goes the first one and you know what i’m going to do two marbles on my first go. So now I move the lever over to Dr.Nim’s side and to set Dr.Nim going. You hit the button once and it will choose how many marbles that wants to take. So here we go going for one. Oh wait. It’S gone for a second one.
Oh So it took two marbles and then moved the lever back over to indicate it’s now my go well, I only want one so there’s my one and it’s made it through ever so often we get stuck. I now go fine, dr Nim. All yours. I took one: what are you going to do? That’S going for one going for a second one, its gone for a third one and then switched it back to my go.
Okay, there are four left. I think dr Nim may have me in a corner here. I’M going to take, oh goodness, I’ll, go with two again there’s- actualy! You know what Just one I’ll do. One and gon na go straight back to dr.Nim and you’re on dr.Nim one second one and the winning third one, and just to rub it in as it winds.
It puts the lever back over to say it’s now my go: .. .. to suck .., No matter how many times you play doctor Nim, the plastic jerk as long as the human goes first, as long as you play by all the rules and don’t cheat, it Will beat you every single time? This is based on a mathematical game called unsurprisingly NIM, and this is a plastic computer that has been built to be any human in a simplified version of NIM. Nim is a great game to play it like this piece of plastic.
You’Re, a big fan of beating other people and i’m going to teach you how to always win at NIMH, so you can use it to annoy your friends and family music-. The game of NIM has been known about and studied by mathematicians for well over a century. Although people believe it predates that by a long way, specifically, what we’re looking at here is a version of NIM called single pile NIM for dr.Nim. All the marbles came off one row, the version i’m going to show you all these coins will be in a single line. Technically, proper NIM can have more than one pile, but believe me, the strategies for multi pile NIMH get a lot more complicated as very much another game for another video. The way I would normally play NIMH in a bar or similar setting against friends strangers.
You know chumps would be to use something like 12 coins, we start from one end. Each player can take one two or three coins. Whoever takes the last coin wins. While I absolutely never encourage any form of gambling.
If you were the kind of person who would like to do that, you and your opponent can both put some money on the game, put it under the last coin or token, and whoever takes that one gets the cash in a similar vein. Many years ago we were involved in setting up something called mass of asking where we went outside and did busking with mathematics on the street. One of the routines involved, putting 12 pigs on one of our buskers. The 12 peg had 20 pounds underneath it.
Very importantly. 20 pounds of our money, but we knew if we played the correct strategy, we would always be able to win the game and keep money. Some people found that pretty annoying they would go away. Come up with strategies come back trying to beat us. In fact, there are a few ways: people can try and get you in a corner where you can no longer win, but I’ll get to that in a moment. To start with, here’s how you win 12 coin NIMH a nice way to start is by looking at the end game.
I got myself in before with dr.Nim i had for marbles left or in this case for coins. It was my go and i knew i couldn’t possibly win, and if you get your opponent in this situation, you can always win, because if they take one, you take three. If they take to you, take two: they take three, you take one and they can’t take four according to the rules.
So the goal of the game is to get them into this situation. But how do you guarantee that situation? Well, imagine it earlier in the game, and there are eight remaining and it’s their go.
You’Ve got the same deal going on with just these four to leave these four left. If they take one, you take three, they take to you, take two: they take three. You take one as long as between them and you you take for away you’ll, be left in that end game. We can now go one step back to the very beginning of the game where there are 12 coins, all together, you’re thinking of them in lots of four for there for there for at the end, for each round of full, the other person goes. First, you go.
Second, you need to make sure you take enough coins after their go so between you. You have taken four in total once you know, what’s going on it’s a very straightforward game to win, they take one you take three, they take to you, take two. They realize they can’t win, they get annoyed, you get the money, the only problem arises when people realize the trick themselves, and this is what we had when we were basking.
People would go away, work it out, come back and then they would insist that we go. First, instead of them, so what you do is, if any of your friends caughten on to what you’re doing the next time you reset it you do what we used to do you just take out an extra coin and put it on the end. We would suddenly increase the number of pegs to be greater than 12.
You go first and you bring it down to the now multiple of 4. It’S they go and you’re right back in your winning situation, -Some Extra Radical Music-. So how does dr.Nim the piece of plastic play by those rules with the top? We have the 12 marbles, as we would expect, and then, underneath that we have a series of these little toggling plastic Levers.
They keep track of how many models have gone through the game so far and you can think of them as kind of like a binary counter. But it’s not true binary. It’S more of a tally system that keeps track of the marbles. You start with the leftmost one up and the other two flat down the first model release drop the left, one that raises the center one.
If I then send a second one, it drops the things. One raises the right one, the third marble just restore the right. One to being flat only when there’s a fourth marble, your left, my one get raised back up again and we’re right back to where we started that repeats every set of four marbles after they’ve gotten through what are now calling the paddles the marbles can go. One of two different ways: they can either go to the left or they can go to the right if its Dr.Nim’s turn and the switches over on their side, any marbles which go to the left will bump the switch over ending dr.Nim’s go any marbles which go To the right hit the button and release another marble, so we need to save from the different arrangements of the top three paddles, and it keeps track from each set of 4 is the first second, third or fourth ball: do they cause dr.Nim’s go to end or Do they cause them to take another marble? Let’S have a look i’ll just cycle through a few marbles and will keep track. First Marvel out ends.
Dr names go. Second marble. You take another ball. Third, marble take another ball, fourth model and the go, and it carries on like that.
First one will end his go on the left. Second, one goes to the right. Take another one.
Third one go to the right, take another one for one goes to the left. Ending their go, so what does this mean for dr.Nims strategy, where you can imagine all 12 marbles at the beginning works in their groups of four and for each one? It’S dr him get to go on the first fourth model, they’re, going to call their go to an end if they get to have a go on the second or third they’re always going to carry on to another one. When i first got the game – and I was investigating how it works – actually found that a little bit odd, because dr.Nim doesn’t have to end their go on the first marble in theory, the human is always going to have the first model from each set of 4. Why is it designed to go to the left?
Is it just easier to build that way? It turns out. If you read the admittedly casually racist instruction manual, you see they’re acting all different ways of playing doc turn in their options.
For dr need to go first, and you can do the same trick, you can give them extra marbles. The doctor named will just take straight away in. There are other versions where you have a fighting chance. There are some versions of this game where you can actually beat dr.Nim and that’s what this little paddle here is for is called the equalizer paddle and you can set that so initially, doctor named doesn’t play with perfect strategy.
You get a chance at the beginning to beat it, but if you make one mistake, it will take over return to perfect play and you’re not going to win and that’s why dr.Nim has to end its go on the first position as well as the fourth position. It would only end in the fourth position: there are some versions of the game where you may have ended at a whole round of four. In that case, dr.Nim would take four marbles, that’s against the rules and it will have cheated and whoever designed the dr.Nim game to their credit. They made in such a way that it will never cheat. It will always play within the rules, admittedly in such a way that it would normally kick your ass, so they are. That is the game of dr.Nim.
I find it absolutely fascinating as an example of a very early computing based game, the instructions for all their drawbacks to go into a surprising amount of detail of the theory behind how dr.Nim actually plays so. You can see here there’s a whole section next to that fantastic caricature which talks all about whether or not machines can actually think. If you like this kind of real-world ridiculous physical computing, then you’re going to love my Domino computer check it out thousand dominoes arranged in a pattern such as they can do binary. Arithmetic, if you like this general concept of fascinating mathematics, of course, make sure you subscribe to my stand-up mass channel and if you like, winning drinks, money or just admiration of your friends when you do that, how to playing them and please do go, beat them -Last Bit of Epic Music-