Game: Get Home

[@DissectingThoughts]

*Picks a square* "That's a terrible idea. If I go first I'll win." *Picks a different square* "Do you wanna' go first or second?"

[@JavierSalcedoC]

Position where no one can win are called parker squares

[@PersonaRandomNumbers]

Some notes: If (n, m) is a losing square, so is (m, n). For any given n, there is exactly one m such that (n, m) is a losing square. As n increases, so does the distance from each losing square to the diagonal. In fact, if you only consider squares (n, m) where m > n, the distance along a horizontal or vertical line to the diagonal is exactly the number of squares (i, j) where i < n and i < j. Using the above rules, you can recursively generate all the losing squares you like :D

[@TheZotmeister]

Fun fact: this game was invented by a Johns Hopkins mathematician by the name of Rufus P. Isaacs, sometime around 1960. He did not name the game, but Martin Gardner (whose book _Penrose Tiles to Trapdoor Ciphers_ I took that fact from) calls it "Corner the Lady" (he used a chess queen instead of a fish). As others have mentioned here, this game is isomorphic to what is called Wythoff's Nim; Isaacs was unaware of it when he created his version, and was surprised to find that his game had already been solved over fifty years before he designed it!

[@richardfredlund3802]

All the losing squares lie on two radiating straight lines, and are rational aproximation of Phi = (sqrt(5)+1)/2

[@vincentc978]

Isnt this game basically a more complex NIM? Looks like it to me

[@DrDherp]

Good to hear from you! Fun video - thanks for posting

[@richardfredlund3802]

this game is equivalent to a particular game of nim. (i.e. identical games but in different form). All the losing squares lie on two radiating straight lines, and are rational aproximation of Phi = (sqrt(5)+1)/2

[@Naverb]

Fun puzzle! I'll have to work it out later! I think the most interesting part will be looking at the symmetries (or lack of them perhaps) when you split the board among the main diagonal and compare the two halves

[@Keirathi]

So, if you let the other person choose what square they want to start in and if they want to go first or second, why wouldn't they always just choose to start in H8 and take their first turn straight down to A1? Or, start in G8 and take their first turn down to the auto-lose square B3?

[@TheQazqazwsx]

I imagine you have lots of friends right? XDXD

[@zinsch1]

There are six losing squares. He always chose a losing square, guaranteeing a win for him.

[@lennarthurlbrink1422]

It would be smart if one player would choose the spuare and the other one if he wants to be first or not;)

[@matthewwilliams6904]

Yes!! Keep it up James! Was incredible to meet you in person and I enjoy your videos!

[@pegy6384]

Another fun video with Katie! You have cool friends.

[@iceberg339]

It is incredible how every year it passes James doesn’t get old

[@tschumacher]

Well, I found the loosing squares on the 8x8 board. But I also went a little bit further than 8x8 and it seems like two lines are evolving. I wonder if those really are lines and if thats the case whats the angle between them.

[@tschumacher]

So now that my paper ran out I still can't spot an easy pattern.

[@singingbanana]

+timakro excellent. I stopped my video there, but that's the next step.

[@tschumacher]

The x offset to the next loosing square is always 1 bigger than the y offset (vice versa for the other line). By simulating this on a computer I found that the x offset seems to be always either 1 or 2, can't be sure but tested the first 10,000,000 loosing squares (on one line).

[@tschumacher]

By simulating this I found that the ratio between the number of 2's and 1's converges to 1.618033 the golden ratio.

[@anirudhrahul8956]

I think you mean converges to?

[@iteratheist1261]

This is the most wholesome corner of the internet

[@AnonymousFreakYT]

Well, if you get to *BOTH* pick the starting square *AND* choose if you go first or second, you put it in the opposite corner and go first - every time. I have a feeling offering both choices was a mistake, and it should be the choice "place the fish *OR* choose to go first."

[@chrismohan]

You can visualise a square from the bottom left (either 2x2, 3x3 etc) and you want to be just outside that square preferably level with the top right (since you can't go up or right) and as long as you get in that position you can't lose. Ideally the person can go first is guaranteed to win if they know what they are doing. Since the movements are along points joined to the vertice of the square you can always force your opponent to move into a smaller square but never give the opportunity to win :)

[@KeDzOn2801]

Looks like the loosing squares are B3 (Mirror C2), D6 (Mirror F4) and E8 (Mirror H5). Every move from these squares, in a perfectly played game, leads to a loss. However every other square provides either an immediate win, or the ability to place the opponent on a loosing square.

[@ThatGuy-nv2wo]

2:51 why didn't you go back to that evil death square from earlier?

[@XxjazzperxX]

It’s so easy to miss stuff like that when you are working with a real physical board in my opinion. Especially when you feel pressured

[@EllipticGeometry]

I'd redefine the game such that you lose when you don't have any legal moves left. The difference is that starting in the bottom left (if you were to allow it) is then rigorously defined. Otherwise it's merely implied from the hypothetical turn after the other player has just won.

[@NetAndyCz]

This game obviously should work that one player chooses starting location and the other player decides whether they go first or second.

[@1987jock]

It's like that thing where you have to remove 2 or 3 matchsticks so that your opponent is left with one remaining.

[@ExplosiveBrohoof]

I have to watch this video muted at the moment, but judging from the description and the visuals of the video, it seems like the goal is to be the one to make it to the bottom -right- left. If that's the case, then player two has a winning strategy on squares b3, c2, d6, f4, e8, and h5. Everywhere else, player 1 wins. We determine this by looking backwards. Clearly, all of the squares on the a file, the first rank, and the long off-diagonal will have player 1 winning, since he can go straight to the bottom left square. As noted in the video, b3 and c2 are zugzwang positions that force player 1 to move the piece to a position that allows player 2 to win. Hence, if the piece starts on either of these squares, then player 2 wins. From here, we can effectively treat b3 and c2 as end squares, since if you can be the one to place the piece on either of those squares, then the other player is stuck in the situation described above. This means that if the initial position allows you to move the piece onto b3 or c2 from the start, then player 1 has the winning strategy. This covers the rest of the 2nd and 3rd ranks, the rest of the b file and c file, and the upper and lower off-diagonals. Of the squares left, there are two that are closest to the home square: d6 and f4. On both of these squares, you can only move to places that we've already established to be winning positions for player 1. When you move to these squares, you de facto turn player 2 into player 1, flipping the tables. This means that you're forced to give player 2 the winning strategy on these squares, and so player 2 can guarantee himself a win from the start. All the remaining squares allow player 1 to go to d6 and f4, except for e8 and h5, and so through a similar argument, they give player 1 the winning strategy on all remaining squares except for those, where player 2 can win. EXAMPLE: Say the game starts on f8. Player 1 moves to d6. Player 2 avoids the first ranks and files, along with the diagonals, and goes to, say, d5. Player 1 then goes to b3, and no matter where player 2 moves afterwards, player 1 can go home.

[@ExactlyMusic]

You have a good solution, except that the goal of the game is to move to the bottom *left* corner, not the bottom right corner. I found it amusing how you called b3 and c2 "zugzwang" squares, looks like you're applying chess to this puzzle. :P

[@ExplosiveBrohoof]

Whoops, I meant bottom left. I edited the comment; thanks for pointing that out.

[@javabird4168]

I know this isn't related, but both of you are adorable.

[@omikronweapon]

Luckily this didn't involve too much math, as I just kept getting mesmerised by Katie's eyes. And if somehow you can tear yourself away from those, her intricate hair colour grabs you instead :P

[@pianissimo7121]

@@omikronweapon i love that purple hair too, didn't even see what they were wearing

[@Phlip45]

Top left is origin, letters starting from A go from left to right, and numbers starting from 1 go top to bottom: The key numbers are B6, C7, D3, E1, F5, and H4 (Also A8 as that is the victory square). If you end your turn by moving to one of these squares you will win. This means if you start, then you will win unless the starting position is on E1 (or if you can start anywhere on the right hand side on H4). If you are starting on these positions you want to go second. Wherever your opponent moves to from here you will be in range of another key number so move to that position on your turn.

[@Metagross31]

First of all: I'm very glad that you held the chess board the right way up and not rotated by 90°. To the game: Correct me, if I'm wrong, but from what I worked out, there are only six squares, where the beginning player would lose. Those are (If the home on the bottom left is a1): c2 b3 f4 h5 d6 e8 Obviously the Squares on the main diagonal as well as the first rank and the a-file are all winning, since you can one-shot towards the home. The squares c2 and b3 are loosing those, since the only squares you can reach from that are winning squares. Then you can mark all squares, from which you can reach c2 or b3, as winning squares as well. After that you will see, that you can only reach winning squares from f4 and d6, so they are loosing squares, too. Do the same procedure with marking again and you are left with h5 and e8, which are also loosing squares.

[@stevethecatcouch6532]

It's not a chess board. It's a Get Home board. There are no fish on chess boards.

[@liesl7617]

Cool game! I'm going to get the kids to play this. To be honest, we're not going to come up with a strategy, but we'll have fun ☺

[@iamamcnea]

@singingbanana, I think this is a word version variant of this game: kzbin.info/www/bejne/e4XFZ4CneKaiZ7M Funny Story, when this video first posted I tried to find that video and couldn't remember where I had seen it. But it just showed up in my recommended videos today. I guess the google mind reading algorithms are getting pretty good.

[@jumpman8282]

Label the rows bottom-up as 1-8, and columns left to right as A-H. Start by crossing out the definite no-go spots, which would be the bottom row (A1-H1), the left-most column (A1-A8) and the bottom-left to top-right diagonal (A1, B2, C3, D4, E5, F6, G7, H8). Then, for a 3x3 grid, there would be two safe spots (B3 and C2, as shown in the video). This means that, for our 8x8 grid, we would want to avoid the spots from which our opponent can reach any of those two safe spots: B3 can be reached from B4-B8, C3-H3, and the diagonal C4, D5, E6, F7, G8. C2 can be reached from C3-C8, D2-H2, and the diagonal D3, E4, F5, G6, H7. So, for a 6x6 grid we would have two new safe spots (along with the safe spots from the 3x3 grid): D6 and F4, and just like before we cross out the spots from which one could directly reach those two safe spots. D6 can be reached from D7-D8, E6-H6, E7 and F8. F4 can be reached from F5-F8, G4-H4, G5 and H6. Now, the only unmarked spots on our 8x8 grid, including the ones from before, are: B3, C2, D6, E8, F4 and H5. Interestingly enough, for n > 7, these are the only safe spots on any n x n grid.

[@bluecombats]

This seems very similar to how a queen moves around a chessboard (if the queen was in bottom right), you are looking for the ways in which you can't be in line with the queen

[@dAGriddo]

I'm surprised no one has mentioned chomp yet. At first glance this looks extremely similar. Maybe there is a "strategy-stealing argument", too.

[@barmansushi]

A8, B6, C7, D3, E1, F5, H4. worked backwards from the known two solutions, marking the horizontal, vertical and diagonal intercepts and those squares are losing squares. The next winning spot for me would then be the bottom left most square that hasn't been marked which has two solutions: D3, F5 again marking the losing squares from those points onward. leaving two last solutions: E1, H4. Obviously you can only start from the top row so to always win, either Start on E1 and win or go second and lose (assuming they know the strat)

[@rmsgrey]

Wait, so letters are decreasing but numbers are increasing as you play? Why isn't the target square A1?

[@benjaminv3748]

If ending up on one of these marked squares at the end of your turn, you win (if continuously moving to the next marked square closest to the winning square): O O O O X O O O O O O O O O O O O O O X O O O O O O O O O O O X O O O O O X O O O X O O O O O O O O X O O O O O V O O O O O O O Likewise, having to move out of one of these squares will make you lose. Whoever starts always wins if playing optimally. *Unless starting on E8* Thanks for the problem, love your work!

[@Phlip45]

You won't win by going first if the starting column is chosen to be 5th from the left.

[@benjaminv3748]

Phlip That's true, thanks for pointing it out :)

[@rachelzimet8310]

Does this mean you could win with less thought if you say "i'm going second" and put the thing on e8?

[@Phlip45]

I mean the 'less thought' would be a single move on your part. If the starting position and start player is random you would much rather go first for maximum chance to win.

[@vikasmishra1190]

Phlip vbbbbbbbnnmnnjj

[@ooloncolluphid7904]

Interesting little game. That chessboard needs some love, though... I can make out the spots where the pieces have just been sitting there. "Play with me!"

[@JimCullen]

What I don't understand is, you let her choose whether you or she goes first, and you let her choose the starting position. Why can she not just go top right and say she goes first?

[@ExactlyMusic]

She could, but that wouldn't be very interesting to watch, would it?

[@JimCullen]

Well sure, but James made it sound as though it would be a suboptimal strategy for Katie.

[@Antox68]

Lowing squares (row, col): 1, 5 3, 4 4, 8 5, 6 6, 1 7, 2 8, 8

[@ExactlyMusic]

Using chessboard notation, the losing squares are: a1, b3, c2, d6, e8, f4 and h5. Working: A losing square is a square such that if the fish is on that square and it's your turn, your opponent can force a win, which means you're going to lose. This means that if it's your turn and you can move to a losing square, you're winning and thus you're on a winning square. The first losing square is a1 because if you're on a1 and it's your turn, it means your opponent already moved there the previous turn and your opponent won. This means that all squares north, east and northeast to a1 are winning squares. Notice that if all the squares you can move to are winning squares, your opponent can force a win. b3 and c2 are such losing squares because all the squares you can move to are winning squares. Thus, all squares north, east and northeast to either b3 or c2 are winning squares. Repeating this process, d6 and f4 is the next pair of losing squares. The last pair of losing squares is e8 and h5. All other squares on the board are winning.

[@NeatNit]

Edit: found this game on Wikipedia, nice! en.wikipedia.org/wiki/Wythoff%27s_game Original: I've filled out the board with winning and losing squares, but I'm trying to understand something mathematical about it and I can't quite get there. What I've figured out so far, for a board that goes infinitely up and to the right (but with a clear bottom-left corner, obviously): 1. Every column has 1 losing square. 2. Every row has 1 losing square. 3. Every diagonal (top-right to bottom-left) has 1 losing square. 4. Every other square is a winning square. 5. There is symmetry along the main diagonal. Let's define function f(n), where n is a positive integer. Counting from bottom left, it returns the column of the losing square on the nth row. The first of those are: f(1) = 1 (bottom-left corner, by definition a losing square) f(2) = 3 f(3) = 2 f(4) = 6 f(5) = 8 f(6) = 4 f(7) = 11 (outside the standard 8x8 chess board) f(8) = 5 Because of the symmetry, if f(x) = y then f(y) = x. They actually form pairs. So the pairs go: 1-1 2-3 4-6 5-8 7-11 I can't really see a pattern, but I looked up the first elements of the sequence (1,3,2,6,8,4,11,5) on OEIS and got one result: oeis.org/A019444 Honestly... I don't quite understand the pattern, but I think that sequence fits. Shows how much I don't know about math!

[@Hello-fb7sp]

This reminds of that other game (I think it was called Nim) where you had to take 1 to 3 cards/coins/wathever and the player who took the last token lost.

[@massimilianotron7880]

"So I've got Totally Not Nemo™ the fish here"

[@gabrielperezpalacio5106]

There are 7 defined squares to win, so one should always go first in order to set the fish in the proper position

[@origamicentral4441]

THE SINGING BANANER IS BACK

[@Quintingent]

So I worked out a method of generating 'winning squares' - squares where if you end your turn you are guaranteed to win (assuming perfect play). Here's how I worked it out, followed by the method itself: A defining property of these winning squares is that any squares in the same row, column, or north-east diagonal (which I'll call their RCDs)must be 'losing squares' - squares where if you end your turn This is because any square in the same RCDs must either be a square which you can move to the winning square from, or is a square that is moved from the winning square, and if it were also a winning square than the original winning square would not be a winning square in the first place. This leads to the first three main properties of winning squares: 1) Their x-coordinate is unique amongst winning squares 2) Their y-coordinate is unique amongst winning squares 3) The difference between their x-coordinate and y-coordinate is unique amongst winning squares. The first two are self-explanatory, but I'll explain the last one briefly. In short, if two squares are on the same diagonal their differences between their x&y coordinates must be the same for both. I won't prove it here but it's pretty simple with a bit of induction. There is one other property of winning squares: they are reflected in the x=y diagonal. This is because any combination of moves from one winning square is identical to the same combination of that square's mirror image but with left movements being replaced with down ones, and vice-versa. They are functionally the same square as far as gameplay goes. Therefore we have the fourth property of winning squares: 4) If there is a winning square at coordinates a,b then there is a winning square at b,a So now we can (finally) begin generating winning squares. First, we start with our original winning square: 0,0. We then get its mirror duplicate - which is still 0,0. This is the only winning square whose mirror is itself (in this scenario at least). Now for the algorithm proper: Step 1) Find the smallest x-coordinate value that isn't already used in an existing winning square Step 2) Add the smallest difference that hasn't been used in an existing winning square. This is the y-coordinate. You now have a new winning square! Step 3) Swap the x and y coordinates of your new winning square. Unless your winning square was on the x=y diagonal you now have another winning square! And there we go! It's worth noting that the difference will be greater than or equal to 0, which is relatively easily proved, but I've written enough for now :P Using this method we can generate the winning squares for an 8x8 board: 0,0 1,2 2,1 3,5 5,3 4,7 7,4 Remember that 0,0 is the bottom left square! You can easily use this method to generate the winning squares for as large a board as you want. As for strategy, it's pretty simple. If you're going second you want to have the starting point be a winning square (since your opponent going first is equivalent to them going after you). If you're going first you want to start on a 'losing square' since you'll be able to move to a winning square from there. Right, I'm gonna finish now as it's 1:00 in the morning and I need to go to bed. Fun little puzzle :)

[@2nafish117]

Wow so long since your last upload. I wish you uploaded a bit more frequently

[@DevletGiray]

All the "losing squares" in the video are basically cold positions in Wythoff's Game: en.wikipedia.org/wiki/Wythoff%27s_game

[@jesusthroughmary]

2:42 Why would Katie move to f7 when they just showed that b3 is a losing square?

[@atbash9855]

i think she didn't notice

[@xeuszzz]

If home is at A1, then losing squares (where you want to move the fish to win) are B3, C2, D6, E8, F4 and H5. All other squares have at least one winning move.

[@RadicalCaveman]

In both games, Professor Grime could have moved diagonally to b3 (the same losing square he eventually beat her with in the first game) on his very first move. Missed it, Dr. Smarty Pants!

[@abrahammurciano]

Spoiler alert: The losing squares are B3, C2, D6, F4, E8, H5 (and let's say A1 as well because if you find yourself there it's because your opponent just won). All others are winning squares (if you play it right) because you'd be able to put your opponent in a losing square.

[@frankharr9466]

O.K., what if you roll two dice and you get to pick one of the dice and that tells you how far you must move Sammy?

[@noobita4983]

That would be more of luck based game.

[@iNTERS22]

Wait, if you are allowed to go diagonally, can't you just go to the end right from the start??

[@lewman999]

Essentially: The goal is a winning square. (By which I mean: if you can move the piece onto a winning square, if you play optimally you can always win). Any square which is one move away from a winning square is a losing square (if your opponent is playing optimally, you'll always lose if you move the piece to that square) Any square which can only move to losing squares is a winning square. If you can move to a winning square on your first move (in this case, whether the top row contains a winning square) you can always win if you go first (Bonus: Given a value n for the side length of the n x n board, can you figure out if you should go first or second, *without* needing to determine which squares are winners?). Otherwise, you'll win if you go second. A similar strategy holds in similar games, where the state of the game irreversibly changes with each move (e.g there's no way to "cycle" between a sequence of moves - in this case it means you can't go back).

[@julianha5473]

The losing squares form a Parker square

[@GreenMeansGOF]

Hello Dr. Grime. I have found 6 squares that guarantee that the person that lands on them wins. I think that if you go first, you will win but if you go second, you will only win if your opponent does not play optimally. I would love to hear what you have to say about my solution. I think the goal is to make sure you land on the squares. Using standard chess notation, the six squares are e8, h5, d6, f4, b3, c2. I am confident about my solution because you played e8 at 1:44, b3 at 1:58, f4 at 2:52, and c2 at 3:14.

[@sehgaldam121]

Isn't it related to distant diagonal opposition in chess.

[@TheClassicWorld]

Somewhat?

[@kotzzz9]

Another fun easy game: 2 people start counting upwards from 1 to 20 (in ascending order) and each player can say the next 1 2 or 3 numbers. The person to reach num20 wins Edit:Players go in turns Only natural numbers

[@AdrianWoodUK]

Just to check, is the first move starting at 0 (so you can pick 1, 2 or 3), or 1 (so you can pick 2, 3 or 4)?

[@kotzzz9]

Adrian Wood yes, starting at zero the 1st person can pick 1,2 or 3

[@AdrianWoodUK]

Cool, thanks for clarifying: you go first! ;)

[@kotzzz9]

Adrian Wood hahah ;) Starting 2nd actually allows you to win instantly if you know the trick..well, 1 i suppose

[@AgentM124]

SPOILER: 1: If it is your turn on an LL number you lose. 2: if it is your turn on a WW number, try move to an LL number. 3: repeat. 00: LL 01: WW 02: WW 03: WW 04: LL 05: WW 06: WW 07: WW 08: LL 09: WW 10: WW 11: WW 12: LL 13: WW 14: WW 15: WW 16: LL 17: WW 18: WW 19: WW 20: LL

[@guillaumethemapler]

Nice to see you again! Thank you for the video! If you ever find the time could you make a video about what is new in mathematics and what the implication/impact is on the world of science? Thank you very much.

[@Bangkonijntje]

You can find the winning squares by using the Sprague Grundy (SG) Theorem and finding the SG values for all the squares in the 8x8 grid. First give square a1 the value of 0, then fill in the rest of the grid by giving each square the value of the lowest possible number (ordinal) that is not in the list of values of squares that you could move to beginning in that square. So from a2 you can only move to a1 and a1's value is 0, therefor a2 is valued the lowest number not in the list {0}, and that is 1. Repeat this process and you'll find that a1, b3, c2, d6, e8, f4, and h5 are all valued 0 and are by the SG-theorem winning squares. The proof that this works is simple for this finite game. By construction you can always move from a non-zero square to a zero square, otherwise the starting square would have been zero. And conversely you can always move from a zero square to a non-zero square. Since this game doesn't loop (it always ends), moving the piece to a zero square will eventually have it end up on a1 and is therefor a winning strategy.

[@chessthecat]

Or you can just move a Knight's move away from the home square. Done.

[@britpoint7022]

Can't believe I get to play with Sonic The Hedgehog *and* Sam The Fish on the same day! I must be dreaming

[@cnadiajasmine]

Yay! A new video! :D

[@anandchitrao4032]

We call a square winning if we end up on it at the end of our turn and we have a winning strategy from that point. Let's name the squares by ordered tuples (x,y) where x and y come from 1, 2, ...., 8, with the final square (1,1). Now a winning square is (1,1). This is the only winning square of the form (1,x) or (x,1). This is because we assume both the players are perfect in logic. So as you have demonstrated, two other winning squares are (2,3) and (3,2). We also note that these are the only two winning squares in their respective row and column. Now, the "winning" is as good as gettibg to at least one of these squares at the end of your turn. So we change the objective of the game to this. Then it is just a recursive game, with the winning squares "connected" iff they are a knight's move apart

[@Jivvi]

2:48 Could have just gone back to the same losing square again.

[@nielsengordon2889]

He’s using stock fish lmao 😂

[@邱才颙-l2c]

If the chess board is n*n, there are still some definite-winning place (x_n, y_n) (and also (y_n, x_n) is a winning place) and the formula is : x_{n+1}= (x_n) + 1, if there is no y_k such that x_{n+1} = y_k (x_n) + 2, if there exist y_k such that x_{n+1} = y_k in other words, {x_n} and {y_n} is a partition of natural numbers but I can't figure out the pattern.

[@邱才颙-l2c]

And the definite-winning place satisfies this condition: If you go to a definite-winning place, your opponent can't reach a definite-winning place, but after that, you can reach another winning place. sorry for my bad English :( 抱歉我的英语很一般，but I like your video! especially those in numberphile!

[@christiandinkel8481]

"Place a piece a grid" is youtube description poetry :-)

[@jagmarz]

Seems like there are maybe 6 losing squares, to force your opponent on to?

[@AlexKing-tg9hl]

I always like the ending

[@kedrak90]

Spoiler Losing squares at b3 c2 d6 f6. If a1 is the goal. E8 is the only safe position to start without pushing you directly at one of those. If both know the strategy and the both get to choose the starting position or the right to choose who moves first the person with the later guess wins. If he knows the other condition.

[@culwin]

I wasn't watching. But now I have been.

[@msclrhd]

To determine the winning strategy, mark all the current winning positions as W0. That is the left column (A), bottom row (8) and the top-right to bottom-left diagonal. Mark B6 and C7 as L0 -- these are the losing squares identified in the video, as the next player will be in one of the W0 squares and can move to A8 and win. Next, mark the remaining column B and C cells, and row 6 and 7 row cells as W1. These are winning squares as the player can move to the L0 cells, so the next player will lose. Mark D3 and F5 as L1. These are losing squares. If the current player moves to a W1 square, the next player moves to the L0 square. Otherwise, the current player can only move to a W0 square, and the next player wins. Repeat this process for W2 and L2, marking F1 and H4 as L2. If the player on the L2 square moves to a W2 position, move to an L1 square. The winning strategy is to move to an L2, L1 or L0 square, or home, whichever position is accessible.

[@trdi]

I don't think it's possible to beat singingbanana, regardless of the strategy.

[@DiegoTuzzolo]

wait, why not after the person make 1 move, just move the fish to the bottom row. She cant go up and u win.

[@SlipperyTeeth]

It's about who gets to the end, not whether it gets to the end at all.

[@DiegoTuzzolo]

Phoenix Fire But if its a matter who gets to the end, why doesnt she start on the top right cornet and just go diagonally?

[@SlipperyTeeth]

deigo tuzzolo Because the game wouldn't be fun.

[@WhovianMinecrafter]

are they both trying to be the one to get to the bottom right? If that isn't the case then I'm not sure there is any way that she could win. please help, I'm confused

[@SlipperyTeeth]

They are both trying to get to the bottom right. You can't go directly into the line of sight of the goal, because then the next person would win. You have to force the other person into a spot where they have to move directly into the sight of the goal, so you can win. This is basically a 2d version of Nim. In Nim you start at 0, and you can add either 1, 2, or 3, and the first person to reach 20 wins.

[@WhovianMinecrafter]

I watched the nim video, but I'm still confused. Why can't she just force him into the same spot/spots that he was forcing her into?

[@SlipperyTeeth]

She can. She just didn't know it. If she had known which spots where the right spots, she would have won every time. (Let's add the rule that each player has to play a round for the win to count, so that the game isn't an insta-win.) Any spot along the left or bottom will be a win for the second player, using our new rule (and the bottom left square of four can't be a starting position because they would all be either an insta-win or a win after the first player's first move). Every other starting spot on this board favors whoever goes first, except for the spot that is second from the right and second from the top, and the six spots that you have to lead people into. If you start on a leading spot, you have to move out of the leading spot, and you can then be moved back into a leading spot.

[@krajesj52]

Is the game name, "Get Home" copyrighted?

[@Chrnan6710]

james i wanna go home james please

[@Doeniz1]

Is the title of the video and the description in German for everyone? Or is it just translated for everyone with a German account?

[@L4Vo5]

imgur.com/gallery/hg3FA Sorry for *awful* board design. Winning tiles in green, losing tiles in red. I've labeled tiles based on their "class": Class X winning tiles can leave the opponent onto a class X-1 losing tile (or win if they're class 1.. maybe I should've made the destination a class 0 losing tile). Class X losing tiles are forced to leave the opponent at a winning tile that's at most class X.

[@Enigma758]

I think this is just the game of "nim".

[@GrothBrooks]

It's basically a 2D spacial version of Nim.

[@alcesmir]

Moon No it isn't. Regular Nim has a very simple winning strategy. I think this game could possibly even be represented as a game of Nim through Grundy numbers, I know a lot of games like these are. It could also only be translatable to some other Nim like game, and then you sadly don't have the luxury of the simple strategy of Nim.

[@antivanti]

Kind of like a 2D version of Nim.

[@terranceparsons5185]

Only Connect Katie?

[@singingbanana]

Ha. It is.

[@terranceparsons5185]

@@singingbanana but of course she is so much more than a winner of the best quiz on TV!

[@Omni315]

Interesting, it's like a 2d version of nim.

[@bengski68]

Call Bob Seger 'cause I'm working on my knight moves

[@raphaeljacobs4350]

Some gentleman here in the comments I'm reading already figured it out and had basically my same idea, so LOVE YOU SINGINGBANANA MAN I HOPE YOU'RE READING THIS

[@singingbanana]

Thanks.

[@atbash9855]

It is even more interesting if we change the rule: who reached the corner is the loser Still have winning stategy

[@methethpropbut8519]

(2,3), (3,2), (4,6), (5,8), (6,4), (8,5) are the losing squares Every other square wins

[@quinn7894]

Also (1,1) obviously

[@ibhishere]

Says he can win by moving to b3 out loud, but does not do that

[@Far_Gem]

A quick solution to the problem: imgur.com/B0l26hu The reason winning squares are winning squares is because they force your opponent to move to a losing square, which is a losing square because - it gives you the opportunity to move to another winning square OR - it gives you the opportunity to move to the goal

[@atmunn1]

Katie Steckles in the thumbnail = more views

[@recklessroges]

e8 is the only start that favours Player_2. All other locations Player_1 wins. ## Strategy ## Layer1: get opponent to b3 or c2; Layer2: get opponent to d6 or f4

[@MrDamojak]

Are you trying to tell me "Get Home" is just a game for you?

[@exceltraining]

Katie - didn't you used to eat jaffa cakes back in the early 90's ? half moon.... full moon..... total eclipse....

[@xxfazenoscoper360doesnosco7]

I dont know what is goingn on here but im 99% sure it has to do with the golden ratio

[@pmacg]

Ok, lets start on e8. You can go first.

[@UKcuber]

Reminds me of nim

[@NoriMori1992]

Katie Steckles! I remember you being on Numberphile! You're the one who talked about topology and got licked by Brady's dog!

[@robindosanjos9672]

I've written a small script to visualize the winning/losing squares with varying grid sizes. Hope it will help some of you in their research! It is available here: robinsstudio.fr/gethomegame.html

[@alltimelowinzasion]

the first player always wins

[@JavSusLar]

Please add in the description a trivial detail... the GOAL of the game :)

[@singingbanana]

+JavSusLar Done

[@yoram9692]

I wanna see "game: roblox" next

[@ДенисСафронов-е3ю]

I'm so sad because I don't understand English...(((((((((

[@yiuqwfj]

something's fishy about this game :-)