Slight correction: a game value of omega^2 does not mean that there are two instances where black can delay the inevitable by an arbitrary amount of moves - that would be omega * 2. Instead it means that black can delay check mate by an arbitrary amount arbitrarily many times.
@pbsinfiniteseries
7 жыл бұрын
Oops! You're totally right and I misspoke. Thanks for mentioning that! Hopefully there will be a future episode that addresses these chess games with higher ordinal doomsday clocks.
@eval_is_evil
7 жыл бұрын
PBS Infinite Series that's what I love about you folks ...you are human and make mistakes and you don't mind correcting your own.
@BerMaster5000
7 жыл бұрын
orbital1337 this came to me as well. Pin this comment please.
@pbsinfiniteseries
7 жыл бұрын
Thanks Tomi! I think that's one of the great things about math. It's so difficult that we all get things wrong, often. It teaches you to own your mistakes and just embrace it. :)
@kunaldhawan5952
7 жыл бұрын
I am really fond of this new channel. I was waiting for a channel on mathematics and PBS Infinite Series is absolutely wonderful. Thanks a lot!
@eunjunshin9540
6 жыл бұрын
Imagine your queen just get SNIPED out of no where by a rook.
@newtropics4905
6 жыл бұрын
haha
@kayotakeda9494
5 жыл бұрын
Lol
@crypto2633
4 жыл бұрын
infinite chess is fun. It can be scary cuz most people who play it like being snipers
@LapizLazuli07
3 жыл бұрын
Is this gonna be the real Tennison Gambit- ICBM Version?
@josugambee3701
7 жыл бұрын
"And, Commander, it is possible to commit no mistakes and still lose." - Jean-Luc Picard
@pbsvoices
7 жыл бұрын
So many chess nerds in the comments. I'm a huge fan of this.
@davidp.7620
7 жыл бұрын
PBS Digital Studios Not really a lof of them actually
@babelKONI
7 жыл бұрын
I just realized the title's a pun, validate my exquisiteness.
@takethef
7 жыл бұрын
What about the Go fans? Any material on that soon, maybe?
@anim8dideas849
7 жыл бұрын
PBS Digital Studios try infinite horde chess the games are fixed
@anim8dideas849
7 жыл бұрын
or you should look at caplanca chess variation
@danieldagan5947
6 жыл бұрын
It is not possible to have 3 rooks because you cant promote pawns if the board is infinite
@thatoneguy9582
6 жыл бұрын
Daniel Dagan Special promotion squares
@b3z3jm3nny
4 жыл бұрын
You aren’t limited to the standard number of each piece, as she said
@alexanderm5728
4 жыл бұрын
6:16 "There can be any number of any of the other pieces."
@lucashunter6441
3 жыл бұрын
Promotion occurs on the 8th rank, so if we keep the same rules, it would still be possible.
@duck1102
6 жыл бұрын
Still not as complicated as U N D E R W A T E R C H E S S
@rowanz74
4 жыл бұрын
oh no
@lennoxtvthingy7408
4 ай бұрын
You win by checkmate or if your opponent drowns.
@rmsgrey
7 жыл бұрын
Simple proof of Zermelo: a) every ending position is determined - someone has just won, so that player is guaranteed to win given perfect play on their part. b) for any position where every move leads directly to some determined position, that position is also determined - if there's a move that leads to a winning position for the current player, then this position is a current-player win; otherwise all possible moves lead to a win for the other player, so it's an other-player win. Since the game tree is finite (and connected), every position is determined since every future position from that position leads to an ending position in a finite number of moves down every possible path of future moves, so you can backtrack from those ending positions to determine the position you're looking at. In particular, the starting position is determined.
@jlevin60
7 жыл бұрын
I loved this episode! Very clearly and articulately spoken, not too complicated to understand, but also not questioning the viewer's intelligence. Keep up the good work! As for a comment on the video, the only finite doomsday clock setup would have to come in some sort of boxed in situation I imagine, where white physically creates a finite space with the pieces that black cannot delay doomsday from.
@TheRMeerkerk
7 жыл бұрын
Not important but: The decision tree in the beginning has a few mistakes in it. Some branches are connected to the wrong nodes. Some blue nodes with a 2 have only one branch, while a neighboring blue node with a 1 has 2 branches.
@kristiankember8973
4 жыл бұрын
7:45 If you move the black rook above the white rook, your dooms day clock is wrong.
@ExplodoPantsuit
7 жыл бұрын
I would think that an infinitely large chess board with an infinite number of pieces can't fit zemelo's theorem - primarily because there *can't* be a finite number of moves OR perfect information, because those factors are determined by variables which are now no longer finite (which is why the doomsday clock is infinite). No matter how determined the game is to favour one side or the other, as long as both players are *trying* to win (or trying not to lose), the game cannot end. Not to mention that the layout of a chessboard with infinite squares and infinite pieces isn't really a thing we can conceptualize in terms of black pieces on one side, white pieces on another, and space in the middle. The space must be endless, the black pieces must be infinite. The white pieces must be infinite (and how do we determine which pieces are of what variety, beyond the standard chessboard layout?)
@pierrecurie
7 жыл бұрын
Dunsany's infinite chess: regular chess army vs infinite army of pwns
@tsss1179
7 жыл бұрын
I think that perfectly played game of chess will end in a draw, meaning that neither player can make a progress and moves are being repeated. Like a rook versus rook end game.
@NaviaryMusic
2 жыл бұрын
"5D Infinite Chess with Multiverse Time Travel"
@ralphinoful
7 жыл бұрын
I really hate to be nit picky, but you're mate in 6 is actually a mate in 3. Turns in chess are determined by two players making a move. A mate in 4 for white would mean that white needs to make at most 4 moves to win the game, with a total of 7 total moves. But I guess in terms of a doomsday clock it makes sense...
@randywelt8210
7 жыл бұрын
the winning strategy is called deep q learning. search trees are from yesterday.
@landonkryger
7 жыл бұрын
2:30 Super minor error, but there's a line missing from Alice's first 2 choice to Bob's win with 3.
@EthanEves
7 жыл бұрын
any number of pieces? what if just two kings? even on a finite board that would/could be an infinite game, no?
@Acid31337
7 жыл бұрын
In x_o there is always draw in perfect play case. I think result will be same for chess.
@rodrigoappendino
7 жыл бұрын
What do you mean by "no tie"? Because chess can end on a tie.
@Prayer-In-Practice
7 жыл бұрын
Is Blokus determined? Does anyone know what the closest you can get to perfectly tiling the game board using the rules of blokus? I really like blokus, its one of my favorite games.
@robertomalatesta9143
7 жыл бұрын
if at first move the black forces a tower sacrifice the game ends in a draw
@karthik6062
7 жыл бұрын
I think the above chess cannot end. instead of moving black rook top, moving rook(black) right gives black king to escape. And further if both players have specific pieces the game could go on forever. eg:-2 or 1 horses, 1 bishop. if players have these combinations the game last forever. i.e., Infinite game in finite board. Now what will you do?
@Plebasaurus5179
6 жыл бұрын
Actually, you do not capture the king in chess (minus blitz)
@youknowit789
7 жыл бұрын
Black can stop mate by simply moving a rook along that rank
@whatno5090
6 жыл бұрын
Chess can last infinitely many moves though. Isn't the game tree infinite? For example, both players could just move the knight out and back forever.
@dorian4533
6 жыл бұрын
6:30 some say that bisop is still going ....
@TheLolle97
7 жыл бұрын
I wonder if it would be feasible to create a perfect standard chess computer that pre-calculated every move of the one definite winning strategy and stored it in a database. I mean, we have efficient database technologies up to many terabytes, that should be sufficient, shouldn't it?
@MKD1101
7 жыл бұрын
Lorenzo Wormer it's far from it!
@alimustafa2682
6 жыл бұрын
The bishop is still going
@MykhailoIvancha
Жыл бұрын
7:05 it sounds like a song
@scottmantooth8785
7 жыл бұрын
how mind-bendingly strange does infinite chess become when you add chess 4 into the mix and allow for the pieces on either side (in this case all four) to be placed in non standard positions? you did not cover infinite 3D chess...that would have been interesting especially for us geeks out here in the hinterlands of supposedly normal non medicated reality
@MrGiovannisassano
6 жыл бұрын
9:25 wrong after the game gose in to 15 check's the game gose in to a draw so in short u only get 16 turns till a draw is called, in chess.
@tofolcano9639
7 жыл бұрын
why are there 3 black rooks?
@nathanaeltrimm6863
7 жыл бұрын
7:40 what is stopping the middle rook from moving left or right one square?
@ch6ney
6 жыл бұрын
"Yeah, ill play infinite chess with you, let me put my pieces on the edg-"
@shy_dodecahedron
2 жыл бұрын
-e, what, did you expect something different?
@lyrimetacurl0
Ай бұрын
@@shy_dodecahedronomega away
@OLApplin
7 жыл бұрын
I guess Pawns can't become Queens in infinite chess :(
@jaykoerner
7 жыл бұрын
Olivier L. Applin they could after ω1 moves, but that's one more move then infinity.... edit, yeah I guess not, that's just a further expansion on the board/moves so that just makes it harder to become a queen
@oakenguitar3
7 жыл бұрын
maybe we can choose to define a larger promotion zone similar to how shogi or xiangqi works.
@MKD1101
7 жыл бұрын
Jay Koerner it can't be harder. it will be impossible on infinite board. promotion is possible only when the pawn reaches to the last rank.
@purp9267
7 жыл бұрын
M.K.D. I believe it's only to the 8th rank, I don't know if it says final
@purp9267
7 жыл бұрын
M.K.D. Promotion is a chess rule that a pawn that reaches its eighth rank is immediately changed into the player's choice of a queen, knight, rook, or bishop of the same color.[1]
@kayotakeda9494
5 жыл бұрын
Me: checkmate Opponent:w-where?! Me:*points somewhere off In the distance* I put a bishop there a while ago, so I win
@alihesham8167
3 жыл бұрын
lol
@MB-fp9lq
3 жыл бұрын
That's some Japanese anime move right there.
@redforest9269
3 жыл бұрын
@@MB-fp9lq As opposed to a British anime?
@dannysangree6304
2 жыл бұрын
@@redforest9269 its better than korean anime
@chefdeadpool8481
2 жыл бұрын
That's how 5D Chess plays out 😆
@christopherjohnson1873
7 жыл бұрын
"Let's also assume we're playing with some rules that exclude ties." Avid chess player here: that would be absurd.
@maxthexpfarmer3957
3 жыл бұрын
Shogi comes close.
@jonavuka
3 жыл бұрын
Anish Giri has left the chat lol
@FirstRisingSouI
7 жыл бұрын
Aaand that bishop is still going . . .
@twowords2396
6 жыл бұрын
The bishop is rumored to still be continuing it's quest to infinity diagonally...
@paulwhite760
6 жыл бұрын
No more back rank mates
@xnopyt647
3 жыл бұрын
I read that as Anand
@jacobhelbig6967
7 жыл бұрын
Make a video about Ramanujan's infinite sums! It would be really interesting.
@bpanthi977
7 жыл бұрын
watch 3Blue1Brown videos , they are great.
@jacobhelbig6967
7 жыл бұрын
Bibek Panthi I know! But I want more! I think I might be addicted to maths...
@alicaglayanrulzok
7 жыл бұрын
Hi Joel! :)
@joshurlay
7 жыл бұрын
J. H. I know I am addicted to the maths... I just want another video about prime numbers
@khushimehta6574
7 жыл бұрын
J. H. for sure
@d-.-b3412
6 жыл бұрын
Agadmator's fans here?
@ignacioandresv3170
6 жыл бұрын
Yes sir
@papayaspice1155
6 жыл бұрын
Hello everyone.
@shreechaturvedi4170
4 жыл бұрын
@@papayaspice1155 Sorry About That
@rowanz74
4 жыл бұрын
So yeah.
@maxthexpfarmer3957
3 жыл бұрын
@2C (02) Chan Kwan Yu No thanks, I just want to enjoy the show.
@sergiosanchez5439
7 жыл бұрын
love the fact that this channel targets an audience with at least some level of exposure to mathematics beyond the standard highschool and basic university level curriculum (zfc and set theory are mentioned without delving into a long tangent explaining what they are). please continue this
@NLogSpace
7 жыл бұрын
You claimed that chess is a determined game and argued via Zermelo's Theorem. But chess games could possibly end in a tie (stalemate), so how do you get to your conclusion? Is chess really a determined game?
@3geek14
7 жыл бұрын
At 0:57, she says that we'll modify the rules of chess so that it can't end in a tie. Here's one way to do that: One way to think about chess is that the last person to make a legal move wins (except when there's a tie). If I move such that you are in check and can't get out of check, there is no legal move for you to make, so you lose. With draws, it's a draw if we revisit the same position too many times or if we reach a state where one of us isn't in check but has no legal moves. Here's how I'd turn chess into a game satisfying the assumptions for Zermelo's theorem: It is illegal to make a move that ends with you in check. It is illegal to make a move that ends with the board in a position it's been in twice before. It's illegal to make a move that would result in the past 50 moves having no captures and no pawn movement. If it is your turn and you have no legal moves, you lose. The difference between this and chess is that we pick a winner whenever there would normally be a draw. If you cause a stalemate, you win. If you cause a threefold repetition or make the 50th move without a capture or pawn move, you lose. It's still enough like chess that all the other assumptions are maintained. The strategy would be different, but it's close enough for the game theorists. To answer "Is chess really a determined game?", I'll go with "probably not". Chess is a big game, and we don't know if there is a winning strategy. Lots of people (myself included) guess that it is possible to force a tie, but it is not possible to force a win. Since the definition of a determined game is that one player has a winning strategy (can force a win), chess probably fails. However, I think it is a strictly determined game, in that there probably exists strategy pairs for White and Black where, if each player knows the other's strategy, it is impossible for them to change their strategy such that they improve the outcome. I can't remember the name of the theorem, but I'm pretty certain there's one that says chanceless games with perfect information always have this property.
@NLogSpace
7 жыл бұрын
Ah, I missed her mentioning that. Yes, the changes you suppose would make it possible to apply Zermelo's Theorem, but if you translate the statement to the real chess again, it would mean that either can white or black can force at least a tie!
@guest_informant
7 жыл бұрын
"At 0:57, she says that we'll modify the rules of chess so that it can't end in a tie." I don't think that's what she says. She seems to me to say "Chess is a determined game, let's look at that." I think it would be much clearer if she said, _Chess is __*__not_*_ a determined game but we are going to consider a variant, called "Finite Chess" which is played using rules linked to in the description._
@whong09
7 жыл бұрын
Pi Fisher Strategy pairs is an interesting idea. In determined games it doesn't matter if you know what your opponents moves will be. If you are the determined winner you only need to know the response to make to your opponents actual move, as opposed to knowing the winning response to all potential moves. What kind of chanceless perfect information games are there where knowing your opponents strategy can change the outcome of the game?
@DidierPilon
7 жыл бұрын
if it can't end in a tie, it's not a finite game. A perpetual would last forever
@BitcoinMotorist
5 жыл бұрын
0:24 my brain hurts looking at that chessboard. It's set up incorrectly. Why is it so hard for people to get something as simple as the correct starting position right?
@neno8891
7 жыл бұрын
A) Is chess determined? B) Nope, you can draw by repeating moves A) ok, ok, but let's assume you can't repeat B) Well, you might not have enough material to win the game A) Ok, ok, but let's make it a determined game. B) Err... ok? A) So now, Chess is determined, so is infinite chess. Proof B) ¯\_(ツ)_/¯
@vbeis0
7 жыл бұрын
There's also a way to draw the game, where one player doesn't have sufficient material, and the other player could mate but his time runs out
@martinmaguire-music6692
7 жыл бұрын
Armageddon chess is determined, since a draw is a loss for one of the players.
@d_vlc
7 жыл бұрын
6:10 , 9:38 just leaving those here
@Nuclearburrit0
7 жыл бұрын
You can have a stalemate by not having a legal move while you still have all of your pieces
@Thundermikeee
6 жыл бұрын
you can have draws, but i think it was meant to mean that you can force a win, provided you played perfect... same with the piles example, where the first person to move could loose but never has to, privided perfect play... it even makes sense by intuition, if you think about it: white always moves first, and there is nothing that provides a counterbalance to this first move advantage, so it would only be logical that white can win any game, if they play perfectly. you might have to concede the 50 moves rule, that could be true
@landonpowell6296
7 жыл бұрын
6:18 No there can't be. You can't have a king and bishop on each side. That'd result in insufficient material to checkmate. Did I miss something?
@rans55555
7 жыл бұрын
why can't the black move the midlle rook one space left insted of up?
@JamieDenAdel
7 жыл бұрын
physics pony White's queen would move one square up and to the right for checkmate.
@rans55555
7 жыл бұрын
I see it now.
@tipoima
7 жыл бұрын
Move the white rook up to the king and black will have no way to kill it (it's protected) while being dead next turn. If you go right, just do the same from the other side, but move 1 tile. Dead next turn while protected.
@NWRIBronco6
7 жыл бұрын
Could someone explain white's winning move if black goes rook to the right? I'm seeing left clearly, but right has eluded me so far (I'm not much of a chess player, though).
@Noah-fn5jq
7 жыл бұрын
If you move the black rook to the right, the white rook moves one to the left, the king is forced to move one to the right, the queen moves one up placing the king in checkmate. (Took me a while to find that one, guess I'm not that good at chess either :P)
@filipsperl
7 жыл бұрын
Whenever infinite ordinals pop up somewhere, it makes the topic omega times more interesting!
@MrRoyalChicken
7 жыл бұрын
I read the second paper by Hamkins and it's incredibly interesting. I encourage everyone else to do the same. It's definately worth the time and effort!
@holovoid7943
7 жыл бұрын
There is a typo at the bottom left of the game tree Alice v bob where bob takes 2 marbles from 1 marble
@holovoid7943
7 жыл бұрын
Like so they can correct this error
@mattkilgore7323
7 жыл бұрын
There are a bunch of errors on that tree, I have half a mind to scan the correct one I sketched out and email it to them.
@davidp.7620
7 жыл бұрын
Matt Kilgore also the chess posición is not a forced mate
@KingAlexYT
6 жыл бұрын
O Fenómeno yes it is
@WilliametcCook
6 жыл бұрын
(1) | [2] Bobs wins
@Verlisify
Жыл бұрын
This was missing terms like "solved" and "blunder"
@HebaruSan
7 жыл бұрын
Has anyone explored a version of chess where the pieces' coordinates are real numbers instead of integers?
@DaffyDaffyDaffy33322
7 жыл бұрын
That would be really interesting.
@Tehom1
7 жыл бұрын
Then how would pieces capture other pieces? Like, if your rook is on (3.1, 8.2), does my move to (2.9, 8.1) capture it because it's close, or miss it? Well, you could say that moving to strictly less than radius 1 of another piece captures it, so that normal integer moves come out the same while all situations are determined. The bishops would become considerably stronger, about as strong as rooks. A normal light-squared bishop can't reach any dark squares, but a real-valued light-square bishop could simply move halfway along the diagonal - more precisely, 1/sqrt(2) units - and be able to attack dark squares.
@HebaruSan
7 жыл бұрын
Tehom, the details would be up to the person defining the rules; if a given set of rules resulted in uninteresting gameplay, the mathematician studying them could simply note that and move on to some other rules. I do not pretend to have fully fleshed out this idea. Though I admit I am curious about the consequences of "exact match" rules for capture. It's true that a bishop would have much more trouble capturing other pieces, but they would also be harder to capture in turn. I wonder if there would be a fair way to extend the movement rules for pawns and knights.
@einstin2
7 жыл бұрын
Assuming the exact match rules, the biggest problem would be the knights, pawns, and king. These pieces are defined to move not an arbitrary number of spaces, but a defined integer number of spaces. The problem with that is that these pieces become weak. The queen, bishops and rooks can all move any real number of spaces. This means that there are an infinite number of positions that they could be in (big infinity, not wimpy infinity). Not simply board positions like (3.1, 2.3), but positions like (pi/sqrt(3), e^sqrt(2)). It would be basically impossible to set up a capture of one of the free moving pieces except by waiting for the piece to land on an integer number spot (something that wouldn't be required to capture an integer piece). This is because any piece could always take advantage of the infinite degrees of freedom available. In fact, the optimal strategy for this game would be to rush the queen onto one of the diagonals that lead to the king. Once that happens, the king could be perpetually checked until either a) the player makes a mistake and loses, b) the first player allows a stalemate by repetition, or c) the first player disengages in order to prevent a stalemate. (I am not sure which is the most likely outcome.) We could extend the real movement to all pieces by allowing the king, pawn, and knight to move as they normally do, except that the moves can be scaled by a number between 0 and 1. This would allow real movements among all pieces, but would only make the games impossible to win as every piece falls through the infinite folds of the continuum. The king cant be mated (no way to force him into a position he cannot escape from by simply moving an arbitrary unit up or left etc...) and so every game would end due to one of the three stalemate rules. If we replace those stalemate rules with only the requirement that in perfect play, it is possible to capture the king in a finite number of moves, then the game would still be a stalemate. It would be easy to show that there exists a shrinking series formed as the king moves from square A to B that cannot be intercepted by any piece moving linearly. This would apply to all pieces including the knight. In short, exact match is uninteresting and should probably go back to the drawing board. I don't think that ranged capture is more interesting either. It seems to me that ranged capture would simply quantize the board. If the capture range is r (in some fractional unit of a square), then the chess board could be redivided as a new board of NxN where N = 8/r. Play would effectively be the same as a regular integer chess board with NxN size. That is to say, everything we know about finite chess would still be applicable in this example.
@Friek555
7 жыл бұрын
+Adam Billman You could fix that by allowing the pawns and king to move any length less or equal to 1, and allow the knights to move any length less or equal to sqrt(5), with one of their coordinate deltas being double the other coordinate delta (Δx=±2Δy or Δy=±2Δx; (Δx)²+(Δy)² ≤ 5)
@besaved2386
2 жыл бұрын
7.40 slight correction: If black decides to move a pawn, it would be mate in one. The queen could just move up one square. Also if black just moves the middle rook one to the right white can't win in six, or even more turns. (At least from what I've played through) Other han that, Great video, thanks.
@TheDruidKing
7 жыл бұрын
Why are there three black rooks?
@freshrockpapa-e7799
7 жыл бұрын
A pawn promoted by reaching the end of the infinite board lel.
@donkosaurus
7 жыл бұрын
black must have thrown double 4s and played their get-out-of-jail-free card
@WilliametcCook
7 жыл бұрын
You should see the number of pawns in the ω⁴ game. jdh.hamkins.org/a-position-in-infinite-chess-with-game-value-omega-to-the-4/
@tscoffey1
7 жыл бұрын
Affirmative action.
@joelhaggis5054
7 жыл бұрын
tscoffey1 I was going to offer a genuine explanation, but that's just hilarious.
@CarmenLC
7 жыл бұрын
Watch the vid before commenting sheesh
@computo2000
7 жыл бұрын
sheesh, sheesh, sheesh!!
@mr-turnip
6 жыл бұрын
Does halfway count
@zAznInVaznz
6 жыл бұрын
Here from Agadmator :)
@osimmac
7 жыл бұрын
oh shit at first i was like u could just run away for ever, but then i realized the bishop, castle, and queen could make infinite moves
@pandariuskairos3841
7 жыл бұрын
I played two infinite games of chess this morning. I'm still playing one of them.
@GameToony
7 жыл бұрын
0:30 black kings on wrong square, but tbh that's a mistake 90% of people make anyway xD I wonder how many games of chess have been completed with the king being on the wrong square and nobody batting an eye..
@AM-sp6je
6 жыл бұрын
Agadmator fans unite!
@rowanz74
4 жыл бұрын
Hello everyone.
@CrimsonSlug
7 жыл бұрын
I have a couple of questions. 1. What rules are used to prevent ties (for example what happens if both players only start with a king and nothing else)? 2. Why didn't black move his rook to the right in the example game. It seems that this would allow him to break the doomsday spiral?
@Savigawd
6 жыл бұрын
Agadmator ♥
@dantheinsultcomicdog75
7 жыл бұрын
The chess board is set up wrong! The white square is always the bottom right square. It's amazing to me how many times a chess board is setup wrong in movies, ads, videos ect.
@Cellkist
7 жыл бұрын
Dan the insult comic dog It's an infinite board. There is no bottom square.
@alicewyan
6 жыл бұрын
Will there be a video explaining more about the fact that a game's determinacy can depend on the chosen set theory axioms? (perhaps there's one already?)
@awareqwx
6 жыл бұрын
The situation at 7:00 can be easily prevented by simply moving the black rook to the right instead of up. If white proceeds according to the stated moves, then the black rook can capture the white rook and prevent the checkmate.
@MGSchmahl
Жыл бұрын
Now instead White moves the Rook 1 square left. King moves. White Queen one square forward, mate.
@benjaminhackett8896
7 жыл бұрын
It would be much smarter for black to move the rook one space to the right.
@Cellkist
7 жыл бұрын
No. No it wouldn't.
@Cellkist
7 жыл бұрын
It would be much smarter for black to move the king on its side and resign.
@Cellkist
7 жыл бұрын
If you move the left rook to the right, then queen moves directly in front of King. Checkmate. If you move the middle rook to the right, then white moves their rook one to the left, forcing King to go one to the right, then queen moves up two squares. Checkmate. The third rook moving right does nothing.
@stlgaming3799
6 жыл бұрын
guys move the center rook to the right would make things better
@Cellkist
6 жыл бұрын
Myrrh Manalo my man did you read my comment?
@markenangel1813
5 жыл бұрын
Actually, chess has ties, so it might or might not be determined, which is part of why no one knows the "optimal" strategy.
@melodeathkt6252
7 жыл бұрын
Fundamental doubt. How is it possible to make an infinite move on an infinite board? say I'm black in that position in the video, and i want to move my rook infinitely far away. but then my move will never end. Because there will always be another square beyond the square I just put the rook on, so I will keep moving the rook, and it will never be white's turn. Alternatively, if there is a square that I am forced to stop at, then the board is not infinite. How do you deal with that?
@Reddles37
7 жыл бұрын
MeloDeathKT, You can't make an infinite move, that wouldn't make any sense. What you can do is move any finite distance you want, without any limit. That's why the game ends in a finite number of moves even though the doomsday clock is infinite, since as soon as you make a move the clock drops to a finite amount.
@DDvargas123
7 жыл бұрын
Basically, you have to pick an integer of squares to move before moving ur piece. The reason the board remains infinite is because you can choose any finite integer of squares. You are right that you can stay and think about ur move saying. "Hmm maybe I'll move it 5 spaces. Maybe I'll move it 5+1 spaces" and continue thinking forever. But eventually once you make ur move it will take white that number of spaces you chose to deliver mate.
@melodeathkt6252
7 жыл бұрын
Reddles37 that seems like a complete cop-out, and not really an infinite board. what that is, is an arbitrarily large but finite board. Limiting the range of movement to 8 squares back means the chessboard is 8x8, and limiting the range of movement to an arbitrarily large but finite number equally means that the board is arbitrarily large but finite. After all, limiting the range of movement is the DEFINITION of limiting the board. how can you call this an infinite board?
@erikziak1249
7 жыл бұрын
Daniel V: So you will never finish the move in the first place. Or you need an infinite amount of time to finish it?
@DDvargas123
7 жыл бұрын
Move to the first square in 1 second. Then the second square in half a second and the third square in a fourth of a second ... Now you completed your move in 2 seconds yay!
@JermFaceKiLLa
7 жыл бұрын
Quesiton: When you have a doomsday clock of OMEGA, is it considered a SUPERTASK once the piece is captured? Also consider if there are positions of OMEGA squared, OMEGA square times 4 and even OMEGA to the fourth, I would then propose that a HYPERTASK is possible. Thoughts?
@e3Gewinnt
6 жыл бұрын
Chess is determed. correct. But, it's wrong that it means black or white has a wining strategy. Chess could be like tic-tac-toe, where noone has a winningstrategy. Chess could be determed to be draw, if both players play perfect
@maxthexpfarmer3957
3 жыл бұрын
It most likely is.
@SpencerTwiddy
7 жыл бұрын
8:00 isn't it mate in 1 not 2?
@joelhaggis5054
7 жыл бұрын
1 move in chess convention is two moves in game theory convention.
@Naymy
7 жыл бұрын
Moving the Rook was a dubious move by White. A better move would have been to move the Queen instead to get Checkmate in 1. Still, what a fantastic chess puzzle. Your comments and questions please.
@Destroyer83
6 жыл бұрын
Eh, move the rook on the left in and avoid the checkmate entirely
@collinford4221
6 жыл бұрын
Naymy, agadmator will always be better than suren
@julliosantoro
6 жыл бұрын
If Black moves the Rook on the left then White's Rook can checkmate the King.
@Sillytake1705
7 жыл бұрын
The goal of chess is to checkmate the king, and capturing the opponent’s king is impossible if all of the rules are followed.
@lukastux3024
3 жыл бұрын
Well, the game ends when one side can't avoid the capture of the king.
@liamcalder5129
7 жыл бұрын
If black moves his rook to the right one square at 7:16 he is safe.
@zairaner1489
7 жыл бұрын
Then white wins immediatly.
@maxiqwee6860
7 жыл бұрын
Liam Calder queen moves one to the right and up, checkmate (or if you mean the other rook, the queen only moves one up without moving right)
@ManSeaweed
7 жыл бұрын
how are you guys missing this? It is absolutely not check mate. you move the king up 1 and left 1, and you're golden.
@maxiqwee6860
7 жыл бұрын
Liam Calder NOT IF THEY MOVED THEIR ROOK THERE!!!!1111elf (on a serious note though, I said itˋs checkmate IF they move that rook to the right because then the king can't escape to there anymore
@ManSeaweed
7 жыл бұрын
I worked it out on a chess board with a former professional and putting the middle rook one space to the right would end up in check mate, but not by moving the queen 1 right and 1 up.
@rayfangrui
7 жыл бұрын
the definition of "mate in n" is not conventional and is very confusing for a chess player.
@Tehom1
7 жыл бұрын
Right. If white has a mate in 6 moves, that conventionally means that (assuming black plays perfectly) white will move 6 times, checkmating black on the final move. Not that each player moves 3 more times.
@oakenguitar3
7 жыл бұрын
How is it not conventional and very confusing? I have to disagree. Just about every tournament chess player owns a book on mating puzzles. The book I have has 3 sections: mate in 1, mate in 2 and mate in 3 problems with solutions in the back. All the moves are forced for the losing player.
@oakenguitar3
7 жыл бұрын
black's moves are forced, there is no perfect play, theres probably only 1 possible move, its all up to white to checkmate in the correct number of times, missing a forced mate in 3 is embarrassing unless you're in time trouble.
@freshrockpapa-e7799
7 жыл бұрын
oakenguitar, can you please read the comment before replying?
@oakenguitar3
7 жыл бұрын
what comment did I not read rock papa....? I just don't understand how the definition is confusing.
@boptillyouflop
3 жыл бұрын
I've tried coming up with a Turing-Complete setup using chess rules. I couldn't do it, but with a couple accomodations (most likely an infinitely repeated grid of walls and pieces), it looks doable. Promising setups for Turing-Complete chess: - Given an infinitely repeated grid, it might be possible to build a cellular automata such as rule 110, though it might require multiple kings. - If you can build some kind of path with forced king movement, path crossings and one-way path joinings, then with an infinitely repeated grid, you can build a 2-counter Minsky counter machine, using the x y position of the king within the grid to store information. (Snakes and Ladders with an infinitely repeated grid or many other infinite patterns is also Turing-Complete) - Building a more traditional Turing machine with a proper tape is more complex since it requires some sort of resettable 1-bit non-destructive memory cell... I'm not sure it's possible, but if so it requires a 1-dimensional infinitely repeated section still. - The holy grail would be to encode information in the position of some infinitely movable pieces to build a Minsky counter machine, since you would then only need a finite number of pieces/walls, but that sounds very difficult and probably requires a lot of other compromises (fairy chess pieces, weird rules, who knows).
@de_luxe8616
7 жыл бұрын
Hey, slightly correction ;) There is rule in chess which says that a game is draw if there are more than 50 moves without a pawn moving. So the doomsday clock cant be infinit
@professionalmemeenthusiast2117
6 жыл бұрын
Thomas Nordman Yes
@texchip977
6 жыл бұрын
if the board is infinite then pawns can move infinite times
@davidmikan7925
5 жыл бұрын
a dark, twisted dreamworld. not if they’re blocked
@Dashknocker
7 жыл бұрын
There's a small problem with the infinite scenario as presented. There is no White King. Therefore White has either already lost or it is placed somewhere else on the board. Which itself presents a bit of a problem. If we use the Black King as (0, 0) on 2D Cartesian coordinates and the White King is located nearly anywhere outside the shown starting, then Black can force an indefinite number of moves by moving a rook along the x-axis. It is also possible for White to make a losing play in this situation too. The (+x, -y) "quadrant" is a bit tricky. The other 3 are pretty straight forward. Either there is an indefinite delay or there is a loss/trade of material. But the (+x, -y) quadrant is either an indefinite delay forced by Black or an indefinite delay forced by White. If the White King moves away from x = 0, then it is forced by Black. If the White King moves toward x = 0, eventually it will be protected by the Pawn. To remedy a clear loss, Black can move the middle Rook out to put the White King in check after it moves toward x = 0. Then the Black King has an unbounded amount of room to run. Possibly better if the Black King moved back after the middle rook is moved. Note: The Black Rooks cannot attack the White King along the y-axis. The White King could "snake" its way to the rook and take it or force it out of position. Then White would just need to revert to the previous winning strategy. Along the x-axis the attacking rook is protected by the other rooks. So unless the White King is protected by other non-shown pieces, or it is on certain edge cases ((0, -y) comes to mind), White is not guaranteed a win. P.S. I really love this series.
@iwanabana
7 жыл бұрын
4:26 "let us know what you're thinking in the comments" *wipes drool off shirt* uh, excuse me, what? I'm sorry, I was a little lost in your eyes... Anyway, at first I was thinking that the information speed was delivered a bit too slow, but as soon as the infinite ordinals started popping up, it took just that bit more time for my layman brain to catch up, and I appreciated that a lot!
@pvanukoff
7 жыл бұрын
Not creepy at all.
@jwrm22
7 жыл бұрын
At 6:55 if white has a king, black can give check, regardless of it's position. If white does not have a king it's not chess.
@freshrockpapa-e7799
7 жыл бұрын
It can't if it's behind a piece though.
@BelegaerTheGreat
Жыл бұрын
*YOOO, MY PROF HAMKINS IS MENTIONED!!!* Also, incredible how Chess can portray Ordinals, wow...
@FatedHandJonathon
6 жыл бұрын
On your board at 6:59, I don't think there's anywhere, even on an infinite board, that you can position the white king to make him immune to attack by black's rooks. At least one of the rooks will always be able to move into the same row or column as the king, placing him in check, and preventing white from moving forward with its own check. Black can then keep this going by chasing the king around the board with the rooks, and may even be eventually able to force a win; I'm not sure. But in any case, the situation is more complicated than what you've presented. It only really works if white doesn't actually *have* a king, in which case... yeah, you're right, it's hard to imagine a scenario in which they lose.
@ramuk1933
3 жыл бұрын
What if, rather than playing on a infinite board, what if you played it on a torus (with whatever size you want), or a Klein Bottle? What about 3d hyper Klein Bottles?
@TojosWizzyWorld
2 жыл бұрын
7:46 Actually, if black move the middle rook sideways by 1, he will survive longer.
@zestyorangez
Жыл бұрын
winning move for black is to place the rook trillions of spaces ahead and then just run out the clock by being faster at moving the pieces.
@sasha-2574
3 жыл бұрын
The Doomsday clock should be: How many moves before a pawn gets promoted in this infinite chess.
@miikavuorio9190
6 жыл бұрын
Hey uhh... Why not just move the rook to the side in your example. Somebody. Plz egsplain.
@victoriamitchell413
2 жыл бұрын
But there's one more variation of chess that can even blow genius minds 5Dimensional chess 5D chess for short It's like a normal chess game but you can go back into the past according to the Rules of chess Just extended another dimension If you go back into the past they create a new timeline The 2 timelines can be played on at the exact same time if they're both the present The present is the earliest timeline that follows these rules That the type timeline isn't an extra timeline which means it's over one more than how many timelines the opponent has created And that's basically it That's all you need to know about 5D Chess Goodbye
@NaviaryMusic
2 жыл бұрын
I play 5D chess do you play?
@Owen_loves_Butters
3 жыл бұрын
Or more likely, a strategy for both that will always end in a draw.
@YOGIKRASPRO
6 жыл бұрын
After 50 moves without capturing any pice or moving a pon the result of this game would be a draw. ;)
@stinic4263
6 жыл бұрын
Yogi she said let's exclude draw situations for this one. So better luck nect time
@dr.z7958
6 жыл бұрын
Finite chess is determined. At least one player will have a winning strategy. Infinite chess is determined. At least one player will have a non-losing strategy.
@tenneyty
7 жыл бұрын
At about 3:00 one of the lines is drawn incorrectly (in the bottom left corner)
@CarlRozario
7 жыл бұрын
The way the king, castle and rook was moving resembled something like a glider from Conway's game of life.
@ets9191
7 жыл бұрын
I support any type of educational videos, like these! Keep up The good work, and push in as much content as possible Respect
@qwertyquazo673
7 жыл бұрын
We can find the winning strategy of chess using a quantum computer. How cool!
@lyrimetacurl0
Ай бұрын
As it is often easier to "just see" the perfect strategy in games like tic-tac-toe and marbles (I have this ability with Connect 4 also, I could see a way I could force a guaranteed win from the start years before it came out officially) compared to knowing all the possible moves, it makes me think perfect chess is possible for someone who would know. Probably when people beat Stockfish or the top computer then they happen to have used perfect chess without knowing for sure.
@abcvideoyoutuization
7 жыл бұрын
Where do I go to find out why infinite series is a being studied and what benefits has the study produced.
@dxdx666
7 жыл бұрын
Have you heard about *draw* possibilty in chess?
@thealientree3821
6 жыл бұрын
Why isn't it like this? Black Turn 1: move the rook out of the way. White Turn 1: move the rook right next to the king. Black Turn 2: move the king upwards. White Turn 2: move the queen right next to the king. Checkmate.
@marcushendriksen8415
5 жыл бұрын
White bishop: catch ya later bro *slides off into infinity*
@tom2314
7 жыл бұрын
4:07 "No ties" There are ties in chess, so I think that disproves the whole premise of this video concerning chess being determined.
Пікірлер: 1,2 М.