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Checkers Solved, Unbeatable Database Created

Posted by Zonk on from the does-that-mean-we-don't-need-to-play-anymore dept.

tgeller writes "My story on the Nature site announced that a team of computer scientists at the University of Alberta has solved checkers. From the game's 500 billion billion positions (5 * 10^20), 'Chinook' has determined which 100,000 billion (10^14) are needed for their proof, and run through all relevant decision trees. They've set up a site where you can see the proof, traverse the logic, and play their unbeatable automaton. '[Jonathan] Schaeffer notes that his research has implications beyond the checkers board. The same algorithms his team writes to solve games could be helpful in searching other databases, such as vast lists of biological information because, as he says, "At the core, they both reduce to the same fundamental problem: large, compressed data sets that have to be accessed quickly."'"

67 of 359 comments (clear)

  1. Wow. by Anonymous Coward · · Score: 5, Funny

    Wow. Reminds me of how awesome I thought I was when I was 7 years old and I solved Tic Tac Toe.

    1. Re:Wow. by DavidShor · · Score: 3, Informative

      According to TFA, a draw

    2. Re:Wow. by Golgafrinchan · · Score: 3, Funny

      WOPR blows up, the world is saved from nuclear disaster, and the system asks if you'd like to play a nice game of chess.

      --
      My userid is prime!
    3. Re:Wow. by aichpvee · · Score: 2, Funny

      DOUBLE KO!

      --
      The Farewell Tour II
    4. Re:Wow. by Zantetsuken · · Score: 4, Funny

      Well, since it's already playing a board game, would it perhaps decide to play "global thermonuclear war" when it looses checkers/chess? Talk about a sore looser!

    5. Re:Wow. by PCM2 · · Score: 2, Informative

      According to the article, checkers has been "solved" to the extent that they've developed a mathematical proof showing that it's impossible to beat the checkers software the researchers wrote. Even if the human plays a "perfect" game against the computer, the result will be a draw.

      So, in answer to your first question, none. Checkers might be "solved," but the computer is not guaranteed to win. (It is, however, quite likely.)

      In answer to your second question, if both sides play perfect games then you'll always draw. A "perfect" move yields no advantage to the opponent. In other words, you might lose a piece, but you've still played a perfect game if the piece is only lost in such a way that your opponent is guaranteed to lose one of his own in a subsequent move.

      Please note that checkers is a considerably less complex game than chess, for example, or Go.

      --
      Breakfast served all day!
    6. Re:Wow. by PCM2 · · Score: 2, Insightful
      Two points:

      a) The post you responded to was inquiring about tic-tac-toe, not checkers.
      No it wasn't. Every game of tic-tac-toe I've ever played used Xs and Os, not black and white pieces.

      b) Checkers is deceivingly complicated...the article mentions somewhere that it is very likely that checkers is likely more complicated than chess.

      Uhhhh... no it most certainly doesn't. It states quite plainly that "chess is even harder to solve than checkers, with a state-space complexity of 10^46," and furthermore that "chess and Go cannot be solved with the type of technology that we have today," but that they might be solved "between 2060 and 2070" (A.D., to you).

      Damn, man. That's got to be the most pathetic example of not reading TFA, or the post you're responding to, or the post before that ... or anything ... that I've seen on Slashdot so far. You might want to look into vocational school.

      --
      Breakfast served all day!
  2. The writing's been on the wall... by Eco-Mono · · Score: 3, Informative

    ...ever since the swelling of Chess's "opening book" began. They randomise starting back-rank positions now in some tournaments, to stave off the eventual "book death" that has already conquered checkers.

    --
    (rot13) rpbzbab@tznvy.pbz
    1. Re:The writing's been on the wall... by dprovine · · Score: 5, Interesting

      They randomise starting back-rank positions now in some tournaments, to stave off the eventual "book death" that has already conquered checkers.

      I made up my own variation with randomness that I call Schrödinger's Chess.

      Let me know if you try it out.

    2. Re:The writing's been on the wall... by eclectro · · Score: 3, Informative

      For those that are interested, I think the parent is referring to Chess960.

      --
      Take the cheese to sickbay, the doctor should see it as soon as possible - B'Elanna Torres, "Learning Curve"
    3. Re:The writing's been on the wall... by SnowZero · · Score: 2, Informative

      Created/endorsed by chess genius and raving lunatic Bobby Fischer: "I don't play the old chess. But obviously if I did, I would be the best."

    4. Re:The writing's been on the wall... by SL+Baur · · Score: 3, Interesting

      They randomise starting back-rank positions now in some tournaments, to stave off the eventual "book death" that has already conquered checkers. Randomize or start with the pieces off the board? When I was still a member of the USCF in the 1970s, someone introduced a chess variant similar to that. Each side starts with 8 pawns on the 2nd on the board and the back rank empty. White still moves first, but the first 8 moves for each side must be to put the major pieces on the 1st rank. This eliminates the memorized opening book openings too and emphasizes chess middle game play which is what the game is about anyway IMO. This adds 16! different starting positions and maybe makes the game complex enough that it can never be solved deterministically in a useful amount of time, I hope so.

      I'm not surprised that checkers has been solved. As a programmer and an engineer, I cheer in the fact that a difficult problem has been solved, as a human being, I'm sad in a way. Computers are tools, humans are well, humans. There must remain some ways we can think better.
    5. Re:The writing's been on the wall... by db32 · · Score: 3, Funny

      Well...if its any consolation, I am reasonably certain we will have the ability to think with our genitals quite a long time before computers ever master that one, if they even can. Logic be damned!

      --
      The only change I can believe in is what I find in my couch cushions.
    6. Re:The writing's been on the wall... by fractoid · · Score: 5, Funny

      Schrodinger's chess is when you set up a chess board in a box with a cat. You then shake the box, and declare that you beat the cat at chess.

      --
      Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
    7. Re:The writing's been on the wall... by crontabminusell · · Score: 2, Funny

      You then shake the box, and declare that you beat the cat at chess. Correction: beat the cat with chess. ;)
    8. Re:The writing's been on the wall... by TED+Vinson · · Score: 5, Funny

      Good idea. Perhaps Checkers can be revitalized by randomizing which piece goes on which starting space too...

    9. Re:The writing's been on the wall... by clickety6 · · Score: 3, Funny

      In 1986, I tried a variant by putting all the black pieces on black squares and all the white pieces on white squares.

      It's now 2007 and we still haven't completed the first game...

      --
      ----------------------------------- My Other Sig Is Hilarious -----------------------------------
    10. Re:The writing's been on the wall... by Faylone · · Score: 3, Funny

      Correction to the correction: MAY have beat the cat with chess.

  3. Slashdot effect. . . by ookabooka · · Score: 4, Funny

    They've set up a site where you can see the proof, traverse the logic, and play their unbeatable automaton.


    Holy crap. . .you have any idea how badly their server is going to be slashdotted now? It's bad enough when its a php driven webpage but now you've just encouraged slashdotters to try a game or two against it. . .if the server crashes in the middle of a game is it considered a win for the human player?
    --
    If you are about to mod me down, keep in mind that this post was most likely sarcastic.
    1. Re:Slashdot effect. . . by garcia · · Score: 3, Insightful

      Holy crap. . .you have any idea how badly their server is going to be slashdotted now? It's bad enough when its a php driven webpage but now you've just encouraged slashdotters to try a game or two against it. . .if the server crashes in the middle of a game is it considered a win for the human player?

      It's a little difficult to play when you can't even load the game...

    2. Re:Slashdot effect. . . by kryten_nl · · Score: 2, Funny

      With checkers, I find that pointing a gun to the person sitting across the table, usually guarantees a win.

      --
      For the perfect anti-Unix, write an OS that thinks it knows what you're doing better than you do and let it be wrong.
  4. It's a draw by elwinc · · Score: 5, Informative
    The New York Times has the story too http://www.nytimes.com/2007/07/19/science/19cnd-ch eckers.html?ref=science:. They claim the best you can do is draw against chinook in deterministic checkers. The Times points out that:

    The new research proves that Chinook is invincible in the traditional game of checkers. But in most tournament play, a match starts with three moves chosen at random. In solving the traditional game, the researchers have also solved 21 of the 156 three-move openings, leaving a crack of hope for humans, at least for now.
    --
    --- Often in error; never in doubt!
    1. Re:It's a draw by $RANDOMLUSER · · Score: 4, Funny

      They claim the best you can do is draw against chinook in deterministic checkers.
      Ooooohhhh! Nondeterministic checkers!!

      <clack....clack....clack>
      "That's a inside giraffe, king me."
      --
      No folly is more costly than the folly of intolerant idealism. - Winston Churchill
    2. Re:It's a draw by SnowZero · · Score: 2, Informative

      A strange game. The only winning move then is not to play.

  5. Flawed proof by eln · · Score: 4, Funny

    Now, far be it from me to criticize the research of a group that can manage to convince someone to give them a grant to play checkers with a computer all day, but their "proof" on that site is a little suspect.

    When I click on the proof, all I get is a Java error saying "Unable to connect to server". While the inability to connect to the Checkers server may make it "Unbeatable" in a Wargames-esque "the only way to win is not to play" kind of way, it's kind of a cop-out.

    1. Re:Flawed proof by The+Flying+Guy · · Score: 2, Interesting

      Quoting about graph theory (to be exact 4 colour theorem): "a good mathematical proof is like a poem--this is a telephone directory!"

      Not sure who wrote it, but the 4 colour theorem was the first computer aided proof.

      And I am afraid I have to agree.

  6. Re:skynet is coming... by moderatorrater · · Score: 2, Funny

    So all we have to do to crash the eventual skynet is move in a direction that isn't diagonal? This is going to be easy.

  7. We'll always have Go by roscivs · · Score: 4, Informative

    Since Go always comes up in these discussions, I'll take this opportunity to point those curious about the game to some places to learn more about it:

    http://playgo.to/interactive/, learn how to play the game in an interactive fashion.

    http://361points.com/atarigo/, play "capture" Go against a simple computer opponent.

    http://www.gokgs.com/, after you've learned the rules, play against others online worldwide.

    http://www.godiscussions.com/, have more questions about the game? Ask them on this discussion board devoted to the game.

    --
    ~ roscivs
    1. Re:We'll always have Go by Derek+Pomery · · Score: 5, Interesting

      'course, Go would be kind of dull too on an 4x8 board (checkers only uses half the squares)
      http://www.chessvariants.com/d.betza/chessvar/16x1 6.html

      --
      -- perl -e'print pack"H*","6e656d6f406d38792e6f7267"' /. ate my old sig. Bastards.
    2. Re:We'll always have Go by Wannabe+Code+Monkey · · Score: 3, Funny

      http://www.godiscussions.com/, have more questions about the game? Ask them on this discussion board devoted to the game.

      I've always wondered what God is... Now I know, God is 'cussions'. Now if only I knew what a 'cussion' is. Is it like a cushion?

      --
      We always knew Comcast was corrupt, here's the proof: http://tech.slashdot.org/comments.pl?sid=1909890&cid=34545432
    3. Re:We'll always have Go by Anonymous Coward · · Score: 2, Interesting

      > 'course, Go would be kind of dull too on an 4x8 board (checkers only uses half the squares)

      Duh? Go is _designed_ to be played on a 19x19 grid; the sheer size of the board is an important aspect to strategy. Chess on a 4x2 board doesn't sound too exciting, either (but I'd try 3/2x3/4 tic-tac-toe any day). For the record, 9x9 go (as played on a chess board) is still quite interesting. As for full size go, here is a quote from http://senseis.xmp.net/, the go wiki: "It is commonly said that no game has ever been played twice. This may be true: On a 19×19 board, there are about 3^361×0.012 = 2.1×10^170 possible positions, most of which are the end result of about (120!)^2 = 4.5×10^397 different (no-capture) games, for a total of about 9.3×10^567 games. Allowing captures gives as many as 10^(7.49×10^48) possible games, most of which last for over 1.6×10^49 moves! (By contrast, [...] physicists estimate that there are not more than 10^90 protons in the entire universe.)"

  8. Checkers, Not Draughts by eldavojohn · · Score: 5, Interesting
    From the Wikipedia entry:

    The most popular forms are international draughts, played on a 10×10 board, followed by English draughts, also called American checkers that is played on an 8×8 board, but there are many other variants. Draughts developed from alquerque.[2] Draughts would be a much much larger gamespace than Checkers. I noticed that draughts appeared in the tags of this story but it shouldn't.

    Also, I've heard before that "it takes longer to learn to play checkers at the master level than it does chess. What checkers lacks in breadth, it makes up in precision and finality." I realize that puts me at risk of being modded as flamebait but I wonder if any other Slashdot reader can confirm or contest that.
    --
    My work here is dung.
    1. Re:Checkers, Not Draughts by Eco-Mono · · Score: 2, Informative

      The same article, in fact the same quoted paragraph states that American Checkers and British Draughts are the same, 8x8 board game. So calling this solution a solution to draughts isn't really that inaccurate.

      --
      (rot13) rpbzbab@tznvy.pbz
    2. Re:Checkers, Not Draughts by tgeller · · Score: 2, Interesting

      Here's a relevant quote from Bob Newell (editor of The Checker Maven) that didn't make it into the story:

      "[Checkers is] a very finely balanced game, and a very subtle game. The subtleties of checkers are not very well appreciated by the average player. You play as a kid and someone always wins. In chess, differences are larger: In chess, you can make a mistake and still recover. In checkers, if you make a mistake, even a small one, you probably won't recover. People are fascinated by this game of minutiae, if you will. At a high level, at least two games out of three, no-one can gain that small advantage and so the game ends in a draw."

      --
      Tom Geller
    3. Re:Checkers, Not Draughts by mebollocks · · Score: 4, Interesting

      I will, therefore, take occasion to assert that the higher powers of the reflective intellect are more decidedly and more usefully tasked by the unostentatious game of draughts than by all the elaborate frivolity of chess. In this latter, where the pieces have different and bizarre motions, with various and variable values, what is only complex is mistaken (a not unusual error) for what is profound. The attention is here called powerfully into play. If it flag for an instant, an oversight is committed, resulting in injury or defeat. The possible moves being not only manifold but involute, the chances of such oversights are multiplied; and in nine cases out of ten it is the more concentrative rather than the more acute player who conquers. In draughts, on the contrary, where the moves are unique and have but little variation, the probabilities of inadvertence are diminished, and the mere attention being left comparatively what advantages are obtained by either party are obtained by superior acumen. To be less abstract --Let us suppose a game of draughts where the pieces are reduced to four kings, and where, of course, no oversight is to be expected. It is obvious that here the victory can be decided (the players being at all equal) only by some recherche movement, the result of some strong exertion of the intellect. Deprived of ordinary resources, the analyst throws himself into the spirit of his opponent, identifies himself therewith, and not unfrequently sees thus, at a glance, the sole methods (sometimes indeed absurdly simple ones) by which he may seduce into error or hurry into miscalculation. Edgar Allan Poe - The murders in the Rue Morgue.
      Great Story!
    4. Re:Checkers, Not Draughts by pugugly · · Score: 2, Insightful

      I've never particularly seen that as an indication of 'subtlety' - Great, it's so subtle that you're allowed one mistake, then your done. By that definition, Tic Tac Toe is a deeply subtle game. Golly Gee.

      Or to put it differently, it's a game so subtle that one bad move will kill you, and tournament chess requires three moves at the beginning just to randomize it a bit.

      I guess I have a Chess bias - [Grin] Pug

      --
      An Invisible Entity of Vast Power whose existence must be taken on faith alone: Liberal Media
  9. Re:Chess? by rustalot42684 · · Score: 5, Informative

    RTFA: 10^46.

  10. So, who wins? by drfuchs · · Score: 4, Interesting

    Right. So, is it a win for the first or the second player? Would be nice to mention somewhere.

    1. Re:So, who wins? by Anonymous Coward · · Score: 5, Informative

      According to the site, it's a draw.

    2. Re:So, who wins? by poslfit · · Score: 2, Informative

      When correctly played, it turns out that it's a draw. The interactive game tree tool lets you explore which parts of the tree lead to which results, and if you start at the root, you can pick an edge at each node that guarantees at worst a draw for the current player. It's worth observing that the tree is not fully computed: it will often tell you that it doesn't know what happens if you make a given move in a given position, because all they needed to do was find a subtree that a player could always stay on.

  11. It's come a long way by djKing · · Score: 2, Informative

    for(int i=60;i>0;i++) was the check they did to make sure Chinook only looked ahead sixty moves and didn't go over it's time limit in one of it's first challenges against a top human player. And yes that's a bug, lost the first game because of it. I was taking an intro to logic and data structures course from Dr. Schafer at the time.

    --
    Free as in "the Truth shall set you..."
    1. Re:It's come a long way by mikeb · · Score: 4, Informative

      for(int i=60;i>0;i++) ... that loop is going to run for some time, especially if i is declared unsigned

    2. Re:It's come a long way by ajlitt · · Score: 2, Funny

      Cue the STL police and their iterator nightsticks.

  12. Re:If it's unbeatable... by $RANDOMLUSER · · Score: 4, Funny

    ...what happens if it plays another version of itself?
    Don't cross the streams. That would be bad.
    --
    No folly is more costly than the folly of intolerant idealism. - Winston Churchill
  13. Strange by hcdejong · · Score: 3, Funny

    the only winning move is not to play...

  14. CmdrTaco = pwn3d by x.Draino.x · · Score: 3, Funny

    http://games.cs.ualberta.ca/~chinook/cgi-bin/statu s.cgi

    GAME 17:
    Opponent: Cmdr Taco (cmdrtaco@slashdot.org)
    Chinook color: White
    Level: Novice
    Move number: 3
    Game analysis: Chinook has a small advantage.

    1. Re:CmdrTaco = pwn3d by UbuntuDupe · · Score: 3, Funny

      LOL look at this:

      http://games.cs.ualberta.ca/~chinook/cgi-bin/statu s.cgi?05

      Someone put:

      Spectator comments about this game:

      Hitler: This kind of reminds me of Poland, in '39.

      --
      Apology to Ubuntu forum.
  15. Re:Theoretical vs. practical by edremy · · Score: 5, Informative
    No. Schaeffer has a book out ("One Jump Ahead") about writing Chinook. He thought the same when he started, but the project got rapidly far harder than he thought. It helped that the existing human champion (Marion Tinsley) was literally as close to perfection as any human has ever been at any game- they exhaustively studied every professional game he ever played and found something like a grand total of 10 actual mistakes in a 40 year career.

    It's a very sad book in many ways- there was a lot of tension between certain members of the team and you realized that professional checkers was dying rapidly. Tinsley and Schaffer set up a world championship rematch between them (Tinsely won the first one) and Tinsely pulled out after six games saying he felt ill. He checked himself into the hospital, was diagnosed with some aggressive form of cancer and died a few months later. Schaeffer basically retired Chinook from human tournaments since nobody else was even remotely close to Tinsley.

    It didn't make many headlines because everyone knows checkers is easy. Except that they are wrong- it's not.

    --
    "Seven Deadly Sins? I thought it was a to-do list!"
  16. Re:What about tic-tac-toe? by Cervantes · · Score: 2, Informative

    I've been developing an algorithm to solve that game for years, and so far all I've come up with is: start with the middle square. Nah, that's false.

    If you're going first, put your mark in the corner. Almost regardless of what your opponent does, put your next mark in an adjacent corner. He'll now have to block you, and then you put your third mark in yet another corner, and voila, you have 2 winning moves.
    The only defense against it is to take the middle square with your first move and then block whatever side X tries to take with your second, and then X has to block your row with his third. That ends the game in a draw.

    The only winning move going second is to play for a draw. You won't win unless your opponent makes a mistake.
    --
    If I knew the wedgies I gave you back in 6th grade would have resulted in this . . . I might have taken a moments pause.
  17. Re:Chess? by youthoftoday · · Score: 5, Funny

    you didn't answer the question. How many gazillion?

    --
    -1 not first post
  18. Chinook wind by hey · · Score: 4, Insightful

    For non-Albertans... a Chinook wind is some hot air the blows down the mountains and melts the winter snow for a week or so.
    http://en.wikipedia.org/wiki/Chinook_wind
    So it an analogy for a bright new idea -- like a lite up light bulb.
    Therefore there are a zillion things called "Chinook" in Alberta.

  19. Hmmmmm by TheOldSchooler · · Score: 3, Funny

    So what happens if one automaton plays another? Does the universe implode in some kind of horrible checkers armageddon?

  20. Re:can non-intelligence make humans obsolete? by DavidShor · · Score: 2, Insightful

    The easiest way to keep "dumb" code from killing us is not to program them to do so. They could mutate their code and decide to kill us anyway, but at that point, they become "smart".

  21. Kobayashi Maru by 3vi1 · · Score: 5, Funny

    The day an automaton is "unbeatable" is the day it's 500ft tall and shoots nuclear rockets from its fingertips. I think I know a relatively easy way to beat this checkers program.

  22. Re:Chess? by justfred · · Score: 3, Funny

    I think it depends; how many Brazilians are in a gazillion?

  23. Re:Chess? by Ecuador · · Score: 2, Funny

    42

    --
    Violence is the last refuge of the incompetent. Polar Scope Align for iOS
  24. Re:numerosity and solutions within bounds by TaoPhoenix · · Score: 2, Insightful

    This type of proof is not the same as "your checkers set comes with a handheld database reader to show you the solution of the position you are in" - because it's NOT about 'average players making mistakes'.

    They went for the proof of the math behind the game. This article will also be a good flash answer against the wailers who say "but there are 500 billion billion *possible* positions in the game..."

    The answer: only a small portion of them *matter*.

    Here's the basic chain logic.

    "All endgames of 8 pieces or less with a 2 checker advantage are wins except the following known cases... (see appendix.)"

    Therefore, any time you can reach that conclusive endgame table, *all further deviations fail to matter*. It matters not that you are an 'average player who played something else'. The remainder of your game became theoretically irrelevant.

    What Schafer and team banked on (and Drew) was that the quantity of Theoretically Critical Positions is far smaller than the Possible Positions. At the Master level of both checkers and chess, the results of games after mistakes are actually less important. Someone else also mentioned that it is even harder to turn a checkers game around than a chess game.

    --
    My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
  25. Re:skynet is coming... by Anonymous Coward · · Score: 2, Insightful

    Hardly. The checkers program has no degree of intelligence whatsoever, it's just a gigantic brute force "tree" of board positions.

    It is no smarter than a choose-your-own-adventure paperback with the "good" endings already mapped out.

  26. Chinook vs Tinsley by Anonymous Coward · · Score: 5, Informative

    One can get much of the overall story online here.

  27. For people wondering what is checkers by marcosdumay · · Score: 4, Informative

    Ok, for other english impared people wondering what is checkers, it is the US name for game of draughts. If you follow that link, you'll instantly recognize the board :)

    Of course, as a brazilian, I had no idea people played that on a 10x10 board around the world. Too bad they can't reuse the chess board :)

    --
    Rethinking email
  28. Gratuitous nostalga post by Joe+Decker · · Score: 3, Informative

    HAKMEM item 93 is solved. Back in 1972 when HAKMEM was written, the AI Lab folks estimated a year or so of computer time then, I'm guessing, given how long has passed, that this was a bit optimistic.

    --
    I'm a nature photographer.
  29. Shaeffer's book about Chinook by ferguson731 · · Score: 3, Interesting

    Jonathan Schaeffer 's book about the development of Chinook (from 1997):

    http://www.amazon.com/One-Jump-Ahead-Challenging-S upremacy/dp/0387949305

    Includes the details of the Tinsley matches and Tinsley's untimely death. Interesting for people interested in the effects of technology on human societies, as well as some of the technical aspects of the program (as it was in 1997).

  30. Re:Chess? by Limerent+Oil · · Score: 2, Informative

    How many gazillion?

    10 ^ (46 - log(1 gazillion))

  31. Funny Story by Cola+Junkee · · Score: 2, Interesting

    I did my undergraduate at the U of A, and had the pleasure of being a number of Jonathan Schaeffer's classes. The man is a gifted professor, and rather quirky on top of that.

    One day, we were learning about the "Dining Philosopher" problem. The problem is about 3 philosophers that have to acquire two (shared) utensils on either side of them before they can eat the food in front of them. Those of you familiar with the problem should understand ..

    Anyway, he came in with a pot of spaghetti, forks, and plates. He actually had some students sit down and go through the algorithm. When the first one took a bite off the plate, he asked "Pretty Good, huh?" (of course the student agreed). He also threw some spaghetti against the wall to prove that it was well cooked.

    So, after the first student went through the algorithm and used the fork, you can imagine the grimace from the second student that had to use the same shared fork as the first student..

    hah! Still makes me laugh.

    I won't ever forget about acquiring mutexes in the correct order, however.

    --

    f u cn rd ths, u r prbbly a lsy spllr.

  32. Re:Chess? by NewsWatcher · · Score: 4, Informative

    Oh yeah, not that complicated, until you consider that in the USA a billion is a thousand million, but in most of the world it is a million million. Or that a sextillion is derived from prefix "sex" which means six, (as in a sextet of ale) but is actually a one followed by 21 zeros.

    A septillion (from the word for seven) contains 24 zeros.

    So what you may ask is a one followed by 22 naughts? 10 sextillion. A one followed by 23 naughts? 100 sextillion. And yet instead of a one followed by 24 naughts being 1000 sextillion, it is all of a sudden a septillion, even though it has nothing whatsoever to do with the number seven.

    I don't even know why I care about all of this. I got to this thread late and the chances of anyone reading my post in the developers section of Slashdot are next to zero. Of course next to zero would be one and minus one. Oh gawd, don't get me started on that....

    --
    If the pattern goes 9am, 10am, 11am, why isn't noon 12am?
  33. Re:Chess? by ichigo+2.0 · · Score: 2, Insightful

    And yet instead of a one followed by 24 naughts being 1000 sextillion, it is all of a sudden a septillion, even though it has nothing whatsoever to do with the number seven.
    number = 1000^(x+1)

    x is the beginning part of the word, e.g. septillion = 1000^(7+1)
  34. Re:Chess? by pelago · · Score: 2, Informative

    See http://en.wikipedia.org/wiki/Billion and http://en.wikipedia.org/wiki/Long_and_short_scales