Re: Nim morphs that have draws Re: There exists a Nim version that is a "draw" OS

From: Archimedes Plutonium (a_plutonium_at_iw.net)
Date: 07/10/04 

Date: Sat, 10 Jul 2004 00:43:40 -0500

Sat, 10 Jul 2004 00:07:11 -0500 Archimedes Plutonium wrote:

>
> question for Gametheory, on whether you can have a VonNeumann game where
> either first mover or second mover can win in the OS of that game yet still
> the game has no draws???
>
> Very tough question.
>
> And further, that another Nim-morph exists where it actually has draws in the
> game itself and that the OS of this Nim-morph is a draw.
>

Tinkering around a little bit, I may have the answers to the above. Question
first: can you have dice rolled in tictactoe or Nim and still have the games
under VonNuemann Game theory?? If so, then here is a Nim morph that satisfies
the above condition where either second player or first player can win and yet
no draws and a *draw OS* And a morph for Tictactoe that has either first player
win or second player win and yet no draws within the game itself.

Nim-morph rule: at the end of the game you roll a dice and if the dice comes up
4 or higher then the last person to pull off the object loses but if the dice
rolls 3 or lower then the person who pulls off the last object wins.

Tictactoe-morph rule: at the end of the game you roll a dice and if 4 or higher
then the 3 in a row player wins but if 3 or lower on the dice then the non-3 in
a row player wins. If in case both players have non-3 in a row then the one who
does not have two-in-a-row wins. This tictactoe morph, provided it is a
VonNeumann Gametheory game especially because it introduces dice roll
probability. Would be an example of where either player can win and the OS is a
win yet the game has no draws.

I have the hunch that these are no longer VonNeumann games because of the dice
probability introduction.

Archimedes Plutonium
www.archimedesplutonium.com
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies

Relevant Pages

  • [Review] Wildside!
    ... Maybe the game felt ... with each player given a "Dice Pad" in front of them, ... six-sided dice (showing a star, moon, raindrop, lightning bolt, and two ... "wild" sides). ...
    (rec.games.board)
  • [Review] Powerboats
    ... Is that alone enough to make the game substantially different ... rolling three-sided dice. ... a player will take and roll one die. ... This, of course, results in damage to one's boat. ...
    (rec.games.board)
  • [Review] Powerboats
    ... Is that alone enough to make the game substantially different ... rolling three-sided dice. ... a player will take and roll one die. ... This, of course, results in damage to one's boat. ...
    (rec.games.board)
  • [Review] Powerboats
    ... Is that alone enough to make the game substantially different ... rolling three-sided dice. ... a player will take and roll one die. ... This, of course, results in damage to one's boat. ...
    (rec.games.board)
  • Re: Guy Macons suggested changes to USCF/FIDE rules
    ... *exactly * the same score as two draws. ... The argument that the guy has lost a game suggests he's done worse ... than the player who scored two draws by some amount x; ... I note that the preface to the FIDE Laws states, ...
    (rec.games.chess.misc)