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 13:32:06 -0500

Sat, 10 Jul 2004 00:43:40 -0500 Archimedes Plutonium wrote:
(snipped)

>
> 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.
>

Well, I do know better and the above is "horseplay" late at night. But horseplay
is not all useless. Horseplay serves a nice function of focusing on where I would
like to be in relation to where I am. And the horseplay above which is patently
wrong because no VonNeumann game has a roll of the dice determinant. But where the
above came in very handy is what to make of a winner in Tictactoe if 3 in a row
was not achieved. So this horseplay focused my mind on the idea that the one with
the most 2-in-a-row would be the winner in tictactoe if no-one achieved
3-in-a-row.

Horseplay is part of brainstorming and it can lead to more good results regardless
of the fact that it is silly and wrong.

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

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