Skip to main content
MathOverflow

Return to Answer

replaced http://mathoverflow.net/ with https://mathoverflow.net/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

By including both players' money into the state of the game, you can analize it using some tools in combinatorial game theory, specifically partizan game tools: even if the original game would naturally be a symmetric game, including both players' money inevitably breaks its symmetry except for a handful of positions, so I would suggest symmetric games aren't the ones you are looking for (so Nim and the theory of nimbers would be of little use).

For a practical example (but maybe too elementary to be useful), you can have a look at this gamethis game and its analysisits analysis, I think it fits into the kind of games you could be interested into.

By including both players' money into the state of the game, you can analize it using some tools in combinatorial game theory, specifically partizan game tools: even if the original game would naturally be a symmetric game, including both players' money inevitably breaks its symmetry except for a handful of positions, so I would suggest symmetric games aren't the ones you are looking for (so Nim and the theory of nimbers would be of little use).

For a practical example (but maybe too elementary to be useful), you can have a look at this game and its analysis, I think it fits into the kind of games you could be interested into.

By including both players' money into the state of the game, you can analize it using some tools in combinatorial game theory, specifically partizan game tools: even if the original game would naturally be a symmetric game, including both players' money inevitably breaks its symmetry except for a handful of positions, so I would suggest symmetric games aren't the ones you are looking for (so Nim and the theory of nimbers would be of little use).

For a practical example (but maybe too elementary to be useful), you can have a look at this game and its analysis, I think it fits into the kind of games you could be interested into.

Source Link
Lorenzo Lami
Lorenzo Lami
  • 153
  • 2
  • 8

By including both players' money into the state of the game, you can analize it using some tools in combinatorial game theory, specifically partizan game tools: even if the original game would naturally be a symmetric game, including both players' money inevitably breaks its symmetry except for a handful of positions, so I would suggest symmetric games aren't the ones you are looking for (so Nim and the theory of nimbers would be of little use).

For a practical example (but maybe too elementary to be useful), you can have a look at this game and its analysis, I think it fits into the kind of games you could be interested into.