Outcomes of Sums of Games
It can be used to predict the outcome of:
- The sum of any nimbers and any tame games
- The sum of any one game given its genus, any number of nim games *1, *2 or *3, and optionally one other nim game with nimber 4 or higher
- The sum of a restive game and any number of nim games of any size
In addition, some restive or restless pairs can form tame games, if they are equivalent. Two games are equivalent if they have the same options, where the same options are defined as options to equivalent games. Adding an option from which there is a reversible move does not affect equivalency.
Some restive pairs, when added to another restive game of the same species, are still tame.
A half tame game, added to itself, is equivalent to *0.
Read more about this topic: Genus Theory
Famous quotes containing the words sums and/or games:
“If God lived on earth, people would break his windows.”
—Jewish proverb, quoted in Claud Cockburn, Cockburn Sums Up, epigraph (1981)
“In the past, it seemed to make sense for a sportswriter on sabbatical from the playpen to attend the quadrennial hawgkilling when Presidential candidates are chosen, to observe and report upon politicians at play. After all, national conventions are games of a sort, and sports offers few spectacles richer in low comedy.”
—Walter Wellesley (Red)