The Game .312 

Status: SOLVED [4 February 2003]

Normal play sequence eventually periodic of length two:

        1  2  3  4  5  6  ...
	1  2  0  2  0  1  ...

the last two values (0 and 1) repeat themselves indefinitely.

Misere play game Values:

1   2   3        4        5    6       7         8     9          10       11    12       13
1   2   2+   g0={2+,1}   2+   2++  g1={g0,2++}  2++  2+++    g2={g1,2+++} 2+++ 2++++  g3={g2,2++++}, ...

Single heap genus sequence:

   1          2       3        4         5         6     ...
1^{03131}   2^{20}  0 ^{02}  2^{1420}  0^{02}	1^{13} 	 ...

which is also periodic of length two (the last two values repeat indefinitely).

How to play misere .312:

Except for the heap of size 4, we can pretend that individual games are adders:

 1  3  3  4  5  6  7  8  9  10 
:1 :2 :4  A :4 :5 :4 :5 :4  :5     etc  (period 2)

Where A (the heap of size 4) is the game g0 of genus 2^{1420} and genus (A+A) = 0^{1202)
We can pretend that  

	A + A = :0.