The Game .121 

'Almost' Stalking (compare with .131, which is similar)

Status: SOLVED [5 February 2003]

TAME, but not with nim-values.   Instead, the values are

   1 0 2 1 2+      0 2++ 1 2+++ 0     2++++ 1 2+++++ 0 2++++++    etc

Normal play nim sequence: 1 0 2    1 0 0 1  (period 4)

Genus sequence (starting at heap size 1)

 031   120   20   031   02   120   13
1     0     2    1     0    0     1

where the last four values repeat indefinitely

misereTable[{0, 1, 2, 1 }, 20, True]

heap 1 n[1]    = MisereGame$[n[0]]
heap 2 n[0]    = MisereGame$[]
heap 3 n[2]    = MisereGame$[n[0], n[1]]
heap 4 n[1]    = MisereGame$[n[0]]
heap 5 g$1342  = MisereGame$[n[2]]
heap 6 n[0]    = MisereGame$[]
heap 7 g$1376  = MisereGame$[g$1342]
heap 8 n[1]    = MisereGame$[n[0]]
heap 9 g$1410  = MisereGame$[g$1376]
heap 10 n[0]   = MisereGame$[]
heap 11 g$1444 = MisereGame$[g$1410]
heap 12 n[1]   = MisereGame$[n[0]]
heap 13 g$1478 = MisereGame$[g$1444]
heap 14 n[0]   = MisereGame$[]
heap 15 g$1512 = MisereGame$[g$1478]
heap 16 n[1]   = MisereGame$[n[0]]
heap 17 g$2941 = MisereGame$[g$1512]
heap 18 n[0]   = MisereGame$[]
heap 19 g$2951 = MisereGame$[g$2941]
heap 20 n[1]   = MisereGame$[n[0]]


How to play the game:

Every position is tame.  Can replace individual games with adders :k as 
given by this table:

 1   2   3   4   5   6   7   8
:1  :0  :2  :1  :4  :0  :5  ...

where the last four values repeat indefinitely.