The Game .131 

'Almost' Stalking (compare with .121, which is similar)

Status: SOLVED [5 February 2003]

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

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

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

Genus sequence (starting at heap size 1)

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

where the last four values repeat indefinitely.

misereTable[{0, 1, 3, 1}, 20, True]

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

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  :1  :2  :0  :4  :1  :5  ...

where the last four values repeat indefinitely.