The Game .14

Status:  OPEN

"Partial" in Allemang, to heap size 16.  He doesn't call out heap size 12 explicitly as an n[4].  

Compare this to his .16 analysis.  The game .16 also has an n[4] in it, but Allemang gives a different equation.

Allemang gives reduction rules

    A+A+A+A = A+A
    B+B = 0
    C+C+C+C = C+C
    
where

    A = h[12]=h[15]
    B = h[14]
    C = h[16]

Normal play nim sequence not known to be periodic [Flammenkamp, 2002]

Information from Winning Ways:

    1) HEAP 18 SHOULD be n[2]
    2) First two non nim heaps are heaps 14 and 16, values a4[3,2,1] and a4[4,2,0]
    3) Other nim heaps:
        h[15] = 4
        h[18] = 2 (already noted above)
    4) No other nim heaps to heap size 23 (which is as far as WW goes).