This section has a survey of the misere play of three-digit quaternary games.
Tetral games are octal games that involve no splitting of piles. Their code digits have 0,1,2,3 only in them.
The two sixteen digit tetrals (ie, .00, .01, .02, 03, .11, etc) were classfied by Allemang. Only .31 (WW's "Stalking", pg 409 does not reduce to nim heaps).
There are 64 "raw" three digit tetrals.
However 16 of these---the ones ending with final code digit 0---are immediately seen to be identical to two digit tetrals.
Also, any tetral that has code digits 3 and 0 only is a subtraction game, and a complete misere theory is known for them (they are all nim-like WW 402).
That leaves 44 games to look at. We've already found that one of them, .123, has an interesting structure and solution (see our paper "Losing at .123")
SUMMARY OF RESULTS [ Notes added 3 Feb 2003]
All of the two and three-digit tetra games have entirely misere nim heap nim values, with the following exceptions:
.31 "STALKING" [ WW pg 409], and its first cousins .201 and .211 (WW pg 102), with tame values 1,2 2+, 2++, 2+++, etc
.121 & .123 "TWO-STEP STALKING" with some 0's and 1's in the pattern and all tame values
.123, perhaps the most complicated game, with a complete misere analysis given by pretending as in our paper "Losing at .123", & NOT TAME.
.312, a game we haven't solved yet, [ Note added 5 Feb 2003: Now we have solved it]
.331, another one we haven't solved yet. [Note added 5 Feb 2003: We've solved this too]
Note added 5 February 2003. We've put up this information at http://www.qxmail.com/mathematics/games/misere/quaternary/index.htm