Le Monde puzzle [#1155]

The weekly puzzle from Le Monde is another Sudoku challenge:

Anahera and Wiremu play a game for T rounds. They successively pick a digit between 1 and 3, never repeating the previous one, and sum these digits. The last to play wins if the sum is a multiple of 3. Who is the winner for an optimal strategy?

By a simple dynamic programming of the optimal strategy at each step

N=3
A=matrix(-1,20,N)
A[1,1:N]=1:N
for (T in 2:20)
for (i in 1:N) A[T,i]=i+ifelse(!T%%2, #parity check
max((i+A[T-1,-i])%%3), #avoid zero
min((i+A[T-1,-i])%%3)) #seek zero

the first to play can always win the game. Not fun!