since poop=1 and roll=0, it's not the first O from poop, it's the p or one of the 'op'
Now since roll=0 and boar=1, it's not the O from boar, it's the b or one of the 'ar'.
now since year=1 and fear=1, the 1 can't come from both the Y and the F, so it came from neither, so either that E, A or R is correct.
Leaving two possibilities: it's the B from Boar and the E from year/fear, OR, it's in the 'AR' ending.
So I'm going to ask BEAR. If BEAR=2, then by the logic above, "B" and "E" are the first two letters. However, if BEAR=0, then "O" is the second letter. And if BEAR=1, then the second letter is certainly not E or O, meaning the 1 comes from the A or the R. By then, though, theCube's "BEER" will have been scored, so in this case, that score is needed like so: if BEER=1, the last letter is "R". If BEER=0 then the second-to-last letter is A. Again, the BEER only comes into play if BEAR=1.
So, summary:
(BEAR=2) (B, E, are first two letters)
(BEAR=0) (O is second letter)
(BEAR=1 and BEER=1) (last letter is R)
(BEAR=1 and BEER=0) (penultimate letter is A)