Actually, assuming "a number of fingers" is in the range 1..10, thats only fair for 2, 5, or 10 players (or maybe some >10) (if it's 0..10, I think it only works for exactly 11 players).
In the case of 3 players you get random numbers (reduced modulo 3): 1,4,7,10 => 1 40% of the time; 2,5,8 => 2 30%; 3,6,9 => 3 30%
Two random numbers produce: 1 @ 33%; 2 @ 30%; 3 @ 37%
And after adding the third number you get: 1 @ 30.9%; 2 @ 34.9%; 3 @ 34.2%
(These percentages are all exact BTW.)
So this is biased against player 1 (which is not actually the way I was expecting it to go). And if you want to cheat, you should assume the other players will add up to 3, and pick a number accordingly.
I assume 4,6,7,8,9 out of ten and anything out of 11 work similarly, but I haven't checked the numbers.
If "a number of fingers" is 1..N (or 0..^N) then it's unbiased, but just doesn't work at all for >10 (or >11 respectively).