Actually, the odds of James winning are exactly the same. 1 in 6.
No it's not, if you roll a six sided dice four times the odds of it hitting the same number all four times are extremely low. There's so many combinations of possibilities.
EDIT: I didn't watch the season 6 finale when Janelle was evicted and didn't bother much after Zach was evicted in season 8. I am definitely sticking through to the end for this season though. 
But the dice have ALREADY come up six three times in a row so the odds are 1 in 6. What happens on the fourth roll is not dependant on the previous three rolls. 
The odds remain the same, regardless of how many times the die is rolled. The "dice" have no memory. The "dice" don't know that the same number came up three times in a row. Same as in the game of Roulette. If black comes up ten spins in a row, the odds remain the same that it will be black on the eleventh spin, because the ball has no memory. Each spin is independent.
As far as BB is concerned, there is a human element....therefore, I think the odds may in fact change, depending on people, the task, slop, sleep/no sleep, etc.