And you can calculate given an actual fair N-sided dice the proportion of wasted flips/rolls:
1: 0
2: 1/2
3: 7/9
4: 58/64
N: 1 - (N-1)! / N^(N-1)
By the time you have a typical 6-sided dice, you only get 6 different rolls in 6 rolls 1.54% of the time.
I haven't calculated what happens when bias is introduced but my intuition is that with more bias you would discard more. (Based on the extreme case that if one of the sides can never roll you would never accept a result.)
1: 0
2: 1/2
3: 7/9
4: 58/64
N: 1 - (N-1)! / N^(N-1)
By the time you have a typical 6-sided dice, you only get 6 different rolls in 6 rolls 1.54% of the time.
I haven't calculated what happens when bias is introduced but my intuition is that with more bias you would discard more. (Based on the extreme case that if one of the sides can never roll you would never accept a result.)