Generating unbiased numbers with a biased six sided die? Eve takes a fair six-sided die and adds some heavy paint to the side of the die with the 6 on it. This results in a biased die that rolls a 6 with probability 2/7, and each other number (1-5) with probability 1/7.

If Alice learns that the die is loaded in this way, only has this die, and must generate 20 fair/unbiased random numbers between 1 and 6, what procedure can I propose that she can use to generate these fair numbers with this unfair die and computing how many times (exact or on expectation) Alice will have to roll the tampered die to conduct this procedure.
Each biased die result has >2.52 bits of Shannon entropy. Each unbiased die result has &lt;2.59. So 21 biased rolls have more entropy than 20 unbiased ones.

Alice can concatenate 21 biased results into $r$ and use $r_i = H(s||r||i) \bmod 6$ as the unbiased results, where $H$ is a hash function like SHA-256 and $s$ is a unique salt she decides just before rolling.

(If Alice wants to cheat, she must use >$2^{52}$ work to find an $s$ with biased outputs. If this is insufficient, roll more dice or decide $s$ in a way that does not allow this.)