Probability: simulate fair coin flips from an biased coin

a shallow answer given, more in depth answer to come in future video

[PowerALTube]

Not quite. Almost. Consider a very biased coin with P(H) >>> P(T). You would get a run something like this:

So this algorithm will choose heads every time which is not what you want. First minute was correct and removes the bias. Selecting pairs from the same SEQUENCE reintroduces the bias.