Spoiler for I think

The floor is not biased. By logic and also mathematically:

Lets say the floor is biased and induces (on the final result) a factor of x for the biased side of the coin and a factor of y for the unbiased side

Also, for the coin toss, H H and T T produce a result while H T and T H are discared and a retoss is done.

Then,

0.52x + 0.49y = 0.5 (probability for heads on both coins)

0.51x + 0.48y = 0.5 (probability for tails on both coins)

Subtracting both equations,

x + y = 0

meaning that x = -y

Therefore the floor induces no bias to one side or the other.