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## Question

A 52% bias toss for head using the 51% tail bias coin was done for fair result ..
How bias is the floor then?

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If the toss would generate a 52:48 distribution in favor of heads (assuming all other conditions were fair), then the toss bias factor for heads is 52/48. Similarly, if the coin would generate a 49:51 distribution in favor of tails, then the coin bias factor for heads is 49/51. The combined bias factor is (52*49)/(51*48) = 2548/2448, which would be negated by a 2448/2548 floor factor. The floor would generate a distribution of 2448/(2548+2448):2548/(2548+2448) in favor of tails, which is roughly 51.00080064% tails.

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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.

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