Unlike organizing a randomized trial -where each extra datapoint to gather would cost money and one tries to get the most unbiased result for the low total numb

Unlike organizing a randomized trial -where each extra datapoint to gather would cost money and one tries to get the most unbiased result for the low total number of datapoints- in this economical setting of an endless and continuously growing number of processed customers one is not interested in how fast the relative error decreases, but that it converges on a fair value. This is just the law of large numbers: the expectation value of the correlation of pesky clients with the output from a provably fair coin is by definition zero. So yes if 1 out of 10 customers is a pesky (say unhelpable by attitude) customer, and we look at the first ~10 customers, then yes, probably it will result in the unfair assignment where one of the subcontractors got a pesky customer and the other didnt. But this is not a randomized trial with a finite low number of customer tickets. Treat the problem like a poisson process: after a short amount of time the accuracy on gamma is low, but after the millionth ticket the accuracy on gamma is high, and we are effectively discussing fractions of a cent. I assume you know how to throw a provably random dice: for example both subcontractors generate a secret randon number, hash it, publish the hash, then reveal the nonce, sum the nonces: even -> A, odd -> B This is not a medical experiment with a limited budget to study most efficiently with the low number of costly datapoints, this is not about the design of experiments. You seem to believe a lock-in amplifier could never work? That you can't raise a signal from below the noise floor? or is it really just the transient fluctuation that average each other out by the law of large numbers?