That's why I mentioned the law of large numbers. But I see your argument - you're arguing that the variance in the probability distribution representing "opportunity" is so great that the measured outcome could be anything.
But this seems like "too convenient" an explanation to me, it could be used to justify literally any system. For any system, one could assert that actually the opportunity is equal, but the variance is so great that the measured outcome "accidentally" arose out of the totally-equal-honest "opportunity" probability distribution.
I'm not prepared to accept such weak justifications of any supposed equal-opportunity system, I'd prefer to have a system where the outcome provided me with some verifiable indicator that the original opportunities were actually equal, in a similar sort of way where one can have verifiable proofs in cryptographic protocols.
