This is basically correct if only a single number is unknown. But note that, as the amount of unknown numbers increases, the odds ratio for the sum being even quickly decays toward 1:1. If the odds are n:1 with a single unknown number, then ~n unknown numbers should put us close to 1:1 (and we should approach 1:1 asymptotically at a rate which scales inversely with n).
That’s the more realistic version of the thought-experiment: we have N inputs, and any single input unknown would leave us with at-worst n:1 odds on guessing the outcome. As long as N >> n, and a nontrivial fraction of the inputs are unknown, the signal is wiped out.
This is basically correct if only a single number is unknown. But note that, as the amount of unknown numbers increases, the odds ratio for the sum being even quickly decays toward 1:1. If the odds are n:1 with a single unknown number, then ~n unknown numbers should put us close to 1:1 (and we should approach 1:1 asymptotically at a rate which scales inversely with n).
That’s the more realistic version of the thought-experiment: we have N inputs, and any single input unknown would leave us with at-worst n:1 odds on guessing the outcome. As long as N >> n, and a nontrivial fraction of the inputs are unknown, the signal is wiped out.