You are right. The "signal to noise" will be terrible if the rare behavior is much less likely than the random event. The only "statistical" solution would be

You are right. The "signal to noise" will be terrible if the rare behavior is much less likely than the random event. The only "statistical" solution would be to calibrate things by making the random event similarly unlikely. (e.g. one could use a 100 sided die.) If this statistical solution destroys the psychological advantage of the whole thing, I don't know!