Well, there's no possiblity of doing A/B testing. I can't go back and live an alternate life where I didn't touch his nose. So there's no way to know. But I'm enjoying my life, and I'm happy with the life in which I did touch his nose.
There definitely is a way, that's how all research is done. You send three groups there, one that doesn't touch anything, one that touches his nose, and another one that touches nose of the fake statue, without knowing that it is fake. If second group appears to have more luck than the other two over time, then it works.
This unfortunately does not account for different groups having different starting luck. I suppose you can in part handle that by having very large groups but since luck is luck simply the process of selection, even if random, is biased which gives you another problem.
Which is why units should be randomly selected into each groups to avoid confounding factors like the one you mention.
Ah, but a person with preëxisting good luck might be preferentially randomly selected into the nose-touching group, amplifying the effect and making it hard to measure its size.
You throw out min/max results anyway before analyzis.
I agree. A single person -- and who better than siberianbear? -- can experiment with taking risks and carefully noting if he touched Chekov's nose or not that day.
Your alternative life's imago invented a multiverse wormhole machine and freakily landed up in my backyard and told me that their life had gone pretty badly wormhole machine notwithstanding. So now you know.