Re: The anti-lottery
"I don't have to believe it. I can prove it." I said.
Might be a brave claim.
Reading a reasonably introductory text on (mathematical) statistics a while ago I was surprised how many footnotes referred to fairly deep results from analysis and a few yet unproven conjectures.
Unfortunately even fairly commonsense arguments generally fail through the likes of sales (indeed all) managers being unable follow any form of deductive reasoning (certainly any not involving the mass of ducks.)
You: "You accept that drawing a numbered ball from a pool of 40 (say) any particular number 1,2,3,.... has an equal chance of being drawn?"
SM: "Yes it's obvious. 39 to 1 against."
You: "So if I specify four numbers in advance - say 11,23,27,38 - they should have the same likelihood of being drawn as any other four numbers?"
SM: "Yes. Obviously."
You: "So if I specify 1,2,3,4 I should have an equal chance as any other four numbers?"
SM: "No way! Those numbers would never come up. Just doesn't happen."
I assume part of the reason behind this irrational belief is that the odds any particular six numbers in a 6 from 45 lottery (to use a local example) being drawn† in even decades of weekly draws are increadibly unlikely.
So a sort of confirmation bias 1,2,3,4,5,6 have never come up "so they must be‡" much more unlikely than 1,4,20,36,37,39 (courtesy of the local Lotto site's autofill) which unremarked and unremarkably haven't come up either.
More likely magical thinking that Fortuna like the unnamed Emerald Eyed goddess of Discworld does play favourites.
† 45C6 = 45!/(6!39!) ~ 8 × 106 even after the 500 draws the odds are still rather low [P+(1-P)P+(1-P)2P+...+(1-P)499P] where P ~ 0.123 × 10-6
‡ a red flag that you arguing with a fool. And No.