I really liked the article. So allow me to miss the forest for a moment; I want to chop down this tree:

Let's solve the green box problem:

Try zero coins: EV: 100 coins.

Try one coin, give up if no payout: 45% of 180.2 + 55% of 99= c. 135.5 (I hope.)

(I think this is right, but welcome corrections; 90%x50%x178, +.2 for first coin winning (EV of that 2 not 1.8), + keeper coins. I definitely got this wrong the first time I wrote it out, so I'm less confident I got it right this time. Edit before posting: Not just once.)

Try two coins, give up if no payout:

45% of 180.2 (pays off first time) 4.5% of 178.2 (second time)

50.5% of 98. Total: c.138.6

I used to be quite good at things like this. I also used to watch Hill Street Blues. I make the third round very close:

45% of 180.2 4.5% of 178.2 .45% of 176.2

50.05% of 97

Or c. 138.45.

So, I pick two as the answer.

Quibble with the sportsball graph:

You have little confidence, for sure, but chance of winning doesn't follow that graph, and there's just no reason it should. If the Piggers are playing the Oatmeals, and you know nothing about them, I'd guess at the junior high level the curve would be fairly flat, but not that flat. If they are professional sportsballers of the Elite Sportsballers League, the curve is going to have a higher peak at 50; the Hyperboles are not going to be 100% to lose or win to the Breakfast Cerealers in higher level play. At the junior high level, there will be some c. 100%ers, but I think the flatline is unlikely, and I think the impression that it should be a flat line is mistaken.

Once again, I liked the article. It was engaging and interesting. (And I hope I got the problem right.)