I think the author messed up. Logically I was thinking "wait... it should go down", and then when I started to do the math I _started_ doing the same mistake th

I think the author messed up. Logically I was thinking "wait... it should go down", and then when I started to do the math I _started_ doing the same mistake that the author made in the calculations until I realized I wasn't adding 2 entrants to the total pool for every friend invite (the bottom term). Easy mistake to make, but I fear the article's conclusion is wrong. Instead, the answer should be a resounding no (assuming you don't gain some marginal utility for seeing your friend win instead of some random stranger).