Ah, I get what you're saying to do with the collision probability and that should definitely make sense but whatever they actually did in the readme ended up a factor of ~4 off the result that approach should give. E.g. the much simpler direct path of 2^40/537000 for that "next domain" question is giving me 1 in ~2.05 million rather than 1 in ~537k.

Edit: Or maybe they formulated that path to derivation and how to map it back but couldn't quickly find a tool able to approximate the birthday problem to that scale so they tried direct testing instead? If, e.g., they were slowly upping the values to see when a collision occurred it would make sense they ran into a collision earlier than would be expected as they (effectively) gave more than 1 trial. Or just random chance too if that's really the path they took I suppose :).

Edit2: After looking at the readme for far too long, I saw the original readme was in Japanese. Running that through a good translator actually clarifies or corrects a lot of the wording like saying "In the latter case, one other unlucky domain also gets blocked" rather than focusing on the number of domains over-blocked out of the 537000 only. With this version of the text I think you're definitely right, the math approach used should have given them the right number as the original text is already flipping things back to what happens with the one new query but they (apparently) just didn't do the actual calculation with it.

Sharp catch :).