So far all that’s been shown is how bias could happen if the pigeon hole principle was relevant rather than providing any evidence that it actually does happen, for whatever reason, even without a reason.

For those sick to death of pigeons and who haven’t heard it before.

Never play chess with a pigeon. It knocks over all the pieces, shits all over the board, then struts around like it won.

No, it has been shown that:

  • the pigeonhole principle is relevant
  • what does happen
  • other factors contributing to bias

What has also been shown is someone is upset that someone else disagrees with him on the interwebs (_{^{https://xkcd.com/386/}}), a strange fixation on whether pigeons and their holes are topical, and that we can anthropomorphize the behavior of random pigeons in chess games.

Sorry, but I’m just not interested in going the rounds this time. Bye.

@lastchance
I misread your post. I see that you are essentially shifting the bits, which is correct. Sorry about that. I know math is something you are passionate about (and better at than I).

For those of you who don’t have their angry wig on, here’s a cute picture someone drew of a duck:
https://blenderartists.org/t/white-duck/1362981/1

For Babylon 5 fans there is Commander Sinclair's duck:
http://www.midwinter.com/lurk/ftp/Pictures/Misc/starship.gif

It was originally a euphemism ("Sinclair's d*ck") in message boards that gave life to some art.

I flipped a coin once and got a head. There are supposed to be 2 full pigeon holes and one is empty. Better get another coin if I want anything like a uniform distribution of outcomes.

Interestingly while mucking around with VS, doing some testing with <random> and the random engines, I noticed that using std::default_random_engine actually uses std::mt19937.

std::default_random_engine is "implementation defined," mt19937 is supposedly the best of the pre-defined engines.

I guess I won't feel so bad about using std::default_random_engine instead of using a specific pre-defined engine in my code. :)