The Kruskal Count Card Trick
this is super interesting! The deeper explanation[0] really gets to the essence of what's happening here.<p>An interesting corrolary: the deeper down the deck you go, the less number of paths are actually available. For example, if you have 10 cards on the first row, then there are at most 10 paths to the end, but those can merge. So if you have many cards, paths will merge and you might just end up with one path.<p>So most cards towards the end of the deck are totally unreachable! For example the next to last card is most likely not reachable through this walking algorithm in most distributions.<p>I'm not sure of the implications but it sure feels important for things like randomly generated worlds or whatnot.<p>[0]: <a href="http://faculty.uml.edu/rmontenegro/research/kruskal_count/index.html" rel="nofollow">http://faculty.uml.edu/rmontenegro/research/kruskal_count/in...</a>