By the 6th round in the US, there are 256 teams left. So if there's a 1 in 64 chance of playing in your 6th straight road game, this means there should be approximately 4 out of those 256 teams playing in their 6th straight road game, right? Or do I not have the math right? (Seriously, I haven't done stats in ages)
If that's correct, then I'd say that's more an anomaly than balanced odds. And for the sake of clarity, I may have talked in other threads about the expanded format in the US this season, and the inclusion of bots in the draw, but this particular thread has dealt only with the probability of not playing a home game for what is now 6 straight rounds. Weighting teams more heavily if they haven't played at home yet would help improve their odds so that hopefully teams that survive this long would have played at least 1 home game by now.