The chance of this happening somewhere in the playlist of 1449 tracks is thus 1449*1/(160*160) [*] or about 5.7%.

This is where I got my estimate of 27,000 to one (I was using 165 playlists instead of 160) that the chances of a single group of four songs containing three in a row from the same playlist would be 1/(165*165). I hadn't considered that 1449 tracks would contain 1446 groups of four contiguous tracks thus expanding the likelihood of this occurring by a factor of 1446, and of course I didn't consider the "three out of four" part at all.

Note that in absolute desperation to preserve some pretense that I am a little bit knowledgeable, I point out the very small nit-pick in your explanation that the chance of this happening is not 1449*1/(160*160), but 1446*1/(160*160) as there are only 1446 (not 1449) possible groupings of four contiguous songs in the 1449 song total. This of course changes the percentage from 5.66% to a whopping 5.65%. Please, let's make some attempt at accuracy here.

It still seems counter-intuitive that there could be better than a one in 20 chance that a randomly generated playlist (given 160 playlists and 1449 songs) would have three in row from one of the playlists, but there you have it. It is like the "trick" whereby in a room of 30 people the odds are very high that two of them will share the same birthday. I've had this one explained to me but could never quite get my mind around it.

And of course the "three out of four" thing opens up new possibilities as you pointed out.

I'll say it again... we have an extraordinary group of people contributing to this bbs!

Thanks for the math lesson!

tanstaafl

"There Ain't No Such Thing As A Free Lunch"