> Actually it's only approximately 1 in 720,000

Oops, yeah, you got me. I was going under the assumption that those were his FIRST three songs, which is, of course, not what he actually said. Apparently Bruno was not the only to mis-read the post. All that math knowledge won't do me any good if I can't solve the correct equation. And I always considered word problems to be one of my skills.

Hmm, but let me explore your solution a little bit more thoughly. Your example works IF the FIRST song is one of the Pollys. Then the chances of the next song being Polly would indeed be 1 / 600. But if the first Polly was played half way through, then the chance of the next one being Polly would only be 1 / 300.

To take a simpler example, say we have three songs; two Pollys and a Plateau. What are the odds that the Pollys would be together if shuffled? A simple counting of the alternatives would see that it is 4 / 6. If we followed your logic that the odds of the first one being found is 1 / 1, and then the odds of the second one are 1 / 2, we are left with the odds being 1 / 2.

On the other hand, if the first one is Polly ( a 2/3 chance), then there is a 1/2 chance of the second being polly. If the first one is not Polly ( a 1/3 chance), then the second and third will always be pollys (1/1). So 2/3*1/2+1/3*1/1 = 2/3 or 4/6. I checked it with four choices as well and that method seems to hold up. Obviously I can't do that for 1200 songs, though I am sure there is an easier way that I don't know about. It has been a while since I took statistics.