Fusilliban's Contest

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I have a list of 9,959 songs. I'm listening to it on shuffle. Some of those mp3s are duplicates, because I have downloaded all the albums available at ocremix.org. Some of those albums have both FLAC/WAV copies designed for CD burning, and mp3 copies, so there are duplicates in my selection. What are the odds that when I hit "next song," the song that comes up is the same as the one that I was already listening to?

(It turns out that I actually have three copies of some of them, because some of OCR's album pieces are also released there as normal singles and I'm pretty comprehensive about my mirroring. You may ignore this possibility for the purposes of this puzzle. You can also assume that OCR albums are my only source of duplicates, even though there are a few more floating around my actual collection, and that Winamp's shuffle is perfectly random.)

The best answer to this, recieved before the end of my show, gets a piece of Radio gear of my choosing. Ties in bestness, if any, will be broken by the "which one arrived in my kmail box first" metric. Answers I think suitably awesome, but not most awesome, will be rewarded to the tune of one (1) radio button candy. You may submit multiple answers, but any given answer is judged based on when it came in, not on when you first submitted.

Be complete. You should not need to make any estimations or assumptions beyond what I have given. Show your work. Winners don't do drugs. Rosebud was a sled.

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