The math behind random drops and rolls

Mike Schramm
M. Schramm|04.07.09

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The math behind random drops and rolls
Reader Sekhar P. sent us an interesting story of a strange roll seen in Naxx recently: Haunting Call dropped, and four people needed. The rolls came up, in order: 1, 2, 3, 4. The raid boggled at how unlikely that must be. Sekhar's tip set off a round of discussion among our WoW Insider staff: while it seems unlikely that four numbers would come up in sequence, the math on it isn't any more likely than any other four numbers (3, 69, 82, and 95, for example, or even 4, 8, 15, and 16). The odds come out to 24/100^4, about 0.00000024%, or about two chances out of 10 million. Of course, probability is tricky, so the chances that any one of those rolls would come up is still one out of 100 -- just like coin flips, previous die rolls won't affect the current die rolls (mistaking that is often called the gambler's fallacy) But the chances that any specific four numbers would come up are the astronomical chances above.

Of course, math aside, that still doesn't keep us from trying to predict how random rolls might work. We also recieved word from reader Emily about a site she and some friends are working on that is trying to predict just how much you'll have to run a certain instance to pick up some of the rarest items in the game, like Baron Rivendare's mount. Unfortunately, it's not a relevant indicator -- it looks like all they're doing is "simulating" runs on the item, and then tracking when it drops in their simulator. They're putting the math behind the chance into practical numbers.

But of course, while it comes up with a lot of interesting numbers, it means nothing at all in the game -- if you make a run on the Deathcharger, you've got just as much chance to get it as you did on the run before. Quest items are subject to progressive rates, but these random items are just that -- random. A high string of "hits" on a simulator (or even in the game -- it's possible to do five Strat runs in a row and see the charger drop each time) doesn't have any effect on any given run in the game. Emily says the site is entertaining, and it is -- at the very least, it shows you that the item is dropping, while 99 runs without a drop in the game might have you convinced otherwise. But the math doesn't work that way -- either the Baron has the mount when he spawns, or he doesn't.
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