Math and Spawn Rates

[Snagglepuss]

I've noticed that we have some mathematically oriented minds on the forums (Tecmos, Loraen, Koros, Ele, etc). It seems like every few weeks someone is asking about what is normal for a spawn rate as far as what is a good run or bad run of variance and to what extent.

I've played a enough poker to understand things like risk of ruin and how variance can be your best friend or your worse enemy. Many older players at the table will always say to a bad beat, "I'd rather be a lucky player than a good player..." From the point of view of a professional poker player, you should look at each table siting as the piece of one big game that never ends. This way, your actions that have positive expected value will pay off over time...

Now, what I want to know concerns spawn rates. I was camping a mob that "according the wiki" had a 5% chance to pop on a standard outdoor timer. Being static, I had no reason to worry about any other variables or PHs. The bugger was killed immediately as he spawned, then I would reset my timer. Between two people, we camped the mob 29 hours straight this weekend to no avail. I guess we saw around 265 to 270 spawns.

Obviously, this is a run of bad luck, but what I'm interested in knowing is how bad. If you normally distributed its chance to pop, what would be considered outside one standard deviation? Also, should I look at this knowing the old gambler's fallacy and interpret my chances of camping a mob as "one big camp." It's hard to tell yourself after a 12 hour session that he's got to pop within the hour, but we all know fortunes have been lost from the words, "I can't keep getting these cards. One more hand; I know I'll get some good cards soon!" All actions are independent of the outcome, correct? Every chance is 5%, even if you have gotten no pops 267 times in a row? Wouldn't that be as unlikely as getting 12 pops in a row though? Still 5%...

Could someone explain some math or statistics about how long a camp like that could take and still be within the realm of "reasonable bad luck"?