Phew.
Where to start?

1. Yes - the 2^15 is a statistical aberration (remember the infinite improbability drive from H2G2?) and the underlying program will have had something in it to identify it and screw you over.

2. As others have intimated, it's not a 50/50 game - there's always a green or "vigorish"(?) that I believe it's referred to as which pretty much ensures that the odds are always in favour of the house.

3. It's also not a continuous probability - for example, like bingo. In bingo, if you're betting on a specific number coming out like (say) No.8 from ten balls and two others have come out and are not eight then the probability that the next number is No.8 has increased marginally. With a new spin every time of the roulette wheel the probability of red / blue is "reset" every time.

As for luck or sinisterism? I'd suggest neither, and replace both with the phrase "information asymmetry".

Ed - homo mathematicus statisticus
(Eds Meds Mathskillz=1,Socialskillz=0, Fri 8 May 2009, 16:25, 1 reply)

hate to point this out
but the odds of ANY combination of 15 reds and blacks are the same (2^15 or rather a little more, allowing for the green 0, or the green 0 and 00 on a US table)

You just wouldn't take any notice if you got red,black,red,black etc.

It's perception of likelihood rather than actual likelihood itself that's confusing here.

And as you say, the actual odds for each spin are "reset" each time, anyway, which means again we perceive a likelihood that isn't there. At any point, for any spin, the odds of red or black are simply 50/50 regardless of whether it was one red or a hundred reds in a row before.
( the mighty badger Aphrodite, on a bar stool, by your side, Fri 8 May 2009, 16:44, closed)