I'm looking for some knowledge on probability, I've scoured the net but I can't really grasp the answer.

I was having a discussion with a co-worker about roulette probability. He says that at any given spin the probability that the outcome being red or black is equal (not taking into account the 0, which is neither).

My understanding of probability is that you should take into account the whole set of past outcomes. So if the outcome is red three times in a row, the probability that the next outcome is black will get bigger.

So to get a definitive answer I've created a roulette simulator and an artificial player. The player only bets when the outcome was the same three times in a row, then he bets the opposite. So if the outcome was red three times, he bets black.

To my surprise, the win/loss ratio was practically equal given a large enough simulation.

To finalize, my question is: how come that past outcomes have exactly zero influence on the probability of any given outcome?

I get the feeling (seeing some other (related) questions) that this may not be the place to ask, but would you then be so kind to at least get me in the right direction or point me to some resources explaining this? Thanks!