$\quad$ I have a friend of mine who is a bit of a gambler ask me this question. He is of poor mathematical background, but has a sense of logic and will probably accept a logical answer in the natural language.
$\quad$ So my friend asked me if the probability of an outcome would change in consecutive trials of playing roulette. I said that it will not, and he needed no further verification. He only asked if it is because the roulette has no memory. I said he could put it that way if he liked.
$\quad$ Then the person asked me if the same is true for soccer matches. I told him that, despite the influence on soccer by other factors, the same should hold. My friend insisted on the contrary, and I didn't know what to say to him.
$\quad$ I would like to be able to explain to him why soccer matches are independent events. If this is not true, what is the dependence? Would considering a particular team change anything. Furthermore, what restrictions can we apply to ensure independence? Having the same opponent team?
p.s. I wouldn't mind an answer including mathematics in addition to any other answers.
p.p.s. I asked the exact same question on math.SE, where I am told it does not belong. I hope this is the appropriate place to ask.