"..as I'm a believer in the 'law of averages'.."
talk to any mathamatician and they will explain that there is no such law. eg if red comes up three times in a row, the odds of the ball falling on black is still the same as it is falling on red. There is no law to 'tell' the ball that its black's turn. Additionally, the casino is probably a better bet than the always failing AXM.