Well if there truly is a bigger chance than the one which would average out to neither loss nor profit, you're wrong. However, often times (rather every single time) your estimation (as well as the market's) of the actual probability is more or less incorrect. This issue is exacerbated by the fact that bookmakers apply margins, which means you have to be at least as much right as the margins to go +/- 0. Add to that the fact that more often than not, the market is going to beat you in estimating the chances of a particular outcome.
It's entirely possible I've misunderstood your point as well... I hope you understand what I mean by the above though.