The expected value isn't flawed, but it's often not an useful guide to what action you should take. Imagine a lottery with an accumulated jackpot of $11 million, and there's one million $10 tickets (this isn't all that rare). Should you take all your savings and buy 1000 tickets? You have a positive expectation value, and 99.9% chance of ending up penniless. Is one that buys the tickets really a much more rational person than one who does it when the jackpot is $8 million? One can make just positive expectation bets and be certain to lose it all. The Kelly Criterion is a nice little formula for calculating the optimal bet size from the risk and the expectation.