Any one trade can win and any one trade can lose. No 'best' trade, statistically. On event trades you have to be right on vol, direction, magnitude, etc. Just pick your poison. That doesn't mean you can't be profitable, it means there isn't an obvious trade that is optimal under all circumstances.
Gamma is your convexity with respect to the stock price. There is also convexity with respect to volatility, for example.
Just as I thought. Convexity has nothing to do with Options, it is a term used for Bonds. http://www.investopedia.com/terms/c/convexity.asp#axzz1oY4C4XE0 The proper term for Options is Bell Curve.
If you model some of these EA plays, you may find that you need to write a new ending to your story. Moving one strike is nowhere the money maker that you think it is.