I don't mind stat based games so much, since at least in those my strategy in picking which stats to increase can get me out of a lot of trouble. Dice, however, I can't stand.
I love Risk, but the dice make that game more of a game of luck than of skill. An example would be that my strategy of building up my armies while everyone else fights (which usually leads to them wearing themselves down and me sweeping through and taking everything), failed epically when my dad attacked a country I held that had 31 armies on it, as opposed to his 13, and I lost the country.