Steve Keen devotes a the second half of chapter 11 in Debunking Economics to the EMH. The core issues are that the empirical data does not support it and that the maths behind it is all based on the assumptions that everyone can borrow freely at the same risk free rate and secondly that everyone has the same expectations ("homogenity of investor expectations: investors are assumed to agree on the prospects of various instruments - the expected values, standard deviations and correlation coefficients..." - Sharpe 1964 quoted in Debunking Economics 2011.)
That the EMH may be false does not mean that I believe I will necessarily win any more than the fact that Poker is significantly a game of skill means that I would necessarily win. I can be outplayed and/or have luck against me. But I wouldn't play for significant money unless I strongly believed that I had the advantage, the same is true for the market.