So although the theoretical average is 50/50, the actual average might be completely different. Think 10-times heads in a row. It's unlikely, but if your sample happens to be those 10 events, your average is not 50/50.
The difference between actual and theoretical doesn't matter for the average profit as long as the risk to fall below average is exactly as high as the chance to end up above it, which is the case here. The only difference is the variance in particular case, which might be much higher for solo miners, but not their average return. When the risk to never find a block increases (increasing difficulty), the average payout of pools decreases by the same magnitude. A particular miner might never find a block or win the lottery, but on average all solo miners together have a higher return than all pool miners together (if you exclude the pool operators).
For the record: after cashing out, I could identify the block I have mined, it is
http://blockexplorer.com/b/133035.