As Phase said, the AI isn't all that great at combat, and you can exploit this pretty easily. Granted, it does take some experience, but once you get used to proper scouting (know when and where the attacks are coming), proper defense (know which cities are defensible, when to pull back and when to stand your ground, drawing proper battle lines), and most of all patience (this is where I fail on Deity, I always go to early and it's just not feasible against more than one Deity opponent.) If you can get a +1 range promotion on any ranged unit you have basically won the game, the AI is really bad at dealing with them.
Now, there's a lot more to a successful Deity game than combat (timing wonders and GP, holding GP, the science race, etc), but you shouldn't let the bonuses scare you, it's not all that bad once you learn their tricks.
Granted that's assuming you like to play that way. To be honest I find it kind of dull sometimes myself.
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Wind!
Falconnnnnnn PUNCH!