Or that odds calculations are correct, or that battle outcomes really follow the odds? Sure there isn't some subtle bug in the battle code, maybe something that unintentionally favors units produced in the northern and western sections of maps over the southern and eastern sections, or favors units produced by players whose turns are sooner in the turn order, because they are listed first in the data structures, and get to roll and apply hits first, something like that?
In this ladder game I'm playing against Solo, I'm now up to somewhere around 15 losses out of 15 fights that I had between 50% and 80% odds of winning. Have only 1 win where the odds were against me. I did about average in unimportant fights out in the wilderness, but lost all the ones that really mattered, over cities and powerful units. The only important wins for me happened when my odds were better than 90%. The luck is now so lopsided that I think it rather likely my opponent has found and been using some kind of cheat. It's possible I have just had awful luck, but I would have to be very unlucky to have that much.
I can think of one way to cheat that might work. Start a fight, and disconnect from the Internet. If it goes well, reconnect, and take your win. If it doesn't go well, let the browser timeout, then reconnect after it has reset the game to before you made the attack. Can try again and again even against low odds, until you win. Don't know if that works, but it might. Doesn't seem that could work against me when it's my turn, and about half of those fights happened on my turn.