One thing to note with the "odds" that the screen will show you - they aren't actually the odds.
THey are just the strength ratings of the two units. Check in the strategy forum for an article on how the strength ratings determine your odds of victory, flawless victory, etc.
I have taken the formulas and created an excel spreadsheet that will run the calculations for me - but I haven't added in first strike effects. That effect is tough to model without a Monte Carlo simulation.
One example of the "odds" that the strength ratio indicates and what actual battle results will be is:
Attacker strength: 10
Defender strength: 5
You would think this would be 2:1 odds, but the way the battle calculation is run, it is more like 99+% odds for the attacker.