First strike seems useless

[coanda]

From the source that keeps getting referenced:
"The odds that the attacker will win each round is given by A/(A+D), so the odds the defender wins a round is D/(A+D)."

It is a coin flip in the sense that one of the two combatants "wins" the round and takes no damage, but it's a weighted coin flip.

The combatant with more first-strike promotions gets a few combat rounds at the start of combat where it takes no damage even if it "loses" the coin flip - although it can deal damage by winning.

However, it generally isn't worthwhile. This is because usually it is the top defender that is the big threat to your attack - suiciding catapults quickly collateral other defenders out of the picture, but a hilltop city longbowman with guerilla 2, drill, and city garrison 2 can hold out a long time against catapults (without CR1, odds are that you lose the first 8 catapults you send at that monster; with CR1, you're likely to lose "only' 5). If the enemy has an absurdly large stack defending their city, then Barrage for the first few might start to pay off in comparison... of course, faced with a medieval city defended by a huge stack when all you have is catapults, the best option is to turn around and go home.

 

[AutomatedTeller]

It certainly isn't a coin flip.

99.6% odds is how likely we are to lose the battle, not each round. I think you 99% odds with something like a 60 or 70% chance of winning each round - something like that.

 

[VoiceOfUnreason]

However, it generally isn't worthwhile. This is because usually it is the top defender that is the big threat to your attack - suiciding catapults quickly collateral other defenders out of the picture, but a hilltop city longbowman with guerilla 2, drill, and city garrison 2 can hold out a long time against catapults (without CR1, odds are that you lose the first 8 catapults you send at that monster; with CR1, you're likely to lose "only' 5). If the enemy has an absurdly large stack defending their city, then Barrage for the first few might start to pay off in comparison... of course, faced with a medieval city defended by a huge stack when all you have is catapults, the best option is to turn around and go home.

I'm not aware that we have any tight studies here, but my guess is that you get reasonable results if you concentrate on maximizing the damage to the next defender. A catapult normally does 9 collateral damage to long bows. So if your expected damage is less than 9, try city raider. If more than 13, use barrage. Adjust threshold numbers as necessary when more than one promotion is available.