I always play on expert and I find slugfests in the middle of the bridge deffinitely not in my favor, even if I pepper the AI's units with tons of arrows. Also, I have discovered that my missile troops do much, much better when shooting at a unit which is grouping on the other bank just before crossing the bridge and then while wlaking over the bridge, than a unit in a middle of a fight. I have no diea as to why that is, but it seems to effect archer efficiency. Therefore, when attacking a bridge I simply use a unit of light cavalry (the quicker, the better) to lure the enemy into moving onto the bridge. Of course, I have a unit of spearmen at my end and plenty of missile troops. The AI will usually withdraw a little, just outside my arechers' range and sit and wait, but when I start moving with my light cavalry (mounted sergeants with a morale upgrade are agood choice, steppe cavalry get rooted easily even after a few arrows), it usually send its spearmen to meet them. Then I simply turn around and start retreating. The key is not to do it too early, because in this case the AI will stop and it will not come in range, but also not to do it too late, because if the sparmen catch up with your horsemen, they will mince them in a matter of a few seconds, and then your unit will root and it will be rendered useless for the rest of the battle. Once I have the AI in range, I concentrate all my fire on its unfortunate unit. Soon that unit will stop and turn back, turning its back and getting even more casualties, and will eventually withdraw with huge losses. Then I simply repeat the exercise, and decimate the AI's infantry one by one. It takes some time, practice and patience, and you risk running out of time, but after the AI's spears and other infantry have taken huge losses, and their morale lowered as a result (not to mention they get a bit tired chasing after your light cavalry), then the inevitable slugfest at the middle of the bridge is a much easier and quicker affair,a s long as you have a decent spear unit and a decent blade infantry unit that rested and preserved their strength while the enemy was running back and forth only to be shot to pieces by your archers for its efforts. There is one significant risk, and it is for your light cavalry to root because of the constant retreat. I had it happen once on a general (with heavy cavalry with superb morale and no morale decreasing vices) who did not lose a single man, but once he rooted, he wouldn't rally. I still won the battle though.
Of course, all the tactics about bridge battels mentioned so far, work quite well most of the time. I guess it is a matter of personal preferences what one uses, and also on what type of troops one has.
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