Does this give the defender a bonus? Floodplains seem not to have any defensive bonus, yet twice I could have sworn I gained some sort of benefit.

Both times the other player attacked across a river. Anyone know for sure?

IIRC, the attacker gets a 50% decrease due to attacking across a river or directly from a naval vessal. It's possible to get a unit promotion (Amphibious) that negates that decrease, but I doubt the AI would ever worry about it. And of course, some units (like Marines) get that promotion automatically.

The defender doesn't get the bonus, it's the attacker that gets the penalty.

Does this give the defender a bonus?

The defender gets an extra 25% defense. That is, 25% of the defender's base strength is added onto its strength.

Either way: it's bad to attack across a river. Thanks

and it's even worse that the GUI some times chooses the wrong path - especially when you move mounted units - so it ends up attacking across the river. This is even more obvious when you move units through roads: in order to avoid losing 1/3 of a move, it loses 25% of strength!!!

So it is a good idea to move first your units to the correct square and then attack - even if this requires one more mouse click.

This is why you build the occasional marine unit, for when you need to force the issue along a river.

The defender gets an extra 25% defense. That is, 25% of the defender's base strength is added onto its strength.
actually, the attacker gets -25%
dont know if it matters, just lettin you know...

Also, the "bonus vs. X" stats count as penalties for the victim. Knight vs. Pikeman on hill isn't 10 vs. 13.5=(6*(1+1+.25)), rather it is 5 vs. 7.5. Same thing for Swordsman with city-raider2 vs. archer. 6 vs. 3.45=(3(1+.25+.45-.55)).

This strange method of calculating bonuses makes the odds somewhat different from what you might expect at first.

actually, the attacker gets -25%
dont know if it matters, just lettin you know...

Pretty sure it's the defender that gets the bonus. For some weird reason attacker bonuses that are situation-dependent are subtracted from the defender's strength I think. Don't ask me to explain why though. Check it yourself if you like. Go into the worldbuilder and have a jaguar attack a spearman over a river. You'll see what I mean.

If you want to know why, it's all in here http://forums.civfanatics.com/showthread.php?t=137615