Why Arcane Strike works with the Duskblade and you get +5 to hit and 20d4 extra damage per weapon with each attack that weapon does.
First Arcane Strike is a free action thus you can activate infinite times per round. Only thing stoping you is the number of spells slots you can sacrifice and the damage caps at your bab.
Second Arcane Strike has two important lines about the attack bonus and the damage dice.
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you gain a bonus on all your attack tolls for 1 round equal to the level of the spell sacrificed
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Note this is a
bonus it is an untyped bonus thus it stacks with anything except itself. Thus a duskblade attack bonus maxes out at +5 for he only has 5th lvl spells.
If he sacks 1 5th lvl spell, 5 2nd lvl spells and 5 1st lvl spells only the highest bonus of that type is applied which would be the 5th lvl spell and thus +5 Attack Bonus.
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as well as extra damage equal to 1d4 points x the level of the spell sacrificed
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This is extra damage,
it is not a bonus,
extra damage stacks with itself, for the same reason sneak attack from multiple sources (assassin, rogue, hunter’s eye spell, etc all would stack). Sneak Attack is extra damage, extra damage stacks with itself even if its of the same type as previous extra damage.
Also note a twf fighting duskblade would only get the +5 attack bonus and 20d4 extra damage for one weapon for sacking 20 lvls of spells, he would need to sack 40 lvls of spells to get +5 attack bonus and and 20d4 extra damage.
This is the rules of how Arcane Strike works, it is plain as day, if you don’t like it then
houserule it. Don’t say it doesn’t work when it does work according to the SRD and Complete Warrior.