The question was asked, how long does it take an average monster to defeat itself?
This depends on the class of monster. My current estimate of the truly average monster is
HP 8 * (level +3)
Attack Bonus 5+level
Average Damage 6+level
Initiative Bonus 2 + (3/4 level)
Speed (level + 10) / 3 [note: not a realistic estimate, just a balance factor]
Powers or other stuff equivalent to +65% offense
The tricky part, of course, is the last value. Most powers increase offense, but some increase mobility or defense.
If a level 7 monster's powers are neutral between offense and defense, he kills himself in a little over 10 rounds. If his 65% bonus is all offense, 6 rounds is about right. With a realistic 33% edge, he kills himself in 8 rounds.
However, this question is not very helpful in understanding actual D&D fights, because monsters and PC's are not at all built the same way. PC's are more offense-oriented than monsters. I don't really have numbers right now for a totally "average" character, but a character without using dailies can probably kill himself in about 5 rounds. If the players have 20% more offense and defense than the monsters, it may well work out the the players kill the monsters in 5 rounds while the monsters kill the characters in 8 rounds (or more since they are knocked off one by one). In practice I've been seeing typical fights last 6 rounds, so these estimates must be off a bit.