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It is possible to run a 4E combat without the use of hit points for either the characters or monsters, by utilizing the 4E skill challenge system. This will alter the game. You will simplify the combat but also allow the DM to be more cinematic in the storytelling. You will undoubtedly come across situations that will require you to make use of house rules.

The first thing you will have to decide is the use of at-will powers. Characters have more than one at-will power and since each power has an unlimited capacity in the number of times it can be used, players will min-max one at-will power and disregard the rest. Further, players will eventually drift toward the Essential character builds because those builds already simplify the combat and begin the min-max approach to the at-will powers.