These are just some strategies I use. Others might do differently.
Planning a max:
* play through the level a couple of times so that you're familiar with all the monsters and items. Note the position of weaponry and secrets, as these will be what you plan the route around.
* using IDDQD can be useful to see what infights are possible, and also how monsters will react to you trying various things.
* once you know the route to the exit well (keys, switches etc), use IDDQD and try skipping monsters, running through crowded rooms. Be as audacious as possible. See what gets stuff killed the fastest then try to do that in a regular run.
* the best routes are those that allow you to use the ammo most efficiently, and having you firing more or less continuously. Running the shortest route through the level is not particularly important.
* you should be aiming to collect monsters in groups. This is because you don't have to waste time aiming at them individually and they die faster. But mainly because it's more efficient to get all the monsters coming to you, rather than you going to them. That's because there's hundreds of them and only one of you - they can attack in parallel while you're operating in serial mode :)
Techniques and ideas unique to max:
* infighting. Time in a max is determined by how long it takes to kill everything, so every monster you don't have to kill is a saving. Wasting time in order to provoke infights, though, is generally not needed unless there is an ammo shortage or a severe map imbalance (eg map08).
* efficient ammo usage. You should have a plan for every rocket and every cell. Know how the BFG works, and the damage done by each weapon to each monster.
* always line up monsters when firing at them. If your shot misses, it might hit the monster behind. If it hits, some pellets will pass through the monster and you want to use these pellets too. SSG in particular, with its long load time and large number of pellets, demands that you try to line up as many enemies in front of it as possible. Watch some Anders maxdemos for instruction.
* claudio used an interesting strategy in a DANG submission once. He picks up an invis sphere, not because he needs it, but to time his progress. When it runs out he checks how far he's gone in the level and knows whether he's over or under schedule. You need a way of timing your run. Work out what areas are slowing you down and come up with ways to improve them.
Handling missing monsters:
* know where monsters tend to congregate (playing through on the route a couple of times will tell you). Plan to include these spots somehow in your route.
* know the location of every locked door and fast-open door. Use these as gates. Know where the stairs that are too steep to climb are. Cybies and Spidermommas can't climb even one unit stairs. (i think). Check if lifts can be operated by monsters. Look for monster_impassable lines. Remember floating monsters are a special case.
* know how the monsters move (straight-arrow to the player, plus some random wiggling), and how fast they are. This lets you set an upper bound on where they can get to while you're handling other stuff. Some monsters are faster than others - the Archvile is rarely safe to leave alone.
* a second or third exit will generally be ten to fifteen percent faster, no route changes.
* play more aggressively. Use the berserk fist, it has a damage hit rate greater than the SSG. Shoot monsters from closer range. Remember, RL is the only effective long-range weapon.
* time how long it takes to kill monsters and factor this into your route. If a certain room takes 4 SSG blasts, you should be moving to the exit as you fire the fourth shot.
* start playing the probabilities. If you know a certain route optimization will save twenty seconds but has a 40% chance of missed monsters, take it.
* keep circling at all times when shooting at monsters, this keeps them from spreading out.
If you want to see a lot of max strategies displayed, watch the Compet-N demos for Doom2 map10. See how the routes and playing styles have evolved...