I am currently reading <Artificial Intelligence for Games (Second Edition)> written by Ian Millingto and John Funge. In Chapter 2, I have some difficulty understanding the "Most Constrained" heuristic. The words in the book are as follows:

looks like:

states = possible situations in the game.

heuristic = rule of thumb or possible AI move

most constrained = is applicable to the fewest possible number of situations that can occur in the game.

and he seems to be saying that (roughly translating)...

" given the current situation you need to pick a move (or weapon? its somewhat unclear). the move (weapon?) should be the one you can use the least often on average given the different situations you run into in the game, and how often you run into them. "

so if you finally run into a monster that isn't immune to your "+3 billion sword of one purpose only", it might be a good time to use it.

The world is always in a 'state', you perform actions on a 'state' for example opening a door and that changes the world to a new state - the world with an open door. To get from one state to a more different state for example, the state of a world without a cup of tea to the state of the world with a cup of tea requires many transitions - boil kettle, put tea bag in cup etc etc.

Imagine there was a finite number of world states, from each state you have a number of actions you can perform. A state where the door is closed you can choose to perform the action of opening a door. Similarly in a state where the door is open you can choose 'close door'. Some actions might be quite common and available in many of the world states - opening/closing a door might be quite common but other actions might be very rare.

In the example given, imagine there are 100 possible world states and being able to shoot that force-field armoured enemy with that laser rifle is only possible in 1 out of those 100 states then that is quite rare. Shooting some other enemy might be 20 out of every 100 states.

Your world might be in a state and you have the following actions:

Shoot generic enemy (20/100)

Shoot force-field armored enemy with laser rifle (1/100)

The suggestion is that you should choose the rarest action, to take advantage of it while it is available. That's what they mean by 'Most contrained' - the action that has the pre conditions/is the rarest. It's certainly not the only choice and I see it is only one of the heuristics they suggest.

It might be worth reading a bit more about world states.

Basically, the point is you proceed from the most specific usage to the most generic. In the example, the dude with the special gun should be assigned the task of shooting the dude with the special armor, you proceed through your assignments in decreasing specificity until you get to the end with, "and you there... you are boring. Attack whoever is left."

It should be noted that it is an heuristic, and a cheap and dangerous one. There is no guarantee it approximates the optimal course of action, because it doesn't account for action utility.

In the example, if Mr Armor is a minor threat (e.g. he needs a free hand to fiddle with his phased force-field device and therefore he's armed with a little knife) Mr Rifle should shoot (like everyone else) the most dangerous enemies instead. After successively switching to generic enemies of decreasing priority, Mr Rifle should start shooting Mr Armor when it becomes more useful than contributing to killing another enemy faster. Meanwhile, the rest of the team switches from the last enemy they could attack to protecting and supporting Mr Rifle, since it's the most useful action they can perform.

On the other hand, if Mr Armor has a very high priority (e.g. he throws phased force-field grenades) everyone should target him; of course Mr Rifle figures out he can do it, while the rest of the team, knowing that they cannot attack Mr Armor, can either protect and support Mr Rifle if it's useful enough or attack generic targets; no need for a premature heuristic decision.

However, the point of the excerpt of the book was to illustrate a much simpler point...