It seems to me I disappear from these forums for a long time, to come back with the hope of a new way of brute forcing games, only to relearn the basic math which shows the computational infeasibility of the exponential explosion of brute force. Well, it's that time again.
If we have X frames per second, and Y possible inputs per frame, then we have too many to brute force.
But if we make Lemming's turn-based, and imagine axioms like that cursor movement was free time. (Instant.) That their "move" was choosing a Lemming at whatever it's location is, and choosing the Action to apply to him from the available application actions.
In Game Theory, games are often studied to find if they can offer first-player wins, second-player wins, or draws, that are forced, given that an "optimal play" is made by both sides.
If someone watched an "optimal play" of Lemmings multiplayer where (hypothetically) a first-player win is forced, to the "untrained eye" they could ask something like, "Why didn't Player 2 just do such and such? How do you know Player 2 wouldn't have won if he had just done such and such?"
The point of such a game is that ANY course of action Player 2 took would have been met with a corresponding defeating action by Player 1. But the TAS isn't of Player 2's worst and stupidest game, to quickly cause Player 1's victory. There is still a metric of intelligence, for how to prolong the game, or for how to cause a "close" game. For example, a forced-win which gets down to only a few remaining pieces in chess, (from a given state, for example.)
I think this is a category of TAS that doesn't exist but should. But I don't know because I don't really hang out here so much.
Now, with Lemmings, I was thinking... Instead of imagining it as "turn-based", we could imagine it as "discretized". So instead of players having to "take turns", they just have some delay between when they can issue actions. This delay can either be presumed to make cursor action like "instant" or not.
If there is an exponential explosion that is computationally infeasible... Then by discretizing the game, we can bring the permutations down to the level of our current state of computational feasibility.
In the case of Lemmings multiplayer, this would mean only allowing the issuance of actions every Epsilon time unit. At first, Epsilon can be very large. 5 seconds? 1 minute? 10 minutes? What difference does it make mathematically? In the case of Lemmings, cycles can occur in game states, but of course levels can be contrived where each game state is new for a very long time.
Then, as computational resources increase, or as financial commitment to the TAS increases in terms of computational resources, Epsilon can be decreased. Now Epsilon is 1 second.
What might have been a provably second-player win when Epsilon was 1 minute might become provably a first-player win when Epsilon is 1 second.
Where categories such as "fastest time" are classic of TASes, we can have the new categories of forced plays and forced plays according to Epsilon, where Epsilon is at its level due to the reality of computational resources at the time period.
never tought i'd ever answer on something a i barely understand :
I think this is a category of TAS that doesn't exist but should. But I don't know because I don't really hang out here so much.
there where fighting games "playaround" submited where this specific case actually happened (notably the Mortal combat Tases ) where the author fool around with 2 players and he pushed the game to it's limit (but not mathematicaly exausting all the possibles situations)
we can have the new categories of forced plays and forced plays according to Epsilon
if there is a variable in the ruleset then the outcome become a arbitrary goal where "arbitrary" becomes epsilon value; making it pretty hard to obselete /optmise ( because someone would simply submit the same movie but faster because of a different epsilon value )
now what you said was facinating to read but as the computer world showed us; while brute forcing is the easiest solution, it's almost never the optimal one
i think that the only way we can optimaly achieve perfection is simply thru advanced reverse engenering and mathematical models based on the reverse engenered set boudaries (dragster being the perfect example for that.)
lastly:
in theory we aim to make the "perfect movie" based on one of those two fixed goal : to finish the game with the fastest time or to entertain the viewer to a maximum.
your lemmings case would definitly fit in the second category (make a movie so entertaining and so incredible that the viewer wouldn't be able to say "why didn't he do that")
it's like playing chess with yourself adding a time value would simply makes it "timed chess"
you should hang more around here, your level of rationality would produce some really interesting Tases
Depending on the epsilon value, the moves or consequences a player has to face may be radically different.
One couldn't simply submit a movie with a lower epsilon. They'd have to make it or produce it. If what into it was the pinnacle of computing power available at the time, or whatever, it would be hard to submit a movie with a lower epsilon.
then another problem would arise : you need to use a versus game where the time between actions would have consequences
if we take street fighter, between player actions, there is no outsides factors expect the time out and it would always favor the 1st character taking an action
one game where this concept could be applied would be 2player marble madness
but it would simply end's up making the gameplay look chopped the moment epsilon gets too big, and peoples would end up actually setting for a slower epsilon that would simply match all the cycles of a set course
Just to mention that after skimming what you wrote I have no real clue whether you want/intend to TAS any lemmings games, but if you do, I speedran the first half of the levels on SMS and it has quite a lot of glitches that could be exploited better that way.
