Recently I have been developing a theory that going out of our way to get the top hammer on the rivet screen is costing us points in general. I believe that if aggressive strategies are developed which bypass the top hammer in many situations then we might add hundreds of points to our level averages.
Obviously, recommending always skipping the top hammer is sort of a broad, blanket statement that is likely incorrect as there are bound to be plenty of exceptions to optionally playing the screen in this manner as well as lots of situations where getting the hammer is more or less required in order to efficiently complete the screen. Right now, my theory does not have any hard numbers to back it up -- it's more of a gut feeling based on observation over a large sample of games. But these observations are significant enough that I think a discussion among the community is overdue. That's what this thread is for.
I think that we should look at the math behind this decision in various common situations (perhaps screen shots can be provided by those who are good at such things), diving into the code and looking at such factors such as:
-- How many frames does it take to jump vertically? (Leeching Kong's foot)
-- How many frames does it take to lose 100 points from the Timer on each Level?
-- How many frames does the hammer last before expiring?
-- What is the expected value of smashing a Firefox on each Level?
-- How many frames does it take to run various distances (such as from the bottom of the top right inner ladder to the hammer)?
-- How many frames does it take to climb up or down the top most ladders?
And so on.
There are many important situations to be discussed, but here is one to get the ball rolling:
You are on the right side of Kong, currently leeching his foot with "lots" of time remaining on the Timer. All rivets are unplugged except for the one second from the top on the right side. All 5 firefoxes are trapped on the top left corner of the screen, including two freezers. There seem to be four reasonable approaches to finishing the screen from here:
1. Normal Grab: Leech Kong's foot until the Timer has only enough time remaining so that you are able to grab the hammer and use the entire hammer time trying to smash firefoxes, expiring just before time runs out.
2. Early Grab: This involves making an early attempt to grab the hammer with "lots" of time remaining on the Timer, but before any firefoxes have been observed freezing. Especially useful on Level 1 because freezers cannot freeze until they reach internal difficulty of 3 or higher. But might also apply if freezers have not yet frozen anywhere on the screen yet (some additional code analysis would be helpful here).
3. Late Grab: This strategy consists of leeching an extra few seconds and then grabbing the hammer at a later point in time so that only about half of the hammer cycle can be used before being forced to finish the screen before running out of time. Might be more useful in variations of this situation where one or more firefoxes are trapped on the top RIGHT corner of the screen. In particular, if two non-freezers are trapped here then this seems to become the best strategy.
4. No Grab: This is the point of this thread. If the hammer is ignored in this situation and leeching is continued until the last possible moment before completing the screen, observation shows that this quite frequently yields the most points in this particular situation. But let's crunch the numbers and figure it out for sure.
I am starting us off with this scenario because it seems to be the most mathematically solvable decision, and this will give us a good framework to expand the thought processes into more complex scenarios.