Rivet Screen Top Hammer: To Get Or Not To Get?

[up2ng]

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.

Discuss!

[homerwannabee]

From my perception one tactic seems horrible.  That's the early grab where the person has 4000 bonus, and they just grab the hammer, and start smashing the left side fireballs.  Quite often the person has to finish the stage with plenty of bonus time remaining.  I think it has to do with impatience more than anything that people do the early grab.

[Adam_Mon]

Interesting points,
I've noticed Dean recently using the "no-grab" method and if you think about it, it's not a bad idea.

if all 5 firefoxes are trapped on the left I would usually wait until 500 on the bonus timer then stop leeching, decend and grab the hammer to get smashes on the left but all too often I either don't get any, maybe 1 or 2 if lucky and most of the time they would end up being 300's anyway.

Not grabbing the hammer means you can leech kong for the remaining 500 on the bonus timer + 2 extra jumps after 0000 bonus.

I loaded up a level 5 rivet save state and if you start leeching right as the bonus timer hits 500 you can get 9 straight jump leeches decend and pull the rivet for 1000.

so thats a guarenteed 1k vs risking the hammer grab at 500 bonus timer..

@500 bonus after you grab the hammer, even if you got 3x 300 smashes (from the left side trapped firefoxes) + the rivet pull that means you'd still only break even.

So I guess the dilema for that scenario is do you keep the guarenteed 1000? or do you go for the potential multi smash on the left, 800 miracle smashes ("Marky...how!"  ) and also the chance to re-spawn the smashed firefoxes again on the right side and hopefully get them before rivet pull (again pretty rare)

[jwade614]

High score is the goal. A player should always be willing to sacrifice some EV in exchange for a potentially higher score. For the situation given, grab the hammer every time. (Well, unless you are on 21-6 and the guaranteed leach points plus KS gets you a WR or something.)
 

[danman123456]

Interesting points,
I've noticed Dean recently using the "no-grab" method and if you think about it, it's not a bad idea.

if all 5 firefoxes are trapped on the left I would usually wait until 500 on the bonus timer then stop leeching, decend and grab the hammer to get smashes on the left but all too often I either don't get any, maybe 1 or 2 if lucky and most of the time they would end up being 300's anyway.

Not grabbing the hammer means you can leech kong for the remaining 500 on the bonus timer + 2 extra jumps after 0000 bonus.

I loaded up a level 5 rivet save state and if you start leeching right as the bonus timer hits 500 you can get 9 straight jump leeches decend and pull the rivet for 1000.

so thats a guarenteed 1k vs risking the hammer grab at 500 bonus timer..

@500 bonus after you grab the hammer, even if you got 3x 300 smashes (from the left side trapped firefoxes) + the rivet pull that means you'd still only break even.

So I guess the dilema for that scenario is do you keep the guarenteed 1000? or do you go for the potential multi smash on the left, 800 miracle smashes ("Marky...how!"  ) and also the chance to re-spawn the smashed firefoxes again on the right side and hopefully get them before rivet pull (again pretty rare)

Thats why I dont get it until about 300-400. I think "overall" that is a better strat if you have them all pinned in because while sometimes is only 2 smashes ive gotten 4 or 5. If you just say forget it and just save the top right rivet you get 400-500 points leeching the foot plus another 4 jumps for 800-900 points.

If I save the 2nd from the top and leave at 400 points generally the WORSE case is 2 smashes (While I have gotten none that is ultra rare I think) for 600 points. While in better situations 4 or 5 smashes. 5 smashes is 1500 points guaranteed and I've gotten crazy points as well (2 800's, 2 500's and a 300 which is 2900 points.)

So given that 2900 vs 900 means im +2000 while if it is only 600 vs 900 im -300 negative.
that 2000 can cover almost 7 levels of NOTHING but -300 points.

Odds are good that one smash out of 3 will be at least a 500 or 800 points so that will mean you are always going to score more as a whole.

The real stats only matter when you really look at how many of these situations arise in a game. It's not common to get all 5 smashes with the bottom hammer to get all 5 trapped on the left. Maybe what 3 times a KS game on avg? In the grand scheme of things its not a big deal either way unless you are trying for a huge 1.1x+ game. You can lose maybe 900 points over the course of 3 attempts but likely will gain a few thousand points. Whooooooooooooo

[f_symbols]

 

[xelnia]

jry chart lit

This all assuming that the only rivet remaining is the 2nd from top on the right.

Chart explanation:

Frames: The number of frames remaining at the given Bonus times. At 000, there is 3 frame run-off, followed by a 256 frame countdown. So, there are actually 259 survivable frames at 000 Bonus.

Leeching: The number of points that can be earned if the leech jumps begin exactly at the Bonus time indicated and are performed with maximum efficiency (47 frames per jump). Note that this takes into account the 92 frames required for the short walk and climb down to clear the last rivet, so this is NOT a table that represents what is possible when only the top right rivet remains.

Diff: The actual number of points earned over the remaining Bonus time.

Smashes: The number of smashes required to match or better the points earned by leeching, using an EV of 450 points per smash. This assumes that the player is clearing the last rivet at the last possible moment. It takes a minimum of 393 frames to climb down, grab the hammer, walk to the left-most pixel possible with out Staal-falling, then return and clear the final rivet. The latest Bonus time that the player can leave to grab the hammer is highlighted.



Also:

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) 47 frames
-- How many frames does it take to lose 100 points from the Timer on each Level? 120 frames for Level 1, 100 frames for Level 2, 80 frames for Level 3, 60 frames for Level 4+
-- How many frames does the hammer last before expiring? 511 on-the-ground frames
-- What is the expected value of smashing a Firefox on each Level? 450 points
-- How many frames does it take to run various distances (such as from the bottom of the top right inner ladder to the hammer)? Pass 
-- How many frames does it take to climb up or down the top most ladders? 99 frames up, 82 frames down

[up2ng]

From my perception one tactic seems horrible.  That's the early grab ...

In the situation described in the OP, the main purpose of the early grab is to try to be able to smash the freezers before they have had an opportunity to enter into a pattern where they will be unsmashable.  The idea is that the player will complete his hammer cycle and then will return to the spot next to Kong to continue leeching for the remainder of the board.  The advantage is the potential for more smashes while the disadvantage is the potential for respawns on the right side to eventually interrupt the leeching time before the board is complete, leading to lost points.  In addition, there is additional travel time involved (the extra climb back up and then back down the ladder) which is more lost points as compared to spending that time leeching.  There is merit to this approach in certain situations, but the average result as compared to other methods is debatable.

if all 5 firefoxes are trapped on the left I would usually wait until 500 on the bonus timer then stop leeching, decend and grab the hammer

I loaded up a level 5 rivet save state

To be clear, if you are referring to Level 5 when making this decision with 500 on the clock, then you are using the "Late Grab".  From there, you are likely grabbing the hammer with somewhere around 200 on the clock.  This means that you are using about half or two-thirds of your hammer cycle before running out of time and being forced to complete the screen.

I think there is some real merit to this approach and has become sort of a "compromise" method.  You bank "some" of the leeching points that you would normally give up with your "normal grab" strategy and sacrafice some hammer time.  The idea is that in this particular situation, the majority of smashes tend to occur relatively early in the hammer cycle and the last half of the hammer cycle is often relatively ineffective.

High score is the goal. A player should always be willing to sacrifice some EV in exchange for a potentially higher score.

I disagree with this in general.  Donkey Kong is a long game which involves thousands of decisions.  I think that the player who consistently makes "the best" decisions throughout the game will end up with the higher score.  It is statistically implausable that making decisions that consistently underperform on average but occasionally yield very good results will be able hold up in a positive manner throughout the course of a full game.  This is basically the difference between tool-assisted runs and live game play. 

The only exceptions to this will involve the first few screens of the game where the decision making can be more "home run" oriented since games at this stage can be aborted with less of an impact on the player's session quality than would be otherwise possible.

[jwade614]

High score is the goal. A player should always be willing to sacrifice some EV in exchange for a potentially higher score.

I disagree with this in general.  Donkey Kong is a long game which involves thousands of decisions.  I think that the player who consistently makes "the best" decisions throughout the game will end up with the higher score.  It is statistically implausable that making decisions that consistently underperform on average but occasionally yield very good results will be able hold up in a positive manner throughout the course of a full game.  This is basically the difference between tool-assisted runs and live game play. 

The only exceptions to this will involve the first few screens of the game where the decision making can be more "home run" oriented since games at this stage can be aborted with less of an impact on the player's session quality than would be otherwise possible.

"consistently underperform on average but occasionally yield very good results"

Couldn't this phrase be used to describe point pressing? Couldn't we all increase our average scores by playing safer?

What is a player's "session quality"? That sounds subjective to me.

[up2ng]

It's true that there is a similar balance in terms of risk/reward as far as point pressing vs. playing it safe, but I think that's a different concept than what I was talking about which is to make decisions which have the best average result for that particular decision. 

As a simple example, there are times when I decide to take the free pass on the Pie Factory.  The reason for this in my games has nothing to do with wanting to be safe.  I do it when I believe that it will yield the best result on average.  When I take the free pass, assuming that there is little chance of additional delays, I know that I will score about 8200 to 8500 points almost every time.  If I decided instead to decline the free pass and I go out of my way to grab both hammers -- sure there is a chance that I would have ended up with a really big score for that screen.  But, I evaluated how the screen was playing out and at the moment of this decision I decided that it was the statistically better choice (scoring-wise) to take the free pass.  If I never took the free pass, there is at least some chance that I would have been better off on each of those screens, but throughout the course of a full game there is a much smaller chance that I would have been better off for the whole game.  And even if I beat the odds for one game with respect to the free pass decision, there are literally hundreds of similar decisions to make throughout the game in various situations such that it becomes statistically impossible to be better off by consistently making decisions that have a lower expected value. 

[jwade614]

Perhaps I could have been more clear in my original response to this thread.

I said:  A player should always be willing to sacrifice some EV in exchange for a potentially higher score.

"Some" EV. Not any or all. (I could have worded that a lot better.)

The reward needs to be significant relative to the risk. I believe the top hammer rivet scenario, as described in the op, qualifies.

I agree 100% that if there are a large enough number of these decisions in a game, always sacrificing EV for a higher score potential will hurt you over the course of an entire game. This is why the decision to go for the higher score needs to be limited, preferably to the most optimal situations.

Consider this:

Player A and Player B grind DK for some amount of time. Players A and B are equal in every way, except Player B picks one (good) spot every game to sacrifice EV for a higher score potential.

Player B will have the higher expected high score.

Player A will have the higher expected average score, but no one cares about this. Incidentally, Player A will also have the higher expected low score, but again, no one cares.

[jwade614]

Been thinking more about this...

I suppose it could take an unreasonable amount of grinding to expect to come out ahead, due to variance in the rest of the game as a result of the RNG. I'm not sure what the variance is on a complete game score, but I think it's probably massive and going to dominate so much that additional variance added by taking a few EV risks isn't going to move the standard deviation much.