Ok, well it looks like there may not be too many more responses coming so I'll just go ahead and post my "answers". Of course, just because I have an opinion about my own questions doesn't mean I have the best answer so please feel free to continue the discussion!
Thanks to Ethan for actually answering the questions. I apologize if it wasn't so clear this time around. Among all of the responses there were some great ideas and a lot of you seem to be on the right track.
Part 1:
From where we are located at the "Decision Time", there are two very different possible paths. There are two different methods for progressing to the area at the top of the ladder where we'd be finished executing a "top shelf" jump. From that point, the two paths join and the best option would be the one which conserves the most Bonus points on the Timer, adjusting for any auxillary points which are picked up along the way. First, we could go back to the middle structure, working our way up and jump across one of the two "shortcut" gaps, OR we could continue to the right and work our way up the bottom right section of the screen. Obviously, we are pretty well trained to know that the first option is generally considered a "shortcut" for a reason and the other path is known as "the long way around" for a reason as well -- typically the shortcut is the more efficient path, saving valuable Bonus points.
But, let's take a closer look at this particular situation . . .
The most important point to notice about the setup is that we have already grabbed the umbrella! So, by going back to the middle structure from our current position there will be NO prizes to pursue -- it is likely that we will not pick up any auxillary points en route to our top shelf platform going this way. With the fireball on its way back to the top, we will NOT be climbing the ladders in the middle section, we will be jumping back onto the upward elevator.
While there is a decent chance that the timing will work out well so that the fireball will decend again while we are on our way to the top (no delay in this case), there is some percentage of the time where the fireball will camp out at the top and we'll be forced to bail out back to the umbrella platform (which does NOT contain an umbrella). In these cases, we'll be forced to try to coax the fireball back down before proceeding across the top, which will range from nearly right away to several seconds. Just to pick some numbers -- suppose we are delayed 50% of the time and when we are delayed we are delayed by an average of two ticks off the Bonus Timer. In addition, we were forced to jump left and then jump back onto the elevator before jumping right (two extra jumps plus a bit more movement costs at least another 200 Bonus points) -- so we should factor in an average delay of 200 points with this route.
The next point to notice is that the second fireball is currently frozen next to the purse. Understanding the pattern of a frozen fireball while roaming (not frozen at the bottom or top of a ladder), we know that this fireball will move right, hit the invisible wall, come back to the left, proceed down the ladder and then freeze. After freezing, it will climb back up that same ladder to where the purse is located and freeze again at the top of that ladder. By the time it is done doing this, we will be beyond the section of the structure where that fireball could cause us any delays -- so, this fireball can NEVER climb down that second ladder to get in our way in this specific scenario . . . there will be NO delay when choosing this path!
Finally, the expert jump maneuver that was already performed in the setup should imply that we could traverse the bottom section with the greatest possible efficiency WHILE leeching a spring as often as possible!
With all of these points in mind, let's try to calculate the total cost of choosing the bottom section. Riding the elevator the rest of the way down (a short distance) and then jumping to the lowest platform should take about one tick from the Timer (one spring missed). When jumping to the next platform we can leech the 2nd spring. When jumping to the third platform we can leech the 3rd spring. While climbing the short ladder to the next level we'll miss the 4th spring. Next, we'll jump to the middle platform while leeching the 5th spring. After that, we'll jump to the lower shortcut platform while leeching the 6th spring. Finally, we'll have to climb up the ladder to the top shelf platform while the 7th spring goes by as we reach our "goal" for this comparison. So, with this estimation, the total cost of choosing the lower path is just 300 points! (700 Bonus lost, 400 auxillary spring leeching points gained)
(NOTE: If a combination of springs comes up so that it is not safe to efficiently jump horizontally along the structure, there will ALWAYS be a way to perform a vertical jump to leech the offending spring while delayed -- for a zero net loss. The result upon reaching the top shelf platform will STILL be a total cost of just 300 points.)
Remember that our average delay alone on the left side path already costs us 200 points. So, nearly the ENTIRE time that it takes to get from our current location to the top shelf location along the left side route is points lost! Meaning, choosing the bottom path in this particular case is SIGNIFICANTLY superior. I think that result will be surprising to most players.
The absense of the umbrella makes all the difference though. If the umbrella was still there it's virtually always correct to go back up the left side to collect this 800 point prize.
Part 2:
The idea behind this exercise is to begin to think about point pressing the elevators positionally instead of with just good timing. Instead of thinking about "the safe spot" as being a spot on top of the yellow graphics where you can stand and no springs can hit you, consider thinking about the safe spot as a zone which has a left edge and a right edge and that this entire zone moves to the right or left depending on which of the 16 possible springs enters the screen.
In addition, becoming familiar with the 16 possible spring positions should give you a better understanding for which of these allow the most "clearance" on Pauline's ladder -- meaning, how low on this ladder can Jumpman be located and still survive 100% of the time (assume the worst possible "scrunchiness" for this spring position). Having more clearance allows you to begin your approach up Pauline's ladder from a more distant position (or, to have a worse "jump", or timing).
I don't actually know the exact clearance values for every spring position, but I do understand the general trend. The trend is that the very longest springs have no clearance (or, negative clearance) -- these cross so high up the ladder that they will always hit you. As the spring position gets slightly shorter, they will cross slightly lower, allowing for a small amount of clearance. This trend continues until you hit a "sweet spot", where the clearance is greatest (the spring crosses the ladder at its lowest point) -- surprisingly, this is NOT spring 0. Instead, this is probably closer to spring 5 or 6 on my scale of 0 to 15. As we get shorter still, the clearance actually reduces again as the spring is now crossing the ladder on the rebound (on its way back up) and this trend continues all the way to spring 0, which is actually relatively dangerous with a fairly low level of clearance. There IS a very slight horizontal advantage with spring 0 though -- in the time it takes for the spring to travel the additional 16 pixels horizontally, Jumpman MAY have just enough time to climb an additional 1 or 2 pixels higher than he can when dealing with a spring 15. Still, the important point is that spring 0 is NOT the most ideal spring to climb ahead of.
With all that being said, here is my interpretation for what might be possible on the 10 scanarios (these may or may not be correct and are open to debate):
First of all, to my knowledge, there is NEVER any situation where jumping over a spring or leeching a spring is profitable -- I REALLY hope someone can post a video to the contrary, that would be pretty cool!
Scenario 1, Springs: 2, 6, 15, 10, 10
This is the perfect scenario for the fastest possible finish -- A 6 spring is pretty much right in the sweet spot for being the best trailing spring . . .
Run left, stop (2), continue left and DIRECTLY up the ladder from the right (6)!
Scenario 2, Springs: 13, 4, 8, 9, 7
This initial combination is poor for getting to the safe spot, an unfortunate delay.
Wait (13), run left, stop (4), continue left and DIRECTLY up the ladder from the right ( 8 ).
Scenario 3, Springs: 8, 10, 0, 12, 5
Spring 0 is very dangerous here. Big delays.
Run left, stop ( 8 ), continue left to safe zone (10), wait (0), edge to the right (12), climb up the ladder (5).
Scenario 4, Springs: 6, 6, 6, 9, 9
This would be a pretty borderline approach from the right. If that doesn't work, you can definitely get between two 6 springs approaching from the left (in fact, this is probably what we are seeing on Level 6 in D2K).
Run left, stop (6), continue left and DIRECTLY up the ladder from the right (6).
Scenario 5, Springs: 14, 3, 5, 11, 8
This initial combination is poor for getting to the safe spot, an unfortunate delay.
Wait (14), run left, stop (3), continue left and DIRECTLY up the ladder from the right (5).
Scenario 6, Springs: 15, 14, 13, 12, 11
This is nasty. It's hard to know exactly which combination is safe (For example, the "kill screen" in D2K on Level 14 MIGHT be 14, 14, 14 combinations and NOT 15, 15, 15 as many players are assuming). BUT, we CAN move left immediately with a combination like this.
Run left, stop (15), continue left to safe zone (14), quickly turn right and up the ladder (13).
Scenario 7, Springs: 5, 15, 15, 15, 5
This one should be clear -- lots of 15s = big delays.
Run left, stop (5), continue left to safe zone (15), wait (15), edge to the right (15), climb up the ladder (5).
Scenario 8, Springs: 12, 8, 4, 8, 6
This is close at every decision, but doable I think.
Run left, stop (12), continue left to safe zone ( 8 ), quickly turn right and up the ladder (4).
Scenario 9, Springs: 1, 10, 14, 12, 12
A 10 spring seems like it might be pretty long, but I think this one yields pretty decent clearance.
Run left, stop (1), continue left and DIRECTLY up the ladder from the right (10).
Scenario 10, Springs: 0, 2, 4, 6, 8
Another nasty one. I'm not clear how spring 2 compares with spring 10 in terms of clearance, but I'm assuming we might just make it -- otherwise, it might not be safe to approach from the left side until the 6, 8 combo . . .
Run left, stop (0), continue left and DIRECTLY up the ladder from the right (2).
Ok, I hope that was fun and/or useful. Feel free to debate these answers and discuss further.
