I'd like to start out by posing a set of math problems to the group which will require a very rigorous and highly technical solution in order to approach the high degree of accuracy that I am seeking. To add to the fun, I will start out by leaving certain knowledge based aspects of the problem up to the reader to discover and use within their solution. If after some time has passed it appears that no one is being detailed enough in their analysis I will begin to reveal some code analysis level knowledge which is crucial for adequately solving this problem.
This problem involves point pressing the barrel screen. For this problem, I will use the following Ladder Numbering Convention: The Ladders are numbered from #1 through #13 in order of their vertical locations from bottom to top, using the TOP of each Ladder as it's vertical location. For example, the Ladder in the bottom right corner, approximately under the bottom hammer is Ladder #1. The broken Ladder next to the oil can is Ladder #2. Kong's Ladder is Ladder #12. Pauline's Ladder is Ladder #13.
It is a well known point pressing strategy to stand approximately under Kong and next to the top hammer (the "Safe Spot") while intentionally trying to steer barrels down Ladders #11 and #12 in order to group them closely enough together to be able to jump over the grouping in a single jump for increased points. Then, the player often decends the Ladder #9 in order to "rejump" the same grouping of barrels for even more points before ascending back up Ladder #8 (or #9) and returning to the original position to repeat the process. The player's path travels in a generally clockwise manner by using Ladders #8 and #9 repeatedly.
It should be somewhat obvious that it is technically possible to traverse a similar path by repeatedly using Ladders #5 and #6 in a generally counter-clockwise manner OR by repeatedly using Ladders #3 and #4 in a generally clockwise manner. The following problem poses the question of whether it can ever make sense to delay progress towards the Safe Spot in favor of using grouping techniques that rely on a path that uses Ladders #5 and #6 in the SPECIFIC case where the act of continuing to the Safe Spot costs zero points.
For the remainder of the screen, assume that no more wild barrels (including bombs) will be released. Assume that the procedure will not be interrupted by the presence of fireballs.
You are currently standing at the top of Ladder #6. You arrived here immediately after using the bottom hammer. You were at the bottom of Ladder #4 when the hammer expired. The instant before it expired, you were able to smash a wild barrel which was blue (the blue barrel which was released at 6200). The fireball and the other blue barrel were smashed. All other rolling barrels were also smashed. Immediately following the release of the blue wild barrel, three MORE wild barrels were released, which were all bombs (you cannot score points off of these). Kong has just finished releasing the next barrel after that which did NOT turn down Kong's Ladder and is now just barely beyond Kong's Ladder. (Assume that the next barrel after this will also NOT turn down Kong's Ladder.) This has created a situation where there are currently no fireballs or blue barrels on the screen and there are no other rolling barrels above you. You will not miss any barrels if you decide to move directly to the Safe Spot from here. The clock reads 5800.
Using the barrel just released as Barrel #1, determine the EV ("expected value") of points gained from the first 6 barrels released when choosing to move directly to the Safe Spot. Compare this to the EV of points gained from the first 6 barrels released when choosing to stay on our current platform and using the path containing the Ladders #5 and #6 for point pressing. In both cases, the player intends to be located at the Safe Spot just before encountering the Barrel #7 after it has traversed its longest possible path.
Repeat this comparison using the first 12 barrels released instead of 6.
Repeat this comparison using the first 18 barrels released.
How, specifically, are the calculations likely to change if the assumption barring wild barrels is removed?
BONUS QUESTION 2:
Given the starting conditions (but removing the assumptions), estimate the liklihood of each point pressing procedure being interrupted by the presence of fireballs.
BONUS QUESTION 3: After (approximately) 18 barrels are released, how, specifically, will the calculations change if the current point pressing procedure is continued?