Excavation Site Gems
After spending some donuts on shovels, I've noticed that the gem always seems to be next to the rocks. Example: - - - - Rock Rock Gem Rock - - - - Rock Anyone seen it ...
Forum Discussion
"teo47;c-1623593" wrote:
The long term average for HappyGamer73's best strategy so far, in his order as he posted it, is 6.056 shovels per round. I will look later at if it changes anything or how much it changes to start with the outside squares and work in.
The probability calculation was a bit easier than I originally thought it would be, given that the initial placement of the gem is random and it's more or less just a process of figuring out how many squares it would take to find the gem in each of the 36 possible starting points. Average together those 36 numbers and there you have it.
Revisiting this, I redid the calculations using HappyGamer73's strategy, but using the order 4, 5, 6, 1, 2, 3, 7, 8, 9, 10 instead of going in order from 1 to 10. This basically means that you pick the three outside squares first, then the interior squares, then the remaining four if needed.
The average using the 1 - 10 sequence in that order is 6.056 shovels per square. Changing to the new sequence, the average increased by 0.25 shovels per round to 6.306 shovels per square. So it is mathematically better to start in the middle and work outward, although the difference would only be about 1 shovel every 4 rounds in the long run!
