Excavation Site Gems

"tapperino_forums;c-1623642" wrote:

"teo47;c-1623593" wrote:

"jtgroth;c-1623587" wrote:


I haven't done the math yet on long term averages. This is just a gut feeling about what that math might reveal.

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.

Did you take account of hitting a rock, because that is the complicating factor. What are the chances of hitting a rock (given that there are three different arrangements of rocks with three different frequencies), and then the chances of hitting the gem after the rock depending on 2, 3 or 4 squares where the gem might be ?

Yes, I took that into account. When taking into account the chances of hitting the gem after finding a rock, I always first chose the adjacent square above the rock (or to the right of the rock if there was no square above) and went clockwise. So for a square with 3 adjacent ones to check, I had one square that needed one extra square to find the gem, one square that needed two extra squares, and one square that needed all three extra squares. In reality it doesn't matter if you check the adjacent squares with a pattern or not due to the randomness, but the probabilities work out the same as what I did over the long run.

"tapperino_forums;c-1623642" wrote:

"teo47;c-1623593" wrote:

"jtgroth;c-1623587" wrote:


I haven't done the math yet on long term averages. This is just a gut feeling about what that math might reveal.

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.

Did you take account of hitting a rock, because that is the complicating factor. What are the chances of hitting a rock (given that there are three different arrangements of rocks with three different frequencies), and then the chances of hitting the gem after the rock depending on 2, 3 or 4 squares where the gem might be ?

Finding rock vs. gem is only a second order effect and changes the probabilities only slightly. The most important thing is covering more ground quickly to reduce the number of possible locations on the next choice. Don't forget, while the odds of finding gem after rock are a bit lower when there are more adjacent spots, the odds of finding the rock in the first place are higher because you're covering more area. In the end, the difference between the methods probably ends up being less than one shovel per round on average, but over the duration of the event, it might get you a few extra gems.

"tapperino_forums;c-1623572" wrote:

"meinaz;c-1623448" wrote:


Look at the order @davejandals posted above. It is the most efficient way to find the gem. You want to space out the holes so each square is only checked by one hole instead of multiple. (Hopefully that makes sense.)

Thanks, yes. I drew out happygamer73's version, as it is slightly more efficient. And if you alter the sequence it's easier to remember and do - as in effect it is chess moves of a knight all the way up to include 8, and then 9 and 10 in the last two corners.

http://i.imgur.com/aJqrQa7.jpg

http://i.imgur.com/KricXmi.jpg

Ok, I wrote a computer simulator for this and calculated the average number of picks to get the gem for both of these strategies (assuming once you find a rock then you check the neighboring squares).

EDIT: Had a bug in my program :s Updated averages
The strategy in the top picture has an average of 6.056 picks to find the gem.

The strategy in the bottom picture has an average of 6.361 picks to find the gem.

(Sorry, I lost track of which strategy was proposed by whom).

Now I'm going to try and run it on every strategy and see if I can get a better one (doubtful).

Good god I'm so confused ...however I stupidly followed the pattern...but didn't pay attention to the rocks and kept thinking I would hit a gemstone if I followed the pattern. Doh!
Okay. Next time I'll follow the pattern then once I find a rock, start looking at the adjacent squares.
I was very good at battleship honestly!
Thanks to the geeks on this forum for taking time to figure it ou

Oh for crying out loud, just dig... :D

lol I was digging the whole area today and didn't realise that rocks meant there was a gem nearby XD

Can someone please provide me with the best way to find the gems as this thread has me really confused? A simple explanation with a photo would suffice, thank you!

Math is hard.

Guess that's why I became a HS math teacher...job security. :p

And the love for math, of course. :) Thanks all for hard work on your sequences.

"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!

"Echo0006;c-1623718" wrote:
lol I was digging the whole area today and didn't realise that rocks meant there was a gem nearby XD

Can someone please provide me with the best way to find the gems as this thread has me really confused? A simple explanation with a photo would suffice, thank you!

Okay here are the basics:
The Excavation Grid is 6x6, this gives you a total of 36 possible locations where it could be (more information is needed to confirm this if not the amount of tries can be greatly reduced).
The purpose of these examples and numbered options is to reduce the possible locations where the gem and or stones can be found.
The Gem itself is surrounded by 4 tiles of stones, much like a compass, these tiles are located North, south, East, and West of where the Gem is.
This creates a "t" or "x" (i dont consider it x as no diagonal version of it exists)

Finding a group of stones means that the gem is located within 1 tile of the locations where you found the stones.

I'll use the following picture courtesy of @nissa762
http://i.imgur.com/eQtO97I.png
this method use 12 moves to try and determine the location of the gem and or stones, this is accomplished by hitting areas that would fit the shape of the gem and its' surrounding stones: (Example of stones/Gem combos, courtesy @nissa762 )
3 Stone- 1 gem combo
http://i.imgur.com/EYtcsZDl.png
4 stone -1 Gem combo
http://i.imgur.com/5gvcp44l.png
2 stone- 1 gem combo
http://i.imgur.com/8XgS5Yql.png

As you can see the gem will always be within 1 tile of the stones, the above numbered method requires a maximum of 12 tries (12 shovels) to find or locate the stones, then your task is simply to find the gem, this is preferable then trying to search through every tile individually (minimum 1 try max 35 tries) randomly (same odds as before) or checkered (i'm not a calculator, ok i am but i wont do the math for that one).

the method shown by previous posts reduces this amount to 10 moves to find the stones, however i used the 12 method as it has an ingame picture making it a bit easier to understand (hopefully, otherwise someone else write this)

Lastly you need one shovel per try.

"EvaMohlin;c-1623705" wrote:
Oh for crying out loud, just dig... :D

While i understand your opinion, what these players are trying to do is an old strategy called "Min-Maxing" while often related to RPG games i feel TVTropes explained it best as :
Seen from a purely mathematical and gamist perspective, it's an elegant process of minimum expenditure for maximum result.