Worst case scenario: didn't hit gem until 16th shovel. Can't see any here that I shouldn't have dug ?

Don't use this one. This was one of the first ones - we've already determined it isn't the most efficient.

For all others, this thread is really a brainstorming thread where we are looking for a solution to find the gem with the LEAST amount of shovels used so that we can uncover gems with as little resources as possible.

The latest in the thread will likely be the present best solution with the LOWEST max moves.

tl;dr purpose is to use as little shovels as possible to find the gem

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.

Am throwing out a possible tailspin to our theories. We are looking for the lowest max moves, which I believe is the best strategy. BUT should we be tweaking the location of the first few moves for most initial coverage? i.e. corners/edges as first moves will have lowest coverage.

Haven't given this full thought... Is my logic correct?

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.

Thanks for drawing it out. I would say, though, that the first is slightly better just on a statistical basis since it covers more area at the start, so it's more likely to get the gem earlier, using fewer shovels.

Am throwing out a possible tailspin to our theories. We are looking for the lowest max moves, which I believe is the best strategy. BUT should we be tweaking the location of the first few moves for most initial coverage? i.e. corners/edges as first moves will have lowest coverage.

Haven't given this full thought... Is my logic correct?

I was wondering the same thing. I have also been varying where I start based on where I found the gem before.

Am throwing out a possible tailspin to our theories. We are looking for the lowest max moves, which I believe is the best strategy. BUT should we be tweaking the location of the first few moves for most initial coverage? i.e. corners/edges as first moves will have lowest coverage.

Haven't given this full thought... Is my logic correct?

I think the best and most efficient strategy is definitely to test the middle first, as those have four adjacent squares and are more likely to be next to the gem than a square on the outside. If you pick a middle square first, you've got a 1/36 chance of finding the gem immediately but also a 4/36 chance of finding a rock and zeroing in on the gem right away. If you start with an outside square or corner, you still have the 1/36 chance of finding the gem but your chance of finding a rock drops to 2/36 for a corner piece or 3/36 for a side piece not in the corner. This means that you're likely to have to go through more squares to find the rock in the long run.

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.

So, while it may have the same maximum number of moves, do you think that it might be less efficient on average because you are not checking as many spots early on?

In the top version, you have checked for the possibility of the gem in 15 squares by the 3rd move. While in the bottom version you have only checked 13 squares.

Most of the time you won't need all 10 shovels to get to the gem. So not only do we want the least possible moves, but also the lowest average moves. In fact, I would argue that the lowest average is more important than the lowest maximum.

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

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.

Thanks for drawing it out. I would say, though, that the first is slightly better just on a statistical basis since it covers more area at the start, so it's more likely to get the gem earlier, using fewer shovels.

LOL looks like several of us had the same thought at the same time. Amazing. The geek factor in the forum is awesome today.

I just attempted these so called methods on mine. None of them worked. I'm now out of shovels because of it. My theory of it being completely random is still sound.

~Always be Designing~

Don't increase the Item Limit? Then I don't play. Period.

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.

I just attempted these so called methods on mine. None of them worked. I'm now out of shovels because of it. My theory of it being completely random is still sound.

I am not sure what you mean they aren't working. I have been using them and found them to be helpful. There were a couple times where I got to the 8th try before finding stones but most of the time I found them in the first few and then had to search from there.

I just attempted these so called methods on mine. None of them worked. I'm now out of shovels because of it. My theory of it being completely random is still sound.

It is completely random, nobody here denies that. Again, we're just looking for the most efficient way possible. The current patterns gaurantee that you'll find the gem in 10 shovels. If you pick randomly, you could spend 20 or more, that's the point.

Imagine any square you pick first. It's empty. Now we know it's not that square or directly beside it. Would it make sense to pick one of these squares that you know doesn't contain the gem? Or would it make more sense to pick a new area where you can check a square and the 4 new spots beside it? The latter, of course. These patterns try to maximize this by spacing out your picks to cover area faster.

I just attempted these so called methods on mine. None of them worked. I'm now out of shovels because of it. My theory of it being completely random is still sound.

You went through ten shovels following this exact pattern and didn't uncover any stones? If you uncover the grey stones then you stop the pattern and click around the stones to find the gems.

I've done this four times now - it's worked every time - and my average is five shovels to gem.

## Replies

The images don't show.

Sorry, I have no idea how to delete or edit comments.. but this should work

But that's only a 5X6 plot you're showing - the excavation site is 6X6.

Oops. Carry on.

Don't use this one. This was one of the first ones - we've already determined it isn't the most efficient.

For all others, this thread is really a brainstorming thread where we are looking for a solution to find the gem with the LEAST amount of shovels used so that we can uncover gems with as little resources as possible.

The latest in the thread will likely be the present best solution with the LOWEST max moves.

tl;dr purpose is to use as little shovels as possible to find the gem

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.

well of course don't use that one. The whole point was "worst way to do it". Also see my post above

Haven't given this full thought... Is my logic correct?

Thanks for drawing it out. I would say, though, that the first is slightly better just on a statistical basis since it covers more area at the start, so it's more likely to get the gem earlier, using fewer shovels.

Nicely done!

I was wondering the same thing. I have also been varying where I start based on where I found the gem before.

I think the best and most efficient strategy is definitely to test the middle first, as those have four adjacent squares and are more likely to be next to the gem than a square on the outside. If you pick a middle square first, you've got a 1/36 chance of finding the gem immediately but also a 4/36 chance of finding a rock and zeroing in on the gem right away. If you start with an outside square or corner, you still have the 1/36 chance of finding the gem but your chance of finding a rock drops to 2/36 for a corner piece or 3/36 for a side piece not in the corner. This means that you're likely to have to go through more squares to find the rock in the long run.

So, while it may have the same maximum number of moves, do you think that it might be less efficient on average because you are not checking as many spots early on?

In the top version, you have checked for the possibility of the gem in 15 squares by the 3rd move. While in the bottom version you have only checked 13 squares.

Most of the time you won't need all 10 shovels to get to the gem. So not only do we want the least possible moves, but also the lowest average moves. In fact, I would argue that the lowest average is more important than the lowest maximum.

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

LOL looks like several of us had the same thought at the same time. Amazing. The geek factor in the forum is awesome today.

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.

I am not sure what you mean they aren't working. I have been using them and found them to be helpful. There were a couple times where I got to the 8th try before finding stones but most of the time I found them in the first few and then had to search from there.

It is completely random, nobody here denies that. Again, we're just looking for the most efficient way possible. The current patterns gaurantee that you'll find the gem in 10 shovels. If you pick randomly, you could spend 20 or more, that's the point.

Imagine any square you pick first. It's empty. Now we know it's not that square or directly beside it. Would it make sense to pick one of these squares that you know doesn't contain the gem? Or would it make more sense to pick a new area where you can check a square and the 4 new spots beside it? The latter, of course. These patterns try to maximize this by spacing out your picks to cover area faster.

I like routine!You went through ten shovels following this exact pattern and didn't uncover any stones? If you uncover the grey stones then you stop the pattern and click around the stones to find the gems.

I've done this four times now - it's worked every time - and my average is five shovels to gem.