The FOFC Mole Season 2: OFFICIAL GAME THREAD

[Poli]

Originally Posted by BrianD

Which piece is yours?

I6

[BrianD]

Originally Posted by MJ4H

Quoting

[BrianD]

Originally Posted by Poli

I6

I still think a move to H5 is your best bet. Your odds of randomly picking the one right space are pretty low, so might as well go to a spot adjacent to the original king placement and see if that was one of the treasure spots.

[MIJB#19]

Originally Posted by BrianD

I still think a move to H5 is your best bet. Your odds of randomly picking the one right space are pretty low, so might as well go to a spot adjacent to the original king placement and see if that was one of the treasure spots.

agreed.

[Poli]

I6 to H5 then, please.

[MJ4H]

Congratulations, group. You have found your first treasure chest! I will update the board as soon as I can, but I'm headed to a meeting right now.

[MJ4H]

The green treasure chests contain $10,000 each. $10,000 has been added to the group pot. The bishop can also see new squares from the new position, but the treasure that was in the square it sits on is not included in the number it can see from there.

[BrianD]

Finally. It still seems like this challenge should have been more profitable for us. Hopefully this will be the start of something good. How big was the chest?

[hoopsguy]

I'm hoping to start sanity-checking some of the math on this tonight if the challenge, depending on how far along moves go today.

I was putting some time into this while driving to work today and I think that the way to calculate the probability of a hit on a square is the following:

1 piece, using King as example = 2 out of 8 = 25% each square (easy)

2 pieces overlapping a square, using King and rook as example: King = 2/8, Rook = 3/8.
a.) Calculate the chance of failure (nothing in the square): multiply results from above. King = 75% * Rook = 62.5% = 46.875 chance of nothing in square.
b.) Calculate the chance of success: 1 - (chance of failure), using example we have 1 - (46.875) = 53.125% chance of success in overlapping square

So, can someone with a statistical background either confirm that I'm doing the math right or tell me that this is bunk so I do not waste my time on the math later? Or, if it is correct and others have more disposable time during the day then please go ahead and run the calculations on some of the more interesting squares to help determine next moves.

[Butter]

2nd rook should go to H7 next, yes?

That is path12's rook.

[hoopsguy]

Originally Posted by Butter_of_69

2nd rook should go to H7 next, yes?

That is path12's rook.

No, there is a zero percent chance of treasure in that square.Check out post #202 - when the bishop was in spot I6 he had one square he could move to that had a chest. He hit it with his move, meaning that there is absolutely no treasure in the other squares in his paths. Including H7.

The rook has four treasures on the "I" and "7" lines. We know that there is no treasure in the following: H7, I7, J7, I6, I5. That leaves treasure in 4/15 squares where you will be able to move, which should be able to be combined with other pieces for a fairly good shot at some cash.

[BrianD]

I didn't notice before, but we got some unexpected good news with that bishop move. G6 is NOT a treasure spot. That is one king-adjacent spot we can eliminate. Another treasure is at either H7 or G7. I'd suggest moving the rook to H7 and seeing what happens. If that hits, we can take a decent guess with both the Queen and the Knight. If it doesn't hit, we will need to decide which of the Queen and Knight gets the real treasure and which gets to guess.

Hoops, your math looks good. I always forget that in situations like this, it is easier to figure out the probability of failure and using that to get the probability of success.

[Butter]

So, hoopsguy's post would suggest to move path12's rook to G7.

If that hits, the Queen is free to speculate, as is my knight.

[BrianD]

Originally Posted by hoopsguy

No, there is a zero percent chance of treasure in that square.Check out post #202 - when the bishop was in spot I6 he had one square he could move to that had a chest. He hit it with his move, meaning that there is absolutely no treasure in the other squares in his paths. Including H7.

The rook has four treasures on the "I" and "7" lines. We know that there is no treasure in the following: H7, I7, J7, I6, I5. That leaves treasure in 4/15 squares where you will be able to move, which should be able to be combined with other pieces for a fairly good shot at some cash.

Good call, I missed this one. Now we know for sure that the treasure is in G7. Does it still make the most sense for the Rook to collect it and let the other two pieces guess?

[Butter]

We also should move the C3 knight to B5, because that would cover 2 of my knight's possible moves... yes?

[hoopsguy]

As of right now, here are all the places that I believe we know to have a zero percent chance of holding treasure, based on the following:
a.) placing a piece on a spot and not getting treasure
b.) placing a piece on a spot and showing "0"
c.) recovering a treasure in line with movement for a piece showing "1", which is now effectively 0.

A1 - A10
B1, B2, B5
C1, C3
D1, D5
E1, E2, E4, E8, E10
F1, F3, F6, F9
G1, G4, G5, G8
H1, H7 (H5 = hit!)
I1, I5, I6, I7
J1, J5, J7

[Butter]

Originally Posted by BrianD

Good call, I missed this one. Now we know for sure that the treasure is in G7. Does it still make the most sense for the Rook to collect it and let the other two pieces guess?

Ah, I see that now. So, I guess it is a matter of which piece to use to collect that treasure.

[hoopsguy]

Note - the above post shows that we have complete information on 40 of the 100 spaces on the board. I have no idea if that is relatively good or bad at this point in time compared to what we could potentially have uncovered.

I do think that we are going to have some pretty high probability shots with our last couple of moves if we are smart the rest of the way.

[samifan24]

Perhaps someone should post a modified board with red over the spaces without treasure, green in the most likeliest locations and yellow everywhere else. It would certainly help to visualize what we're dealing with here.

[BrianD]

Originally Posted by Butter_of_69

We also should move the C3 knight to B5, because that would cover 2 of my knight's possible moves... yes?

I really like this idea. If we get lucky, the knight will still show a 0 and that will eliminate two more spaces. A non-zero number may not tell us a lot, but it will be more information than we have now and I can't think of anything else to do with that knight.

[hoopsguy]

Why B5 instead of D5? We know it is not getting treasure in either spot, but in D5 it would still have the maximum number of available moves off that square.

B5 - two moves eliminated due to board position, two squares "revealed" are on the A line that we already know is dry. Add the spot that he is moving from, and there is only information on C7, D4, and D6.

D5 - one move already a known zero, where the queen sits. Plus where piece is moving from. That leaves six potential spots for info: C7, B4, B6, F4, E3, and E7.

[Butter]

I am going to just clam up and let the more logically inclined help everyone else out on the rest of this challenge. Someone wake me when it is my turn!

[hoopsguy]

Originally Posted by Butter_of_69

I am going to just clam up and let the more logically inclined help everyone else out on the rest of this challenge. Someone wake me when it is my turn!

I hope that you continue to participate. The thread is more fun when there are multiple people playing along rather than leaving it in the hands of one math guy to drive.

Also, bringing up ideas on what to do allows us to collectively flesh them out which should be a big positive in the long run. Even if the original idea is not perfect it will generate discussion and hopefully lead us to a better move.

[Butter]

Yes, but honestly I think there is probably a clear set of moves that would be most likely to lead us to the highest probability with the remaining moves, but my logic is not math-based enough to lead us there. I would rather some of you folks with the better quality statistical skills to flesh this out.

[BrianD]

I'll give you my thoughts and then wait for your response. I'm certainly open to being persuaded.

Originally Posted by hoopsguy

Why B5 instead of D5? We know it is not getting treasure in either spot, but in D5 it would still have the maximum number of available moves off that square.

At this point, I'm not sure the maximum number of available moves is what we should go for. More specific information on fewer spots might be more helpful than less specific information on more spots.

B5 - two moves eliminated due to board position, two squares "revealed" are on the A line that we already know is dry. Add the spot that he is moving from, and there is only information on C7, D4, and D6.

To me, that is the strength of the move. We know that there is a treasure at G7. That means there are also treasures at 2 of the other 6 spots the knight could move to. If we move the other knight to B5 and we get a zero, we have eliminated 2 of the 6 spots. If we get a 3, we have confirmed 2 treasures. Even a 2 would give us pretty high confidence in 2 spots. Only a 1 would really leave us with not much information.

D5 - one move already a known zero, where the queen sits. Plus where piece is moving from. That leaves six potential spots for info: C7, B4, B6, F4, E3, and E7.

Moving to D5 gives us potential information on a bunch of spots. One of those spots intersects with a move from the other knight, and one spot intersects with a move from the queen. If we get a zero there, we can eliminate one square from each of two pieces which gives us some amount of benefit. Anything lower than a 6 is going to be rather confusing since there are 4 spots that nobody can get to.

My thought is that other than the G7 treasure, we'll be lucky to get just one more. Doing what we can to try to increase the odds of that third treasure seems to me like the best play.

[hoopsguy]

I get your point on "actionable" squares as compared to "absolute" squares and think that it makes sense. But it also reminds me that I really, really need to sink some time into drawing up my map with the calculated probabilities on the "actionable" squares to try and work towards optimal moves.

Fun puzzle, MJ4H.

[BrianD]

Originally Posted by hoopsguy

I get your point on "actionable" squares as compared to "absolute" squares and think that it makes sense. But it also reminds me that I really, really need to sink some time into drawing up my map with the calculated probabilities on the "actionable" squares to try and work towards optimal moves.

I'd love to see that map. I've been talking about generic theory, but the actual numbers might push us in a different direction.

Fun puzzle, MJ4H.

+1 In fact, I'd love to see something like this coded and put online somewhere. Anybody up for a challenge?

[path12]

So I need to move my rook to G7, is that the consensus?

I also want to apologize for not being around much for this challenge, it's been crazy at work......and while I'm at it should note that I'm camping tomorrow through Monday and will have little to no access in the meantime.

[MIJB#19]

yeah, rook to G7 seems to be the best option now, with knight C3 to B5 as the next move to help the queen and other knight

[hoopsguy]

Here is my best effort at mapping out what we have learned so far. Please spot check this for any potential mistakes.

Also, if anyone has tips on how to better format this for viewing on this page I'm all ears.

A B C D E F G H I J
1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
2 0.00 0.00 ??? 0.27 0.00 0.26 ??? ??? 0.33 0.27
3 0.00 ??? 0.00 ??? 0.27 0.00 ??? ??? 0.52 0.00
4 0.00 ??? ??? 0.26 0.00 0.46 0.00 0.27 0.00 ???
5 0.00 0.00 ??? 0.00 0.26 0.26 0.00 1* 0.00 0.00
6 0.00 0.26 0.26 0.51 0.26 0.00 0.00 0.00 0.00 0.26
7 0.00 0.33 0.56 0.33 0.52 0.00 1.00 0.00 0.00 0.00
8 0.00 ??? ??? 0.27 0.00 0.26 0.00 0.26 0.33 0.27
9 0.00 ??? 0.52 0.00 ??? 0.00 0.33 ??? 0.51 ???
10 0.00 0.27 0.00 0.33 0.00 0.51 ??? ??? 0.33 0.26

Assumptions:
Knight1 = 2 of 6 remaining = 33%
Rook = 3 of 9 remaining = 33%
Bishop = 3 of 11 remaining = 27%
Queen = 6 of 23 remaining = 26%
Knight2 (top) = 0 remaining
King = Capped out
Bishop2 = Capped out
Rook2 = Capped out

[MIJB#19]

	A	B	C	D	E	F	G	H	I	J
1	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
2	0.00	0.00	???	0.27	0.00	0.26	???	???	0.33	0.27
3	0.00	???	0.00	???	0.27	0.00	???	???	0.52	0.00
4	0.00	???	???	0.26	0.00	0.46	0.00	0.27	0.00	???
5	0.00	0.00	???	0.00	0.26	0.26	0.00	1*	0.00	0.00
6	0.00	0.26	0.26	0.51	0.26	0.00	0.00	0.00	0.00	0.26
7	0.00	0.33	0.56	0.33	0.52	0.00	1.00	0.00	0.00	0.00
8	0.00	???	???	0.27	0.00	0.26	0.00	0.26	0.33	0.27
9	0.00	???	0.52	0.00	???	0.00	0.33	???	0.51	???
10	0.00	0.27	0.00	0.33	0.00	0.51	???	???	0.33	0.26

Like this?

[hoopsguy]

Love it - so, next steps:
1.) Someone find flaws with my math (pretty high possibility that I do have mistakes in here)
2.) Assuming #1 does not take place, let the plotting of moves continue with our new-found data

[path12]

OK, move my rook to G7 then.

[MIJB#19]

hmmm, the general sense seems to be okay, but the odds for the single pieces all add up to about 1/4th more than they should aqdd up to.

[samifan24]

So it seems like this is about eliminating doubt with as many squares using lower pieces more than it is about finding treasure with those same pieces. What I mean is that we will use the bigger pieces (more mobile, I mean) to scoop up the treasure after we move the lower pieces around so as to eliminate as many question marks as possible, right? Does that make any sense or am I talking in circles here?

[hoopsguy]

I'm not sure that I follow? But I'll try to pick up this conversation a little later this afternoon when I'm back online. In the meantime, I'll hold off on moving my bishop for awhile but my initial thought is that I3 might be a good square to check out if we have enough coverage of the middle areas with the other pieces.

[MIJB#19]

Originally Posted by samifan24

So it seems like this is about eliminating doubt with as many squares using lower pieces more than it is about finding treasure with those same pieces. What I mean is that we will use the bigger pieces (more mobile, I mean) to scoop up the treasure after we move the lower pieces around so as to eliminate as many question marks as possible, right? Does that make any sense or am I talking in circles here?

Let's see what we have left:
knight at C3 (that has to move to B5, right?)
bishop at G5
queen at F6
knight at E8 (moving after knight C3)

At this point I think we should try and get chests with all that we have left. I'm not convinced we can get more info on potential chest squares by sacrifice movement of other pieces. After the knight to B5 move, whe should have more info on the knight E8's possible moves. The queen and afterwards the bishop at G5 can be used to take a shot at the highest odds squares in the knight's range. That's 3 shots to grab another chest.

with 15 in 100 odds,with 16 placements our odds should give us roughly 2.5 chests. It seems we've got 2 already (bishop and the rook to G7) and with 1/3rd or better odds for the last three pieces, we're in a good position to get 3 or 4 chests and call this a succesful mission.

[claphamsa]

someone let me know when this clarified any! I R CON FUZZLED

[MIJB#19]

Originally Posted by claphamsa

someone let me know when this clarified any! I R CON FUZZLED

Consensus seems to be that you're next up and your best move would be to move the knight to B5. Not much to be confused about there.

[claphamsa]

K-B5

[MJ4H]

Sorry guys, first day of school combined with a major tire problem on my car I'm just now getting home and have to get off to bed. I will try to update this first thing in the morning.

[MJ4H]

[BrianD]

That was pretty helpful. We know the two spots in the a-row are blank. There are two treasures in the three spots that knight can get to. Between the other knight and the queen, we can reach two of the three spots. We are now guaranteed 3 treasures with a decent shot at 4.

[MIJB#19]

excellent!

[hoopsguy]

Yep, very good result. Good job to all that pushed for the B5 move.

[Butter]

Originally Posted by path12

OK, move my rook to G7 then.

I think MJ4H may have missed this move.

[MJ4H]

Indeed I did

Shouldn't make a big difference to strategy, though I guess. Right after I finish lunch I will put up that move.

[MJ4H]

Congratulations, you have found another $10,000 treasure! $10,000 is added to the group pot.

[MIJB#19]

Now what? Knight C7, queen D6 and bishop C9?

[BrianD]

Originally Posted by MIJB#19

Now what? Knight C7, queen D6 and bishop C9?

The knight and the queen sound fine as there should be at least 1 treasure in those two squares. I'm not so sure about the bishop though. Of the 7 spots the bishop has access to, we know the top row is blank. That means 3 of the 6 spots are treasures. Picking any one of those six is probably better odds than going to C9. At least I think so. Let me know if your math comes out different.