Creator Response Number Crunching

Blauwfuur

Cowpoke
In this thread I attempt to strip away all the pretty pictures and fun events reminiscent of the video game that the board game brings. I want to get right down to the chance distributions and want to know theoretical optimal tactics.

For those that seek to just enjoy an evening of fun farming and making friends, I asvise you not to read this, as it might take away from the magic of the game.

If number crunching happens to be one of your favourite pastimes (as it is mine) enjoy my rant <3
 

Blauwfuur

Cowpoke
Lets start with the non-animal dice: 3 hearts, 2 junimo's and 1 stardrop on each die. Hence a 50% to roll hearts for example. I will abbreviate these sides with H, J and S respectively. Now lets see what that means for the chances in the game.

Mining. Mining uses 2 dice, and so every chance is a product of 2 6-sided dice. Therefore i will be writing down everything as a chance out of 36. Note that 2 different die results (for example H+J) are doubled because either the first die is a heart and the second a junimo, or the other way around. Hence twice the chance.

H+H = 9/36 = 1/4
H+J = 12/36 = 1/3
H+S = 6/36 = 1/6
J+J = 4/36 = 1/9
J+S = 4/36 = 1/9
S+S = 1/36

So looking at any given mine map, these are the numbers to keep in mind when you are hoping for certain results. It also puts in perspective how effective the first pickaxe upgrade realy is (not very imo)

Possible further answers i might calculate and edit this post for:
-the effect of the pickaxe upgrade on these chances
-when added up all results of the level maps, what is the expected yield of a random unupgraded mining action, spread across the types of recources you can get
 
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Blauwfuur

Cowpoke
Fishing!

Fishing uses 3 dice and therefore the chances are out of 6x6x6=216. I might simplify these chances to percents eventually.

H+H+H = 27/216
H+H+J = 54/216
H+H+S = 27/216
H+J+J = 36/216
H+J+S = 36/216
H+S+S = 9/216
J+J+J = 8/216
J+J+S = 12/216
J+S+S = 6/216
S+S+S = 1/216
Total = 216 yay

So for example if you were to attempt to catch a fish that requires 3 hearts, you have a 12.5% chance to get it.

When trying to catch a legendary fish you have a 27+37+9+12+6+1=91/216 chance to get it. Now we know!

I would like to add that in one of my games i did roll in order: J+S+S, J+J+S, S+S+S, causing me to catch 0 fish in a whole 3 actions. I was losing my mind over these chances. All i needed was a single heart for a herring, which by the way is a 189/216 chance to get at least 1 heart in 3 dice.

Future questions i will attempt to answer (using maybe the list that user kaliomonkey just posted)
-What is the expected yield of an unupgraded fishing action?
-What is the effect of the fishing rod upgrades?
-What is the expected amount of fish you need to "remove" from the fishing track to find a legendary fish?
 
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kailomonkey

Tiller
I do like to mess around with probability, maths and spreadsheets :P However probability gets complex fast so while I was looking into fishing I just produced a randomised sample of 1000 and repeated it until I had an idea of the probability :P I will try to supply it as a chart.
My Difficulty Rating
10​
9​
8​
6​
5​
4​
3​
1​
0​
Averaged Actual (% eyeballed)
4​
13​
26​
42​
50​
60​
70​
88​
An Actual (sample size 1000)
4.10%​
11.10%​
27.90%​
41.20%​
49.00%​
58.60%​
70.80%​
87.60%​
Desired result
3 juminos​
3 hearts​
2 jumino​
1 stardrop​
2 hearts​
1 heart 1 jumino​
1 jumino​
1 heart​
bug meat​

What I found really interesting is that snagging a Legendary Fish by rolling a Stardrop is actually more likely than rolling 3 Hearts or 2 or 3 Junimos! Combinations needed for some non-legendary fish. Adding a list of fish that are harder to catch than Legendary Fish excluding Crab Pot fish which are also debatably harder depending on Bug Meat supply.
Octopus​
Lingcod​
Tuna​
Pike​
Pike​
Tiger Trout​
Albacore​
Eel​
Pufferfish​
Super Cucumber​
Sturgeon​
Catfish​
Dorado​
Squid​
 
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DJModulo

Sodbuster
I love me some number crunching :)

As for fishing, the best approach I have come up with is to calculate the chances of rolling the symbol(s) you need. I'll try and make a chart for less than 3 symbols:

H : 87.5% (189/216)
J : ~70.37% (152/216)
S : ~42.13% (91/216)

H+H: 50% (108/216)
H+J: ~58,33% (126/216)
H+S: 33,33% (72/216)
J+J: ~25,93% (56/216)
J+S: 25% (54/216)
S+S: ~7,41% (16/216)

For fish requiring 3 symbols, I'll refer to Blauwfuur's chart above.
And yes, this evidences that Catfish and Sturgeon are harder to catch than Legends and that Eel, Albacore and Pike are the true final bosses.
 

Blauwfuur

Cowpoke
Goals! How much actions does it cost to complete goals? How many recources do you need. Of grandpa's goals, there are 3 that are completed mostly through money, being the Buildings, Animals and Money goals. Lets take the "Money" goal als a base line and look at the "Animals" goal. Now some animals are cheaper than others, but also you need to build the coop or shed first. Therefore the required recources for that goal grow non-linearly with the amount of players. Lets list the least amount of recources required per player for the animals goal:

-1p: 24 gold + 2 wood (coop and 2 chickens)
-2p: 40 gold + 2 wood (all coop animals)
-3p: 66 gold + 4 wood (and now for the barn)
-4p: 84 gold + 4 wood

Now we can already see how farm animals already requires more than double the gold that the "Money" goal, on top of extra actions to build buildings and buy animals. That is balanced by the opportunity to benefit from the collect from animals action, but the question is, does that make up for it? Now considering the buildings goal; You require about 10 gold and 2 forage tiles (wood or stone) per player plus an action to build. This can be outweighed by the benefit that the building offers. Some buildings like the farmhouse or the mill are always good, some buildings like the stable or shed have the opportunity to be good but can also go nearly un-used.

I will make a list of expected required actions for each goal after i have determined how much money you make in an action.


Money!

I have some questions about money making that I will answer for myself.

-How much money do you need to complete the game? (Which we can answer more easily thanks to above bit)
-Given this amount, what is the most action efficient way to get this money?

So where do we spend our money?
-Vault goal
-Money goal
-Build Buildings
-Buy Animals
-Upgrade Rod
-Remove Joja
-Buying Seeds


I am first looking for the absolute minimum gold required and then for a medium and worst case scenario.

In the minimum case, you remove all joja woth hearts or you dont need to remove them because they are no bother. Also you don't actually need to upgrade or play with the rod at all. And depending on the grandpa's goals, you don't need any money there either. Which leaves the vault. 6 gold per player minimum.

Assuming you get all the gold from farming and you buy new seeds when spot 3 to 5 are empty you get a single parsnip which you wil give as a gift and then every 3 other crops are worth 3, 4 and 5 gold in that order. Which means 12 gold per 3 crops and 1 cost per crop. We can now calculate how many crops we need to harvest this game.

1 player: 6 + 3 gold cost to get 3 crops worth 12 gold total. 1 action to plant.
2 player: 12 + 5 gold cost to get 5 crops worth 19 gold total. 2 actions to plant.
3 player: 18 + 7 gold cost to get 7 crops worth 27 gold total. near 2 actions to plant.

Additional questions:
-What is the effect of the mill? Is the mill worth it?
-What are the effects of watering can, hoe and the two combined?
-Is it more efficient to complete the upgrade tools goal with money for the rod or with other tools?
 
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Blauwfuur

Cowpoke
I do like to mess around with probability, maths and spreadsheets :P However probability gets complex fast so while I was looking into fishing I just produced a randomised sample of 1000 and repeated it until I had an idea of the probability :P I will try to supply it as a chart.
My Difficulty Rating
10​
9​
8​
6​
5​
4​
3​
1​
0​
Averaged actual
4​
13​
26​
42​
50​
60​
70​
88​
An Actual (sample size 1000)
4.10%​
11.10%​
27.90%​
41.20%​
49.00%​
58.60%​
70.80%​
87.60%​
Desired result
3 juminos​
3 hearts​
2 jumino​
1 stardrop​
2 hearts​
1 heart 1 jumino​
1 jumino​
1 heart​
bug meat​

What I found really interesting is that snagging a Legendary Fish by rolling a Stardrop is actually more likely than rolling 3 Hearts or 2 or 3 Junimos! Combinations needed for some non-legendary fish.
Ofcourse, just some number generator, much easier than me sitting out here going on a rant, calculating everything by head xD.
 

kailomonkey

Tiller
I did it so I could order the fish by difficulty to catch for the checklist I was making... Then ended up sorting alphabetically anyway because it suited a checklist better, easier to locate your caught fish. Also calculated value per difficulty.

I think a difficulty with working out your gain per fishing action is going to be representing what will likely be in the fishing track. For example you'd probably only pick out Trash if you didn't roll a fish, and I have the numbers for every fish, but I just don't know what's going to be in the track!

The chance of you getting at least a single Heart is 1-1/2^3 (opposite of chance of not getting a Heart on all 3 dice) so 87.5% just note I did some maths in my head at this level :P
 
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DJModulo

Sodbuster
Lets start with the non-animal dice: 3 hearts, 2 junimo's and 1 stardrop on eacht die. Hence a 50% to roll hearts for example. I will abbreviate these sides with H, J and S respectively. Now lets see what that means for the chances in the game.

Mining. Mining uses 2 dice, and so every chance is a product of 2 6-sided dice. Therefore i will be writing down everything as a chance out of 36. Not that 2 different die results (for example H+J) are doubled because either the first die is a heart and the second a junimo, or the other way around. Hence twice the chance.

H+H = 9/36 = 1/4
H+J = 12/36 = 1/3
H+S = 6/36 = 1/6
J+J = 4/36 = 1/9
J+S = 2/36 = 1/18
S+S = 1/36

So looking at any given mine map, these are the numbers to keep in mind when you are hoping for certain results. It also puts in perspective how effective the first pickaxe upgrade realy is (not very imo)
Funnily enough, I actually consider the Copper Pickaxe upgrade to be quite decent and the Steel upgrade to be the terrible one (Gold(!) and Iridium easily truncate them though)

I'll attempt to model the effect by looking at the possible number of fields that can be chosen by mine roll and pickaxe upgrade (assuming no skull was hit):

StarterCopperSteelGoldIridium
H+H11134
H+J23368
H+S23467
J+J12359
J+S24568
S+S12334
Weighted average~1,56 (56/36)2,25 (81/36)~2,61 (94/36)~4,72 (170/36)~6,39 (230/36)

This chart doesn't take into account how the good rewards are generally skewed towards the stardrop rolls (another point in favor of the gold and especially Iridium pickaxe).
 

Blauwfuur

Cowpoke
I did it so I could order the fish by difficulty to catch for the checklist I was making... Then ended up sorting alphabetically anyway because it suited a checklist better, easier to locate your caught fish. Also calculated value per difficulty.

I think a difficulty with working out your gain per fishing action is going to be representing what will likely be in the fishing track. For example you'd probably only pick out Trash if you didn't roll a fish, and I have the numbers for every fish, but I just don't know what's going to be in the track!

The chance of you getting at least a single Heart is 1-1/2^3 (opposite of chance of not getting a Heart on all 3 dice) so 87.5% just note I did some maths in my head at this level :P
I was thinking we could simulate a random fishing track, representing "the first time you fish" in a game, then having the programme choose a fishing location based on the highest expected yield and that would be a decent answer? But like thats a lotta work prolly.
 

kailomonkey

Tiller
I was thinking we could simulate a random fishing track, representing "the first time you fish" in a game, then having the programme choose a fishing location based on the highest expected yield and that would be a decent answer? But like thats a lotta work prolly.
Nice. I was thinking it will be hard maths wise but a simulation wouldn't be so hard. Might give it a go and see what results come out :)

Well in spreadsheet form I didn't get very far except some abstract numbers like about 1.5 gold per dice from Ocean or Lake and 1.2 gold per dice from River. It's pretty much meaningless as a shortcut to getting something out of nothing. Conceding it will take a lot more work to get something useful :P
 
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Blauwfuur

Cowpoke
Sooo I've written some code... Which doesnt work yet cuz i dont have the data set yet.
It will prioritize a fishing spot where you can catch two fish that both need 2 junimo's that you can't both catch over a fishingspot where you have a chance to catch 2 fish in 1 roll, so it isnt perfect. It will also catch fish from left to right, not from highest value to lowest value. Also i dont understand libraries, only arrays. Anyway here it is. I had to convert it from python to text to upload.
 

Attachments

kailomonkey

Tiller
Cool. Here's the fish bag data to save you going through the tiles, if you wish. Chest value is just an arbitrary value I came up with.
Fish​
Location​
Value (gold)
Hearts
Junimos
Stardrops
Bugmeat
Qty (if >1)​
Chest​
Any​
20
3​
Algae​
Any​
0
Broken CD​
Any​
0
Driftwood​
Any​
0
Glasses​
Any​
0
Newspaper​
Any​
0
Trash​
Any​
0
Octopus​
Ocean​
3
3
Tuna​
Ocean​
3
3
Albacore​
Ocean​
2
3
Eel​
Ocean​
2
3
Pufferfish​
Ocean​
4
2
Super Cucumber​
Ocean​
4
2
Squid​
Ocean​
2
2
Crab​
Ocean​
3
1
Lobster​
Ocean​
3
1
Clam​
Ocean​
2
1
Cockle​
Ocean​
2
1
Shrimp​
Ocean​
2
1
Mussel​
Ocean​
1
1
Oyster​
Ocean​
1
1
Crimsonfish​
Ocean​
6
1
Red Snapper​
Ocean​
2
2
Halibut​
Ocean​
2
1
1
Red Mullet​
Ocean​
2
1
1
Tilapia​
Ocean​
2
1
1
Sea Cucumber​
Ocean​
2
1
Anchovy​
Ocean​
1
1
Herring​
Ocean​
1
1
Sardine​
Ocean​
1
1
Lingcod​
Lake​
3
3
Pike​
Lake​
3
3
Sturgeon​
Lake​
4
2
Crayfish​
Lake​
2
1
Snail​
Lake​
2
1
Periwinkle​
Lake​
1
Legend​
Lake​
7
1
Angler​
Lake​
5
1
Chub​
Lake​
2
2
Largemouth Bass​
Lake​
3
1
1
Bullhead​
Lake​
2
1
1
Rainbow Trout​
Lake​
2
1
Smallmouth Bass​
Lake​
2
1
Carp​
Lake​
1
1
Pike​
River​
3
3
Tiger Trout​
River​
3
3
Catfish​
River​
4
2
Dorado​
River​
3
2
Crayfish​
River​
2
1
Snail​
River​
2
1
Periwinkle​
River​
1
Glacierfish​
River​
6
1
Perch​
River​
2
2
Bream​
River​
1
2
Salmon​
River​
2
1
1
Walleye​
River​
3
1
Shad​
River​
2
1
Sunfish​
River​
1
1
 

Koganei

Newcomer
Lets start with the non-animal dice: 3 hearts, 2 junimo's and 1 stardrop on each die. Hence a 50% to roll hearts for example. I will abbreviate these sides with H, J and S respectively. Now lets see what that means for the chances in the game.

Mining. Mining uses 2 dice, and so every chance is a product of 2 6-sided dice. Therefore i will be writing down everything as a chance out of 36. Note that 2 different die results (for example H+J) are doubled because either the first die is a heart and the second a junimo, or the other way around. Hence twice the chance.

H+H = 9/36 = 1/4
H+J = 12/36 = 1/3
H+S = 6/36 = 1/6
J+J = 4/36 = 1/9
J+S = 2/36 = 1/18
S+S = 1/36

So looking at any given mine map, these are the numbers to keep in mind when you are hoping for certain results. It also puts in perspective how effective the first pickaxe upgrade realy is (not very imo)

Possible further answers i might calculate and edit this post for:
-the effect of the pickaxe upgrade on these chances
-when added up all results of the level maps, what is the expected yield of a random unupgraded mining action, spread across the types of recources you can get
J+S should be 1/9.
 
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