Optimizing Fellowship Adventure

[Sir Derf]

Map 1, No Crossovers (The obvious routes)

Square-hours (Assuming Elves, assuming pre-built Statues)

Badge	Orange	Blue	Green
Brewer	104.16	62.5	166.66
Treant	87.5	0	87.5
Baker	500	500	500
Carpenter	1500	1500	0
Farmer	0	0	4050
Blacksmith	0	0	11400
Flacon	540 270	1560 780	0
Bracelet	900	810	900
Necklace	0	0	0
Statue	0	0	0
Wand	9	0	9
Potion	9	9	0
Hat	0	9	0
Wonder	9	18	9
Guard	0	9	0
Sack	9	26	0

Square-hours (Assuming Elves, assuming pre-built Statues)

Badge	Orange	Blue	Green
Supplies	2191.66	2062.5	16204.17
Goods	1440 1170	2370 1590	900
Spells	18	18	9
Wonder	9	18	9
Guard	0	9	0
Sack	9	26	0

Square-hours (Assuming Elves, assuming pre-built Statues)

	Orange	Blue	Green
Total Square-hours	3,631.67 3361.67	4,432.5 3652.5	17,104.17

For Map 1 direct routes, there is a clear loser, and a closer winner. The Green path is massively overpriced, primarily due to the Blacksmiths required in every segment and one of the two Crossover Waypoints. The Orange path is 18% 7.9% less expensive than the Blue, primarily due to the fewer Flacons required. Of the three pure paths, the Orange path is the minimum cost path on Map 1.

(Note, Platinum Leaf's information on Fellowship Adventures says "Blue (going up the center) is the cheapest way to open the six Switchpoints." It would appear that this is incorrect.)

It will take me a little time to rejigger my spreadsheet to evaluate the other paths...

 

[Sir Derf]

Map 2, No Crossovers (The obvious routes)

Spoiler: Basic info

Square-hours (Assuming Elves, assuming pre-built Statues)

Badge	Orange	Blue	Green
Brewer	20	13	10
Treant	7	12	0
Baker	7	13	13
Carpenter	13	26	25
Farmer	25	26	0
Blacksmith	26	0	25
Flacon	25	26	0
Bracelet	26	26	25
Necklace	0	13	25
Statue	0	13	25
Wand	0	13	0
Potion	12	13	13
Hat	0	13	0
Wonder	51	38	51
Guard	0	0	25
Sack	0	26	63

Square-hours (Assuming Elves, assuming pre-built Statues)

Badge	Orange	Blue	Green
Supplies	24597.92	11845.83	20258.33
Goods	3840 3090	10140 9380	14250
Spells	12	39	13
Wonder	51	38	51
Guard	0	0	25
Sack	0	26	63

Square-hours (Assuming Elves, assuming pre-built Statues)

	Orange	Blue	Green
Total Square-hours	28,437.92 27,687.92	21,985.83 21,205.83	34,508.33

For Map 2, there is a clear winner. The Blue path, requiring 13 Statues, is 23% less expensive than Orange and 36% 39%less expensive than Green.

 

[Sir Derf]

Map 3, No Crossovers (The obvious routes)

Spoiler: Basic Info

Square-hours (Assuming Elves, assuming pre-built Statues)

Badge	Orange	Blue	Green
Brewer	19	44	38
Treant	0	19	16
Baker	29	0	0
Carpenter	58	38	78
Farmer	0	155	120
Blacksmith	115	155	80
Flacon	75	59	0
Bracelet	75	59	75
Necklace	75	0	75
Statue	38	0	38
Wand	19	0	40
Potion	19	0	40
Hat	19	39	40
Wonder	135	135	80
Guard	65	0	0
Sack	135	155	75

Square-hours (Assuming Elves, assuming pre-built Statues)

Badge	Orange	Blue	Green
Supplies	80995.83	135322.92	88191.67
Goods	38370 36120	8850 7080	33870
Spells	57	39	120
Wonder	135	135	80
Guard	65	0	0
Sack	135	155	75

Square-hours (Assuming Elves, assuming pre-built Statues)

	Orange	Blue	Green
Total Square-hours	119,365.83 117,115.83	144,172.92 142,402.92	122,061.67

For Map 3 direct routes, there is a clear loser, and a closer winner. The Blue path is massively overpriced, primarily from Blacksmiths and Farmers. The Orange path, requiring the same 38 Statues as the Green path, is 2.2% 4.1% less expensive than the Green, primarily due to the fewer Farmers required. Of the three pure paths, the Orange path is the minimum cost path on Map 3.

(Note, Platinum Leaf's information on Fellowship Adventures says "Blue (going up the center) is the cheapest way to open the six Switchpoints." It would appear that this is incorrect.)

 

[Sir Derf]

Looking at pure paths, and assuming Elven pre-build of required Statues, it looks like the minimal set of Paths is Orange-Blue-Orange, costing 144.983.33 141,683.33 square-hours and requiring 13+38=51 Elven pre-built Statues. Picking the second choice on each map, Blue-Orange-Green, would cost 154,932.09 153,402.08 square-hours (6.8% 9.4% more expensive) and picking the worst choices on each map, Green-Green-Blue, would cost 195,780.42 194,015.42 square-hours (35% 37% more expensive).

Of note, in none of these computations would evaluating Statues at full price as opposed to half-price have changed the choice of which path to choose on each map.

 

[Giraffi]

Will be interesting to see what ratio of ws sets (5) to t1 sets you come to for optimum production of the badges. That is what you need to build and in large numbers.

As much as there is the mathematical side of playing a FA, you will also have to keep in mind the psychological side. The second part sometimes plays a far bigger role than the first.

 

[sail0r]

Nice analysis. I have also created a spreadsheet trying to find out the best paths to follow. However I didn't try to optimize time as a total. This would be needed if you are so few that it really matters. If you have 10 people in the FA that are active you can easily complete 1 path for each stage in 3-4 days.
With about 15 very active players you can easily complete all paths of all 3 stages.
Now, since completing 1 path for each stage is easy no matter if you have the absolute optimal ratio of workshops to T1 sets what I do is ask the fellows in the FA to tell me how many workshops and how many T1 sets they are going to have available for the FA. Based on the total Workshops (divided by 5) and the total T1 sets and assuming that all T1 sets will produce statues 48 hours before and the workshops blacksmiths 24 hours before the start of the FA I calculate what the optimal path per stage is.
So the input is rather random, meaning everyone can choose if he wants to have workshops or T1 sets, but everytime the optimal path was Orange-Blue-Orange.

 

[Sir Derf]

Thank you, @Giraffi

In order to work out optimum production, you first need to work out optimum needs... Minimum paths necessary to finish maps, the cost of Pit points, the cost/points comparison of extra map Waypoints (individually or as connected sequences), and then Pit needs.

As to your second point, we should probably look at individual issues, as their impacts can vary widely. However, I don;t think there are any "psychological factors" that will improve performance. If they did, then that would be captured in the math.

 

[Sir Derf]

I'm working on the assumption (that I hadn't stated, apologies) that you will have enough capacity to clear all three maps with plenty left over to do extra waypoints and/or Pit rounds. Using this information informs how to build your Shantytowns and schedule your production runs.

The minimum path to complete maps is the minimum path.
The extra waypoints with better cost-point ratios than the pit are what they are.
Now, whether you have the combined production capacity across your entire fellowship to accomplish the minimum path, or to do the desirable waypoints, that's another matter.

 

[Julian]

This discussion relates to my previous thread:
https://en.forum.elvenar.com/index.php?threads/fa-badge-requirements.11925/#post-72447

 

[Sir Derf]

In rewriting my spreadsheet to better facilitate mix-and-match paths and Waypoint/Pit comparisons, I found that I doubled the square-hour valuation for Flacons. I'll go back and adjust my numbers in the earlier posts shortly...

New numbers edited into earlier posts, tiny changes, but no shifts in which path to take.

 

[Laurelin]

Map 1, No Crossovers (The obvious routes)
[table data]

3,631.67

4,432.5

17,104.17

For Map 1 direct routes, there is a clear loser, and a closer winner. The Green path is massively overpriced, primarily due to the Blacksmiths required in every segment and one of the two Crossover Waypoints. The Orange path is 18% less expensive than the Blue, primarily due to the fewer Flacons required. Of the three pure paths, the Orange path is the minimum cost path on Map 1.

@Sir Derf : I'm a bit confused as to the fundamental purpose/application of the data and conclusions here. Do the above totals/conclusions regarding the cost per Badge/path relate only to the current type of Fellowship Adventure, or are you basing your calculations on amounts of 'Badges Required Per Path' which are the average of all known permutations of FA (types A-E1/E2)? If you've already answered this point, my apologies, but if not, wouldn't different types of FAs requiring different numbers/types of Badges to complete each Path/Stage (as well as other permutations, such as the present FA asking for four instead of five of each Badge per Pit Stage) affect the total number and type of Badges required to complete each Path, Map, and/or Pit Stage, and therefore also affect the conclusions as to cost-per-Path/Pit and/or which types of Badge are the most useful to produce?

Alternatively, has the general format of FAs changed, so that all FAs now use the same overall Badge types and totals, possibly (?) distributed differently between Paths/Stages? Or are you intending to analyse only one type of FA, with the intention of drawing conclusions which can then be applied to all possible FA Maps in future? In short: I'm not really clear as to the basis upon which you're making calculations: are they relevant to one specific FA only, or relevant to all possible FAs? Thanks in advance (and apolgies again if you've already explained your overall intentions).

 

[Pauly7]

Alternatively, has the general format of FAs changed, so that all FAs now use the same overall Badge types and totals, possibly (?)

All the most recent FAs have been E type, but as a rule badge numbers are amended from one to the next. I believe this adventure has the exact same badges as the previous, but that's the first time it's happened.

 

[Sir Derf]

Map 1 - All the paths, total points only. I have no idea what's going to happen....

1. No Crossovers
   1. Orange, Orange, Orange (3,361.67)
   2. Blue, Blue, Blue (3,652.50)
   3. Green, Green, Green (17,104.17)
2. Single Crossover
   1. Orange, Blue, Blue (3,547.08)
   2. Orange, Orange, Blue (3,022.50)
   3. Blue, Orange, Orange (4,037.08)
   4. Blue Blue, Orange (4,321.67)
   5. Blue, Green, Green (17,200.42)
   6. Blue, Blue, Green (12,865.00)
   7. Green, Blue, Blue (5,266.25)
   8. Green, Green, Blue (11,371.67)
3. Double Crossover
   1. Orange, Blue, Orange (4,216.25)
   2. Orange, Blue, Green (12,759.58)
   3. Orange, Green, Green (17,095.00)
   4. Orange, Orange, Green (12,235.00)
   5. Blue, Orange, Blue (3,697.92)
   6. Blue, Green, Blue (11,467.92)
   7. Green, Blue, Green (14,478.75)
   8. Green, Blue, Orange (5,935.42)
   9. Green, Orange, Orange (5,650.83)
   10. Green, Green, Orange (12,040.83)
4. Triple Crossover
   1. Orange, Green, Blue (11,362.50)
   2. Blue, Orange, Green (12,910.42)
   3. Blue, Green, Orange (12,137.08)
   4. Green, Orange, Blue (5,311.67)
5. Quadruple Crossover
   1. Orange, Green, Orange (12,031.67)
   2. Green, Orange, Green (14,524.17)

Well, isn't that interesting? Map 1 Orange-Orange-Blue, despite utilizing a crossover, and so doing one extra Waypoint, is actually 10% more efficient than a straight Orange-Orange-Orange. The main reason is in the Carpenters dropping from 10 to 5. Also of note, this path requires a significant increase in Spell and Other badges (+10 Spells, +13 Wonder, +5 Guard and +6 Sack)

 

[Sir Derf]

I'm mostly looking at the current FA, which is identical to the previous, including current 4 badge/pit ask.

Obviously, the number-based analysis will change if the FA changes.

What I'm most curious about is investigating whether conventional wisdom and generally accepted FA practice is really advisable.

I think it is fascinating that the minimum path on the this version of the Map 1 is arguable not a pure-color path, and I'm really curious to see what the rest of my computations will show...

 

[Sir Derf]

Map 2 - All the paths, total points only. I have no idea what's going to happen....

1. No Crossovers
   1. Orange, Orange, Orange (27,687.92)
   2. Blue, Blue, Blue (21,205.83)
   3. Green, Green, Green (34.508.33)
2. Single Crossover
   1. Orange, Blue, Blue (27,312.08)
   2. Orange, Orange, Blue (30,289.58)
   3. Blue, Orange, Orange (30,641.67)
   4. Blue Blue, Orange (28,204.17)
   5. Blue, Green, Green (37,293.33)
   6. Blue, Blue, Green (39,230.83)
   7. Green, Blue, Blue (25,980.83)
   8. Green, Green, Blue (27,373.33)
3. Double Crossover
   1. Orange, Blue, Orange (34,310.42)
   2. Orange, Blue, Green (45,337.08)
   3. Orange, Green, Green (43,399.58)
   4. Orange, Orange, Green (48,314.58)
   5. Blue, Orange, Blue (33,243.33)
   6. Blue, Green, Blue (30,158.33)
   7. Green, Blue, Green (44,005.83)
   8. Green, Blue, Orange (32,979.17)
   9. Green, Orange, Orange (35,416.67)
   10. Green, Green, Orange (34,371.67)
4. Triple Crossover
   1. Orange, Green, Blue (36,264.58)
   2. Blue, Orange, Green (51,268/33)
   3. Blue, Green, Orange (37,156.67)
   4. Green, Orange, Blue (38,018.33)
5. Quadruple Crossover
   1. Orange, Green, Orange (43,262.92)
   2. Green, Orange, Green (56,043.33)

Map 2 - You can do massively worse, but you can't do better than the Straight Blue-Blue-Blue.

 

[Sir Derf]

Map 3 - All the paths, total points only. I have no idea what's going to happen....

1. No Crossovers
   1. Orange, Orange, Orange (117,115.83)
   2. Blue, Blue, Blue (142,402.92)
   3. Green, Green, Green (122,061.67)
2. Single Crossover
   1. Orange, Blue, Blue (163,877.92)
   2. Orange, Orange, Blue (169,646.67)
   3. Blue, Orange, Orange (139,440.83)
   4. Blue Blue, Orange (162,382.08)
   5. Blue, Green, Green (136,686.67)
   6. Blue, Blue, Green (127,452.08)
   7. Green, Blue, Blue (178,027.92)
   8. Green, Green, Blue (183,092.50)
3. Double Crossover
   1. Orange, Blue, Orange (183,857.08)
   2. Orange, Blue, Green (148,927.08)
   3. Orange, Green, Green (158,161.67)
   4. Orange, Orange, Green (154,695.83)
   5. Blue, Orange, Blue (191,971.67)
   6. Blue, Green, Blue (197,717.50)
   7. Green, Blue, Green (163,077.08)
   8. Green, Blue, Orange (198,007.08)
   9. Green, Orange, Orange (175,065.83)
   10. Green, Green, Orange (203,071.67)
4. Triple Crossover
   1. Orange, Green, Blue (219,192.50)
   2. Blue, Orange, Green (177,020.83)
   3. Blue, Green, Orange (217,696.67)
   4. Green, Orange, Blue (227,596.67)
5. Quadruple Crossover
   1. Orange, Green, Orange (239,171.67)
   2. Green, Orange, Green (212,645.83)

Map 3 - You can do massively worse, but you can't do better than the Straight Orange-Orange-Orange.

 

[Sir Derf]

So, the final minimized set of paths to complete the three maps would appear to be:

	Map 1	Map	Map 3	Total
	Orange-Orange-Blue	Blue-Blue-Blue	Orange-Orange-Orange
Points	2000​	3000​	4500​	9500​
Supplies	1462.50​	11845.83​	80995.83​	94304.17​
Goods	1560​	9360​	36120​	47040​
(Statues)	0​	13​	38​	51​
Spells	28​	39​	57​	124​
Wonder	22​	38​	135​	195​
Guard	5​	0​	65​	70​
Sack	15​	26​	135​	176​
Square-hours	3,022.50​	21,205.83​	117,115.83​	141,344.17​

	Map 1	Map 2	Map 3	Total
	Orange-Orange-Blue	Blue-Blue-Blue	Orange-Orange-Orange
Points	2000​	3000​	4500​	9500​
Brewer	6​	13​	19​	38​
Treant	2​	12​	0​	14​
Baker	5​	13​	29​	47​
Carpenter	5​	26​	58​	89​
Farmer	0​	26​	0​	26​
Blacksmith	0​	0​	115​	115​
Flacon	25​	26​	75​	126​
Bracelet	9​	26​	75​	110​
Necklace	0​	13​	75​	88​
Statue	0​	13​	38​	51​
Wand	9​	13​	19​	41​
Potion	14​	13​	19​	46​
Hat	5​	13​	19​	37​
Wonder	22​	38​	135​	195​
Guard	5​	0​	65​	70​
Sack	15​	26​	135​	176​

 

[Sir Derf]

I think I'm going to take a little break at this point... Next up, the possibly controversial topic of "Are extra Waypoints worth it?"

 

[C-Nymph]

I think I'm going to take a little break at this point... Next up, the possibly controversial topic of "Are extra Waypoints worth it?"

Only if you want to go for the big points, otherwise, no.
But if you decide you want to try for top 3, then calculating which waypoints to skip is important, as some badges are worth more when spent in the pit than when they are spent on a waypoint. Not just point/badge ratio, but point/production hour ratio. For waypoints requiring 65 blacksmiths, the 300 points they give is a terrible reward for spending 1440 production hours (and that's only looking at the blacksmiths, as waypoints require 3 types of badges). Those production hours when spent on badges for the pit could be worth a whole lot more points. Choose wisely where you spend your badges as you can only spend them once and time is finite in the FA
Also, communication is key when you decide to skip certain waypoints. Make a plan, share it with all fellows well before the start, so everyone knows what the plan is, and remember to send out reminders often, people tend to 'forget'.

 

[Sir Derf]

Extra Waypoints...

So, you've completed the waypoints for the minimum path for your map. Should you do any of the remaining Waypoints before ending the map? What you're really asking is, "Would the time I spend on Badges that would go to that Waypoint(s) give more points than if I spent that time on Badges that will go to the Pit?"

So, what is the Pit worth?

Currently, the Pit is best analyzed as the repeating sequence of three different Waypoints, that collectively want 4 each of Brewers, Treants, Bakers, Carpenters, Farmers, Blacksmiths, Flacons, Bracelets and Necklaces, and collectively giving 150 points. All together, the Square-hours needed to produce all those badges is 5,798.33. This is a Square-hour/point of 38.66.

[Earlier FAs had pits that wanted 5 of each badge, so had a cost of 7,248.33 square-hours, and still gave 150 points total, so the magic number at that point was 48.32.]

So, the decision we are making is whether or not extra expenditures are less expensive (< 38.66) or more exxpenseive (> 38.66).

This decision can take two forms. If an accessible waypoint is, on its own, < 38.66 sh/p, than that is a Waypoint worth collecting. The reverse, however, is not necessarily true, in that if an accessible waypoint is, on its own, > 38.66 sh/p, that does not necessarily rule out that Waypoint. In that case, we need to continue analyzing the aggregate ratio of additional newly-accessible waypoints after that one. If a a chain of waypoints collectively achieves a < 38.66 sh/p ratio, then that group is worth collecting. If the group stays above 38.66 sh/p then that whole group gets rejected.