There is some evidence that 2 artillery is sufficient to deal with 3 tyrants, but the amount of data is a bit small. I couldn’t see any other change I could make which wouldn’t lead to at least some measurable risk of loseing. Risking being eaten to impress my superiors feels like a poor trade off, especially as they should hopefully be at least somewhat impressed with winning a battle at 10:16 odds, so I will stick with my initial selection. (Though I’m pretty sure that someone who was willing to take some risk of being eaten for extra prestige would be well advised to take one fewer artillery.)
Yonge
Karma: 140
The more soldiers that come, the higher the chance of victory. We however will be outnumbered by at least 6, and previous squads that were outnumbered this badly only won 58 percent of the time.
There is no massive difference where the presence of one weapon and alien leads to victory, or where an alien is present but a weapon absent leads to defeat.
Looking at the cases where 1 soldier fought 1 alien:
- Artillery reliably win against venomopede, tyrants, scarab (only 8 records), crawlers, abominations
- Flamethrowers reliably beat crawlers, scarabs (only 5 records), normally win against venomopede, but normally lose to abominations, and consistently lose to tyrants.
- Grenades reliably win against abominations, crawlers, scarabs (only 6 records), venomopede normally win against tyrants—
Lance reliably win against venomopede, scarab (only 6 records), crawlers, abominations normally win against tyrants
- Minigun reliably wins against crawlers, scarab (only 3 records), venomopede reliably loses against abominations, tyrants
- Phaser reliably wins against venomopede, scarab, crawler, normally wins against abomination reliably loses against tyrants
- Torpedoes reliably wins against abominations, crawlers, scarabs (Only 5 records), venomopede normally wins against tyrants
Tyrants look like the strongest enemy followed by abominations.
When 1 soldier faced 2 abominations they always lost unless they either had torpedoes, lance or artillery. Torpedoes seem best but aren’t perfect.
When 1 soldier faced 2 crawlers they always won if they were equipped with grenades, lance or phaser.
When 1 soldier faced 2 scarab they always won unless they were equipped with artillery or torpedoes.
When 1 soldier faced 2 tyrants they always lost unless they were equipped with artillery which won about half the time.
When 1 soldier faced 2 venomopedes they always won if they were equipped with grenades or lances
When 2 soldiers go into battle they are never equipped with the same weapons.
When 2 soldiers faced 3 tyrants the only combinations with victories were (torpedoes + mini gun and torpedoes + lance). 1 Artillery was insufficient. Suggest 1 artillery is insufficient to deal with 3 tyrants.
Looking at battles where only scarabs are present suggests the following limits on the number that can be defeated by a single type of weapon reliably:
- Artillery and tropedoes: 1
- Grenades and lances: 2
- Rifles and flamethrowers: 3
- Phasers: 4
- Minigun: 5It looks like that if you have enough weapons to reliably win against each type individually then you will win reliavbly against the group.
This suggests that the following would give us a 100 percent—epsillon chance of victory:
- 3 artillery (Deals with Tyrants)
- 2 mini guns (Deals with Scarabs)- 3 torpedoes (Deals with Abominations)
- 1 grenade (Deals with crawlers/venompede)
- 1 lance (Deals with crawlers/venompede)I suspect it can be done with fewer soldiers, however this is my provisional lineup if I don’t get a chance to look at this further.
>!Grey turtles have a much lower weight than most 3.9->7.9
Greyish green turtles have a lower weight then the green ones, though the ranges overlap. Lowest 13 highest 42.9
There is a big spike in the number of green turtles with a weight of 20.4
Suggests we are dealing with multiple distinct species.
The spike in green turtles with a weight of 20.4 all have 6 shell segments.
No green turtle with 6 shell segments has a weight other than 20.4.
Therefore Harold has a weight of 20.4
All gray turtles have fangs, and no other coloured turtles do. Means we can ignore this as any effect will be entirely contained in the colour.
There appears to be a slight increase in weight with the number of wrinkles, scars, shell segments, and miscellaneous abnormalities, though the rate of increase depends on shell colour, and to a lesser extent on nostril size.
Fitting a linear model explains just under 80 percent of the variation for grey turtles, and a little over 50 percent for the rest.
There is no obvious pattern to the deviations, and there is clearly a lot of randomness as a lot of identical turtles have widely differing weights.
My best estimate for the weights of the turtles based on the linear model is as follows:
Abigail 20.0
Bertrand 17.3
Chartreuse 22.8
Dontanien 19.2
Espera 16.5
Flint 6.8
Gunther 25.5
Harold 20.4
Irene 21.7
Jacqueline 18.6
If I wanted to maximise my income from the constitutional despot I should bump up the estimates a bit, however I don’t need the money, and frankly my reputation as an honest scholar is worth more than a few gp. And who knows if enough people ignore perverse incentives like this he may stop offering them and become a less wrong constitutional despot? I can dream at least. As for the unflattering portrait, you can always judge someone by the quality of the pepole you have offended. Coming from him that is going to be seen as a compliment by the people that I care about, not an insult. So I will just give him my best estimates and move on.
Looking at this further, by far the strongest effect is the latitude, and that looks more like a rectangular effect than a trigonometric one. Replacing the trigonometric fit with one that modelled a rectangulat latitude effect and no other yielded a model that explained most of the variation. By itself this looks better than the previous model.
The next biggest effect looks like it is due to variation in murphys constant. This looked vaguely quadratic.
The next biggest effect looked like it was due to variations in the value of Pi. It looked vaguely triangular, with the point ust below 3.15.
The next biggest effect looked like a vaguely sinusoidal variation due to the longitude.
Including all of these in a model yielded one with a standard deviation of 4.9, and predicted that the following 12 locations were the best:
76804 VALUE:87.95301643603202
16965 VALUE:88.18566645580597
104815 VALUE:88.34280034001172
8415 VALUE:88.39346893009704
18123 VALUE:88.50303192064138
107929 VALUE:88.5221749787355
99595 VALUE:88.59004262250107
80395 VALUE:88.59313676878352
42742 VALUE:88.72736581213306
40639 VALUE:88.80584599223495
65607 VALUE:90.36919375244607
94304 VALUE:90.63981001558145This is currently my best estimate. As the predicted values are all < 100 I will have to file a report on this with the empires colonisation department in case there is every any interest in making another attempt, but I won’t risk the empresses’ rath by attempting to colonise any of them.
Thank you for posting this. My findings are as follows:
Only 2 existing locations have > 100 performance. Both of these have:
- No strange smell
- Mint air
- Adequate Feng Shui
Most other high performers (But sub 100) have the same properties. Addittionally the weird sounds of the high performers are either:
- Eerie Silence
- Otherworldly Skittering
This suggests it would be sensible to restrict ourselve to locations with these properties. This alone increases the average performance from 23.12 to 46.92High values of murphys constant are bad, though the affect seems to become small at around 3.5. There is some evidence to suggest that amongst the high performing section (But not the others) too low a value of murphys constant would be counterproductive, though it is a small affect. It may be a statistical fluctuation. Restricting to locations with a value < 3.5 would leave an average of 62.77
A value of pi below the normal value also looks harmful, though one that is too high also looks counterproductive. It looks like a relatively modest effect though and I don’t wan to exclude too many possible locations, so I won’t exclude any locations based on the value of pi.
There are few high performing ones between latitude −38 and +38.
There are few high performing ones around shortitude 0, and +-90
There are few high performing ones around deltitude 0, and +-90
But this might be caused by the small number of bases in these areas.I then fitted a simple linear trigonometric model to the records that had the other properties that were identified with high performance. This gave the following model:
90.40498684665667+1.0177516945528096*sin(deltitude)+11.356095534597717*cos(deltitude)-0.17160136718146096*sin(shortitude)+14.734915658705445*cos(shortitude)-2.41427525418688*sin(latitude)-62.034325081735766*cos(latitude)+5.158741059290979*sin(longitude)+8.287780468342245*cos(longitude)
Standard deviation of error is 13.19479724158273 The no of records was 180I found that the standard deviation error was reduced when degrees were converted to radians using the local value of pi, so that is what was used.
This predicts that the following 12 possible locations have the best performance:
38730 VALUE:110.47214318466737
103420 VALUE:110.67976641439135
91328 VALUE:111.69109272372066
26403 VALUE:112.35848311090837
7724 VALUE:112.40205758474453
21409 VALUE:113.21091851443907
89352 VALUE:113.88444725998731
3090 VALUE:113.89351821821175
65317 VALUE:121.11038526877846
57364 VALUE:123.12690147352956
26627 VALUE:132.5469987591373
91627 VALUE:134.17450784571542
In practice I think it is unlikely that all of them will be greater than 100, but it looks like it will probably be good enough to please the empress.
My best estimate is:
Hammer Hurler
Matchlock Marauder
Professor PyroThis is also my entry for the PvP contest
I found this problem late. Could I have an extra day or two please?
I think this would have worked better if there had been less data. Looking at the other responses I’m not convinced that adding serval hundered thousand addittional rows did anything significant other than to extend the time needed to scan across this. This stopped me doing a more extensive analysis.
Also I found this one less interesting than the previous ones. I suspect a lot of this has to do with the introductory storyline which didn’t make much sense to me. Possibly this was because I hadn’t heard of the “homestuck” story before, and didn’t have any relevant pre-existing context to relate this to.
I found this one much more difficult to get into than the other problmes in the series. Possibly irrationally I suspect this is because the back ground story was rather convoluted. I was able to load all the data, though it took about 20s to scan all over it which felt like an inconvenient delay.
Based on a rather cursory analysis I hope that the following two won’t be too bad:
Page of Hope and Heir of Space
I haven’t had a chance to analyse any effects that depend on Waking-Time yet. But based on the other data every other Snark that was hunted that matched one of B/G/H/P/Q/Y was successfully hunted so if this was for real I would play it safe and go with:
B G H P Q Y
To maximise value:
A B C D G H J K L M N P Q R V W Y
Looks like it will yield an expected value of just over 14, albeit with an uncomfortably low 84 percent chance of survival. This is my provisonal entry to the bonus task if I don’t get a chance to analyse Waking-Time dependant effects.
Thank you for posting this. I didn’t think this was too straightforward. Prior to reading the solution I actually thought it was one of the more difficult ones. Possibly because I focused on trying to copy the allocation helms early choices instead of on the ratings.
Some traits definitely go better with some houses, however I couldn’t see much in the way of clear cut rules. I constructed the following highly provisional allocation by considering students that were sorted when the helm was still reasonably reliable, and then combining the probabilities of a student with each of the 5 ratings being sorted into each house, and selecting the one which on balance seemed most likely.
A Dragonslayer
B Thought-Talon
C Serpentyne
D Dragonslayer
E Humblescrumble
F Serpentyne
G Dragonslayer
H Humblescrumble
I Humblescrumble
J Thought-Talon
K Dragonslayer
L Dragonslayer
M Dragonslayer
N Dragonslayer
O Serpentyne
P Thought-Talon
Q Dragonslayer
R Humblescrumble
S Serpentyne
T Humblescrumble
After staring at the data a bit more:
Woodcutters are only valuable at low coal levels. At coal level 1 an extra miner is consistently more valuable than a woodsman
Brewers seem to be actively harmful to fort value.
There is a big fall in fort value when no warriors are present.
The previously observed drop off in the value of additional miners after 5 seem to occur because it makes it less likely for other valuable types to be present, not because it is intrinsically bad. 6 miners and 2 smiths/crafters seems to be much better than 5 miners and 3 smiths/crafters.
My final selection for the fort of Magh Loduhr is therefore:
4 farmers
6 miners
1 smith
1 crafter
1 warrior
Some more observations:
- Having no farmers, brewers or warriors leads to 100 percent expedition failure. If there is a warrior present there is a small chance of success (Raiding for food?).
- The chances of failure when there are >= 4 farmers present and no brewers/warriors is statistically indistinguishable from about 99.5 percent regardless of the number of farmers. 3 farmers with no warriors/brewers gives a much lower success rate. Adding warriors only makes a distinguishable difference when the number of farmers is small.
− 4 brewers and no farmers/warriors do about as well as the farmers, but 3 brewers do better, but 1 or 2 do worse. Adding warriors only makes a difference when the numbers of brewers is small.
- Looking at forts with 4 farmers the additional value of each additional miner decreases, so we shouldn’t go too miner heavy. In particular there is a sharp decrease after 5.
− 3 miners and 1 smith is better on average than 4 miners. 2 miners and a smith is about as good as 3 miners when no crafters are present. A similar pattern holds for crafters.
- Crafters do better than average when silver or hematite is present, a bit better than average when tin or copper are present, but don’t do well with magnetite or gold
—Smiths do better than average when hematite is present , a bit better than average when tin and copper are present, average when magnetite is present, but worse than average when silver or gold is present.
- Warriors do better than average when copper and hematite, about average when hematite, magnetite and silver is present and worse than average when gold is present
- The average for smiths is better than for crafters which is in turn better than warriors.
Which lead me to the following provisional roster
− 4 farmers
− 5 miners
− 2 smiths
− 1 crafter− 1 warrior
-
A few observations:
- There is a weak correlation between expedition size and the probability of the fort surviving, so we should choose 13 dwarves.
- Farmers and brewers are crucial to the survival of the city. Specialising in one type seems more efficient than having both. 6 farmers or 6 brewers guarantee survivial, but if you have a mixture you need at least 10. Farmers seem slightly better than brewers. 3 farmers give > 99 percent survival, but 4 brewers are needed to do as well. Warriors marginally increase survival odds when there are fewer farmers and brewers, but nothing else seems to have a positive impact.
- Miners seems to generate most of the value
- Having one woodcutter offers a meaningfull boost, but there doesn’t seem to be much benefit in haveing more. The boost is biggest at low coal values
- Forts with 2 warriors seems to do best, though the gap between 1 and 2 seems to be modest, and maybe due to them haveing fewer lower value types.
- Haveing 1 smith provides a modest beenfit, though haveing more is counterproductive.
- Crafters are similar to warriors, except the effect is much smaller.
- When no smiths or craftsmen are present then the for value is significantly reduced.
- Smiths and crafters do better when different resources are present.
Which suggests something like this is needed to maximise value, subject to the constraint of minimising the risk of loseing the fort:
− 6 farmers
− 1 warrior
− 1 crafter
− 1 smith
− 4 miners
An alternative strategy which accepted a small risk of fort loss in exchange for makeing much more money would be:
− 3 farmers
− 1 warrior
− 1 woodcutter
− 1 crafter
− 1 smith
− 6 miners
I only had time for a very superficial analysis, however hopefully the following isn’t too bad:
Rainbow Rays of Rahl
Alatar’s Abyssal Armor
Solomon’s Solar Shield
* When Monstrous Regeneration and Anomalous Agility is assigned to every hero it results in a
* 36 percent win rate. When they are chosen there is only a 21 percent win rate. The sample
* size is to big for this to be dismissed as a statistical fluctuation. With the DM ruling out
* any difference in God assigned cheats or other time dependent effects it looks like heroes
* are making their decisions based on some hidden variables we don’t have access to.
*
* Many combinations of traits assigned by the Chaos deity also show substantial differences
* (sometime better, sometimes worse), than when they are chosen. This suggests the provisional
* decision to go with Radiant Splendor + Enlightenment probably isn’t optimal after all.
*
* The best set of traits chosen by the Chaos Deity for Heroes in our class is :
* Temporal Distortion + Anomalous Agility. (95 percent win rate based on 20 records)
* Barrier Conjuration + Mind Place (92.3 percent Win rate based on 13 records).
* Rapid XP Gain + Monstrous Regeneration (91.7 percent win rate based on 12 records)
* Barrier Conjuration + temporal Distortion (88 percent win rate based on 25 records)
*
* Temporal Distortion + Anomalous Agility does almost as well when these cheats are chosen as well.
*
* On balance I think it would be a good idea to change my cheats to:
* Temporal Distortion + Anomalous Agility.
For heros with our traits:
- Temporal Distortion and Rapid XP gain are the best 2 overall which seem to work well with anything. The best single combination however is Enlightenment + Radiant Splendor (94 percent win rate). Shapeshifting is just terrible and should always be avoided. The others work well with some traits, but not with others;
The following combinations are very poor (< 1⁄2 win rate) and should not be given to other heroes like me:
- Anomalous Agility + Barrier Conjuration
- Anomalous Agility + Monstrous Regeneration
- Anomalous Agility + Uncanny Luck
- Barrier Conjuration + Monstrous Regeneration
- Barrier Conjuration + Uncanny Luck
- Enlightenment + Hyper Competent Dark Side
- Enlightenment + Monstrous Regeneration
- Hyper Competent dark Side + Mind Place
- Hyper Competent Dark Side + Radiant Splendor
- Hyper Competent Dark Side + Uncanny Luck
- Mind Place + Uncanny Luck
- Monstrous Regeneration + Radiant Splendor
- Monstrous Regeneration + Uncanny Luck
- Rapid XP Gain + Uncanny Luck
When looking at records for all trait a different picture emerges. Here MindPlace is the ability that is terrible, and shapeshifting does reasonably well with anything except MindPlace. The only terrible combos (< 1⁄2 chance of success ) which don’t involve MindPlace are:
- Anomalous Agility + Barrier Conjuration
- Barrier Conjuration + Monstrous Regeneration
- Enlightenment + Hyper Competent Dark Side
- Hyper Compenetent Dark Side + Radiant Splendor
- Hyper competent Dark Side + Uncanny Luck
Radiant Splendor and Enlightenment still does best overall though.
In general our traits seem to be somewhat below average, but Radiant Splendor + Enlightment still looks like a very strong combination. This combination was noticeably less successfull (6/12 times) for heros with our traits when the Chaos deity was involved. The sample size is small, and the effect doesn’t show when all heroes are considered, so this might be a statistical fluctuation; however it may be an idea to avoid further dealing with this deity, just in case it is giving inferior versions of traits to heroes like me to spread chaos.Provisional Decision: Go with Radiant Splendor + Enlightenment
Thank you for posting this.
The need to join to other records was trivial for me.
I think the data model was too complex too fully decipher with a reasonable amount of effort, but this wasn’t a problem as it wasn’t necessary to get a decent answer (I might actually have got the optimal one if I hadn’t blundered and missed that Italia suffered a famine in the previous year—though I was uncertain on a number of points and wasn’t expecting to do as well as I did). In particular the wealth/population dependency completely passed me by.
Overall in terms of difficulty it felt OK.
Those apprenticed under Escher, Geisel, and Penrose never produce impossible structures. Those apprenticed under Johnson and Statmin always do. Self Taught architects sometimes do.
I couldn’t find a reliable way of determining which Self-Taught architects would produce impossible structures, so I will have to go with four of D, E, G, H, K.
All the really cheap structures are made out of wood and dreams. Unfortunately none of the 5 architects proposals have these materials. Excluding these the next cheapest ones are all made out of 2 of wood/dreams/steel, the next set have Glass and one of the other 3, this suggests K will be cheapest. Silver is the next cheapest, so we want D, E and H.
My submission is therefore : D, E, H, K