Monster slaying cost

[Daedalus]

I've been at it some more with the math, so time to errata the underlined statement. Hope I'm right this time.

Exposed facing also affects the actual threat to Heroes quite a bit, but that can't be regularly modeled due to the variables of combat. Two (or more) monsters attacking a Hero on the same turn are more dangerous than two (or more) monsters that may only attack in single file. Until one of the monsters is killed, the extra monster adds it's MSC twice for each turn it out-numbers a Hero and attacks. Likewise, if two Heroes attack a single Chaos Warrrior, it will be killed that much quicker. I guess halving it's avereged MSC would account for this if it alternated attacks between the two Heroes. The program only accounts for 1 monster in combat with one Hero. -[edit] This limits the application of the model to actual combat, but judging things in a simplistic fasion still has some level of usefulness when judging the difficulty of a Quest. A Quest designer should try to account for likely number of attacks the Heroes will encounter in a room or corridor when figuring the difficulty.

The combined MSC for multiple monsters targeting a single Hero, which represents the total damage against the Hero before all of the monsters are eliminated, appears to be governed by an ascending sequence 1, 3, 6, 10.... Since attacks from the monsters of the main system are only possible from 4 adjacent squares, it then tops out, adding 4 for each additional monster: ...14, 18, 22.... Some diagrams to illustrate:

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M = monster    H = hero   MSC of 1.0                                   M  M         M  M  M
                                                       M
                                      M                             M  H  M         M  H  M
                      M                             M  H  M
        M                             H  M                             M               M 
                      H  M                             M                          Turn 1: 4.0
        H                             M                           Turn 1: 4.0     Turn 2: 4.0
                                                  Turn 1: 4.0     Turn 2: 4.0     Turn 3: 4.0
                                  Turn 1: 3.0     Turn 2: 3.0     Turn 3: 3.0     Turn 4: 3.0
                  Turn 1: 2.0     Turn 2: 2.0     Turn 3: 2.0     Turn 4: 2.0     Turn 5: 2.0
  Turn 1: 1.0     Turn 2: 1.0     Turn 3: 1.0     Turn 4: 1.0     Turn 5: 1.0     Turn 6: 1.0
                                                                                 
  Total = 1.0     Total = 3.0     Total = 6.0     Total = 10.0    Total = 14.0    Total = 18.0


For other MSCs other than 1, multiply the appropriate ascending sequence number by the MSC to be used. For example, a Hero with 2 AD and 2 DD facing a single Goblin uses a MSC of 0.6, so the MSC of 4 Goblins attacking the Hero at once would be 10 x 0.6 = 6.0.

Should a Hero manage to reduce his facing, then the top-out principle can be applied with less than 4 opponents. For example, fighting from a corner, a Hero can only be attacked by 2 monsters. Using the same Hero and 4 Goblins from the expample above, the MSC would come to 2 Goblins x 0.6 for the first 2 turns, or 2.4. The last 2 turns has all (2) Goblins adjacent, so use the ascending sequence number of 3 x .6 = 1.8. Totaling the 2 sets of turns, the full MSC is 4.2. Fighting the same Goblins from a doorway would shrink the MSC down to 2.4 (0.6 for 4 turns).

The diagrams can also be applied to a Hero facing different monsters at once. Assume the most dangerous monster is attacked before a weaker one. To illustrate, the same Hero from above is used (2 AD, 2 DD), but 2 Orcs (1.3 MSC) and 2 Goblins (0.6 MSC) are substituted as the opponents. First figure the MSC of the Orcs seperately: 3 x 1.3 = 3.9. Temporarily ignored, the Goblins count as 2 x .6 = 1.2 for those 2 turns, or 2.4 total. When the Hero has finished the Orcs, he then uses the Goblins ascending sequence value of 3 x 0.6 = 1.8 to determine the last 2 turns of combat. Totaling all the values gives 3.9 + 2.4 + 1.8 = 8.1 as the final MSC.

[thequester]

Thanks for the patience guys! Yes, I am really busy, but managed to find some time for a bit more crunching and writing. But first, answers.

It's interesting how at higher Hero Defend Dice and Attack Dice combinations the differences in the monster slaying costs even out. The top right of the table shows this with a Goblin, Skeleton, and Zombie all having identical slaying costs of . 2 and .1. Anybody designing a Quest for powerful Heroes should take note.

I agree, they should The truth is that the msc for Goblins, Skeletons, and Zombies do not become totally identical, they still differ on maybe the third or fourth digit, but we cannot see that in the tables as the numbers here do not have that many digits. Another point is that, in order to have enough precision for more digits, the calculations would have to run an extra many million times.

It's also worth noting that slaying costs for weaker monsters are identical with different Hero combat dice combinations, as long as the dice totals are the same. For instance, a Goblin's slaying cost is .3 vs. any combat dice combination that totals 6, .2 vs. a dice combo of 7 or 8, and .1 vs. a combo of 9.

I wouldn't count on this as a rule. Again, not all decimals are shown (or calculated), and since there are different probabilities for being lucky with attack dice as opposed to defence dice, I would expect just summing them would give inaccuracies. These inaccuracies might only become visible for reeeally powerful heroes though. (Or kick in when we combine a lot of msc numbers in further calculations)

One thing I'm wondering is how does the number of weaker monsters compare to the smaller number of multiple BP monsters. By this I mean does a single Hero with 2 Attack Dice and 3 Defend Dice set against 1 NA Chaos Warrior (msc=6) fair equally well against 6 Orcs (msc+1), or 12 Goblins (msc=.5)? A Hero has just one attack on his turn, so the most Goblins he can kill is one, even if he rolls 2 Skulls and must waste one. Those 2-skull events are applied more efficiently against a NA Chaos Warrior that has a 4 in 6 chance of defending and has 3 Body Points. Does the computer model already reflect this advantage granted to weaker, but more numerous monsters?

Interesting thoughts! For me, considering those kinda situations is not a simple task. The computer program really is just very simple (and dumb ) All it does is throw one hero and one monster into a pit and have them go at each other. It then forces them to do it again, 10 million times.

The Game System table has been applied to a thread question about the advantage of using a Battle Axe in another thread. The short of it: using a Battle Axe is better (safer for the Hero) than using a Broadsword and a Shield.

Interesting result! Thanks for summarizing it! I didn't think of using the numbers to answer that kind of question, but of course they can. I guess they can provide the basis for many different observations.

Have you noticed that I've added in repeated values for some of the as-yet unfinished tables? I hope this saves you some time.

Thanks!

Also, Ogres have been mentioned before when talk comes up about Hero equipment, so I think it would be a great idea to work on Against the Ogre Horde next. After that, my preference would be to then determine the values for the EQP and the BQP. More people appear to be playing or plan to play the Quests from these expansions, so this is where your program can answer the more pressing questions.

Great with a wish-list! I'll definitely prioritize based on that!

@ torilen (first questions) and Daedalus (clarifying reply)
Great clarification! As for the ideas for how to apply the numbers to a whole party, they seem pretty good to me. As the msc numbers themselves are accurate, they provide a good foundation for further calculations. We should just remember (as Daedalus noted) that actual gameplay is very complex, and has many many variables, so calculating stuff like a party against a band of monsters will only be an estimate. Still, estimates are the best we have, and can be very useful for planning a quest.

Pretty neat information. It must be nice to be able to program in number crunching like that.

Thanks! I'm glad it can be of use to others! Programming is a useful skill to learn, but it is not magic. There are limits to what can be done, mainly because of complexity. A full simulator of a Hero Quest quest, for example, is a task so complex that I personally would not undertake it. Might take a programming team years to finish. A few Ph.D.s in computer science could come in handy too

@ Daedalus (going into math thesis mode)
Wow, your thoughts about multiple monster figting look interesting. I'll have a deeper look at that post again next time I'm in a HQ+Math mood.

And now, finally, for the msc numbers I've calculated since last time.

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Hero Attack Dice     1 AD |2 AD  2 AD  2 AD |3 AD  3 AD  3 AD  3 AD  3 AD |4 AD  4 AD  4 AD  4 AD
Hero Defend Dice     2 DD |2 DD  3 DD  4 DD |2 DD  3 DD  4 DD  5 DD  6 DD |2 DD  3 DD  4 DD  5 DD
--------------------------+-----------------+-----------------------------+-----------------------
Goblin EU/NA ........ 1.3 | 0.6 | 0.5 | 0.3 | 0.4 | 0.3 | 0.2 | 0.2 | 0.1 | 0.3 | 0.2 | 0.2 | 0.1
Skeleton EU/NA ...... 1.6 | 0.7 | 0.5 | 0.4 | 0.5 | 0.3 | 0.2 | 0.2 | 0.1 | 0.3 | 0.2 | 0.2 | 0.1
Zombie EU/NA ........ 1.9 | 0.8 | 0.6 | 0.4 | 0.5 | 0.4 | 0.3 | 0.2 | 0.1 | 0.4 | 0.3 | 0.2 | 0.1
Orc EU/NA ........... 2.8 | 1.3 | 1.0 | 0.8 | 0.8 | 0.6 | 0.5 | 0.4 | 0.3 | 0.6 | 0.4 | 0.3 | 0.3
Mummy EU ............ 4.0 | 1.7 | 1.3 | 1.0 | 1.0 | 0.8 | 0.6 | 0.5 | 0.3 | 0.7 | 0.5 | 0.4 | 0.3
Mummy NA ............ 7.9 | 3.3 | 2.6 | 2.0 | 2.0 | 1.5 | 1.2 | 0.9 | 0.7 | 1.4 | 1.1 | 0.8 | 0.6
Fimir EU ............ 3.3 | 1.4 | 1.1 | 0.9 | 0.9 | 0.7 | 0.5 | 0.4 | 0.3 | 0.6 | 0.5 | 0.4 | 0.3
Fimir NA ............ 6.6 | 2.9 | 2.3 | 1.7 | 1.8 | 1.4 | 1.1 | 0.8 | 0.6 | 1.2 | 1.0 | 0.7 | 0.6
Chaos Warrior EU .... 4.0 | 1.7 | 1.3 | 1.0 | 1.0 | 0.8 | 0.6 | 0.5 | 0.3 | 0.7 | 0.5 | 0.4 | 0.3
Chaos Warrior NA ....17.5 | 7.3 | 6.0 | 4.8 | 4.3 | 3.5 | 2.9 | 2.3 | 1.8 | 3.0 | 2.4 | 2.0 | 1.6
Gargoyle EU ......... 5.8 | 2.4 | 2.0 | 1.6 | 1.4 | 1.2 | 1.0 | 0.8 | 0.6 | 1.0 | 0.8 | 0.7 | 0.5
Gargoyle NA .........20.9 | 8.4 | 6.9 | 5.6 | 4.8 | 3.9 | 3.2 | 2.6 | 2.0 | 3.3 | 2.7 | 2.2 | 1.7
Fellmarg Guardian EU  5.8 | 2.4 | 2.0 | 1.6 | 1.4 | 1.2 | 1.0 | 0.8 | 0.6 | 1.0 | 0.8 | 0.7 | 0.5
Fellmarg Guardian NA 11.6 | 4.8 | 4.0 | 3.2 | 2.9 | 2.4 | 1.9 | 1.5 | 1.2 | 2.0 | 1.6 | 1.3 | 1.1
Ulag EU ............. 7.0 | 2.8 | 2.3 | 1.9 | 1.6 | 1.3 | 1.1 | 0.9 | 0.7 | 1.1 | 0.9 | 0.7 | 0.6
Ulag NA .............14.0 | 5.6 | 4.6 | 3.7 | 3.2 | 2.6 | 2.1 | 1.7 | 1.4 | 2.2 | 1.8 | 1.4 | 1.2
Grak EU ............. 5.8 | 2.4 | 2.0 | 1.6 | 1.4 | 1.2 | 1.0 | 0.8 | 0.6 | 1.0 | 0.8 | 0.7 | 0.5
Grak NA .............17.5 | 7.3 | 6.0 | 4.8 | 4.3 | 3.5 | 2.9 | 2.3 | 1.8 | 3.0 | 2.4 | 2.0 | 1.6
Stone Chaos Warr EU.. 4.8 | 1.9 | 1.5 | 1.2 | 1.1 | 0.9 | 0.7 | 0.5 | 0.4 | 0.7 | 0.6 | 0.4 | 0.3
Stone Chaos Warr NA..20.9 | 8.4 | 6.9 | 5.6 | 4.8 | 3.9 | 3.2 | 2.6 | 2.0 | 3.3 | 2.7 | 2.2 | 1.7
Balur EU ............ 2.8+| 1.1+| 0.8+| 0.6+| 0.6+| 0.5+| 0.3+| 0.2+| 0.2+| 0.4+| 0.3+| 0.2+| 0.2+
Balur NA ............ 8.3+| 3.3+| 2.4+| 1.8+| 1.9+| 1.4+| 1.0+| 0.7+| 0.5+| 1.3+| 0.9+| 0.7+| 0.5+
Witch Lord EU .......11.2+| 4.3+| 3.7+| 3.1+| 2.4+| 2.0+| 1.7+| 1.4+| 1.2+| 1.6+| 1.4+| 1.1+| 0.9+
Witch Lord NA .......44.7+|17.2+|14.6+|12.3+| 9.6+| 8.2+| 6.9+| 5.7+| 4.7+| 6.4+| 5.4+| 4.5+| 4.5+
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-HALLS OF DURRAG-DOL   .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Skaven Warrior ......  .  | 0.7 |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
White Seer ..........  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Rat Ogre ............  .  | 1.4 |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Troll ...............  .  | 1.7 |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-THE EYES OF CHAOS     .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ogre ................  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ogre Chieftain ......  .  |16.2 |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Troll ...............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Chaos Sorcerer ......  .  | 7.3 |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-INN OF CHAOS          .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Chaos Sorcerer ......  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Magical Skull .......  .  |  .7 |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-RUNNING THE GAUNTLET  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Cabiri ..............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-A GROWL OF THUNDER    .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Wight ...............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Balash ..............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Balor ...............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-REV. O.T. WEATHERMAN  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ice Gargoyle ........  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Erongil .............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Death Reaper ........  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-AGAINST T. O. HORDE   .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ogre Warrior 3 BP ...  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ogre Champion 4 BP ..  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ogre Chieftain 4 BP .  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Ogre Lord 5 BP ......  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Gargoyle Quest 1 ....  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Stone Orc Quest 1 ...  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Festral .............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Festral's Guard .....  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Xenloth .............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
---------------------  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
-WIZARDS OF MORCAR     .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Zanrath's Chaos Warr.  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Zanrath..............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Fanrax Skeleton......  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Fanrax...............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Boroush..............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Grawshak's Bodyguard.  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .
Grawshak.............  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .  |  .


A + after the cost means the monster/character is tougher to defeat than the number reflects because of additional special skills like magic and the like.

[Daedalus]

This post links to a thread about the lethality of Quest 7 in the Japanese localization. The details belong here, I think. My mission: determine just how bad the Barbarian has it (everybody is split up) using the Monster Slaying Cost table and my methods of calculating damage from multiple monsters. (Basically I sum the MSCs for each turn.) He starts cornered by 2 Mummies. In the following rooms he has to face two Orcs, then maybe a Skeleton, next a Fimir and 3 Orcs together, and finally a Gargoyle. I'm assuming the Barbarian can purchase any combination of equipment because he probably has almost 2000 gold coins after the first 6 Quests of this series (it's a Monty Hall).

First, the constants. The 2 Mummies must certainly be fought. Also, assume the Gargole must be defeated singly. Fighting the 2 Orcs defensively from a doorway or aggressively attacking from within the room both result in 3 Orc attacks, so that is also constant. The Skeleton is optional, so its MSC can simply be added to any total afterwards. The MSCs of the Barbarian's opponents and the various Barbarian equipment kits are as follows:

            4 AD, 4 DD (battle axe, chain mail, helmet)                       4 AD, 5 DD (battle axe, plate mail, helmet)
                     2 Mummies: 2.4 BP of damage                                          2 Mummies: 1.8 BP of damage
                     1 Gargoyle : 2.2 BP of damage                                           1 Gargoyle : 1.7 BP of damage
                            2 Orcs: 0.9 BP of damage                                                  2 Orcs: 0.9 BP of damage
                      1 Skeleton: 0.2 BP of damage                                            1 Skeleton: 0.1 BP of damage

      3 AD, 5 DD (longsword, chain mail, helmet, shield)             3 AD, 6 DD (longsword, plate mail, helmet, shield)
                     2 Mummies: 2.7 BP of damage                                          2 Mummies: 2.4 BP of damage
                     1 Gargoyle : 2.6 BP of damage                                           1 Gargoyle : 2.0 BP of damage
                            2 Orcs: 0.9 BP of damage                                                  2 Orcs: 0.9 BP of damage
                      1 Skeleton: 0.2 BP of damage                                            1 Skeleton: 0.1 BP of damage

Second, the variables, which are the tactical options found in the fight with the Fimir and three Orcs:

* fighting from the doorway and waiting for the monsters to attack--1 adjacent monster.
* immediately attacking the Orc from the corner and waiting for the monsters to attack--2 adjacent monsters.
* immediately attacking a Fimir or Orc with the Barbarian's back to the wall--3 adjacent monsters.
* immediately attacking a Fimir or Orc and being surrounded--4 adjacent monsters.

            4 AD, 4 DD (battle axe, chain mail, helmet)                       4 AD, 5 DD (battle axe, plate mail, helmet)
           1 adjacent monster : 1.9 BP of damage                             1 adjacent monster : 1.8 BP of damage
           2 adjacent monsters: 2.5*/2.8 BP of damage                     2 adjacent monsters: 2.4*/2.7 BP of damage
           3 adjacent monsters: 3.1*/3.7 BP of damage                     3 adjacent monsters: 3.0*/3.6 BP of damage
           4 adjacent monsters: 3.4*/4.3 BP of damage                     4 adjacent monsters: 3.3*/4.2 BP of damage

      3 AD, 5 DD (longsword, chain mail, helmet, shield)             3 AD, 6 DD (longsword, plate mail, helmet, shield)
           1 adjacent monster : 2.0 BP of damage                             1 adjacent monster : 1.8 BP of damage
           2 adjacent monsters: 3.2*/3.6 BP of damage                     2 adjacent monsters: 2.4*/2.7 BP of damage
           3 adjacent monsters: 4.0*/4.8 BP of damage                     3 adjacent monsters: 3.0*/3.6 BP of damage
           4 adjacent monsters: 4.4*/5.6 BP of damage                     4 adjacent monsters: 3.3*/4.2 BP of damage
                                                                      * Fimir is attacked last

Finally, the MSC totals are added together to find how much damage the Barbarian is likely to suffer at the hands of Quest 7. Add either 0.2 or 0.1 to an appropriate total to find the MSC for all monsters with the Skeleton included.

            4 AD, 4 DD (battle axe, chain mail, helmet)                       4 AD, 5 DD (battle axe, plate mail, helmet)
               From a doorway, waiting: 7.4 (+.2)                                   From a doorway, waiting: 6.2 (+.1)
               From a corner, waiting: 8.0*/8.3 (+.2)                             From a corner, waiting: 6.8*/7.1 (+.1)
               From a wall, agressive: 8.6*/9.2 (+.2)                              From a wall, agressive: 7.4*/8.0 (+.1)
               Surrounded, agressive: 8.9*/9.8 (+.2)                              Surrounded, agressive: 7.7*/8.6 (+.1)

      3 AD, 5 DD (longsword, chain mail, helmet, shield)             3 AD, 6 DD (longsword, plate mail, helmet, shield)
             From a doorway, waiting: 7.6 (+.2)                                     From a doorway, waiting: 7.1 (+.1)
             From a corner, waiting: 8.8*/9.1 (+.2)                               From a corner, waiting: 7.7*/8.0 (+.1)
             From a wall, agressive: 9.6*/10.4 (+.2)                              From a wall, agressive: 8.3*/8.9 (+.1)
             Surrounded, agressive: 10.0*/11.2 (+.2)                            Surrounded, agressive: 8.6*/9.5 (+.1)
                                                                      *Fimir is attacked last

Considering the Heroes were already well equipped, its likely the Barbarian would have at least one healing potion in reserve entering this Quest. Therefore, I feel this Quest is actually fair for the Barbarian player.

[Thrawn]

Conan the Barbarian always attacks the Fimir first.

Einstein the Barbarian knows that you always kill all orcs before fimirs (and fimirs before mummies) just like you kill goblins before you kill skeletons, which come before zombies.

[Daedalus]

Conan the Barbarian always attacks the Fimir first.

Einstein the Barbarian knows that you always kill all orcs before fimirs (and fimirs before mummies) just like you kill goblins before you kill skeletons, which come before zombies.

Ha! Einstein the Barbarian--he must have caught some serious flak from the other barbarians for thinking before acting all the time. Gimme that Talisman of Lore and lift something heavy, you egghead!-

Where the MSC data could prove more useful is situations where there are mixes of monsters that have different Attack Dice, Defend Dice, and Body Points. While surrounded, is it better to kill the three Orcs first, or the Chaos Warrior? An experienced player may have a decent grasp of what to do, but as the numbers shift, the room for error grows. It might remove the soul of the game to detail each possibility, but certain questions can now be answered with more than subjective knowlege or opinion for those interested in such matters.

On another tangent, I began to think about how the program assigns attacks while working out the previous calculations,. It appears a Hero attacks first in the sequence. If this is true, I wonder how the MSCs would be affected if the monster was given priority. Then again, maybe the program does things differently.

I also began to think about how monsters with multiple Body Points attack and assign their damage. A comparison of the NA Fimir and Mummy vs. their EU counterparts suggest an extra Body Point multiplies MSC (by a factor of 2 for these two monsters). I therefore made an educated guess and divided the Fimir's MSC into two turns to reflect this, treating it like 2 EU Fimirs fighting from the same square. It did 0.4 of its 0.7 MSC on the first turn, then 0.3 on the second turn before it was killed. This affected how long the Orcs got free attacks while the Fimir was dealt with (or not, if the Orcs were wisely attacked first), so I needed to record two seperate MSCs for each Barbarian fighting scenario.

Of course, Einstein the Barbarian could have told you that there's more than one way to lay waste to a room full of greenskins without all the MSC mumbo-jumbo. As for Conan, there is hapiness enough for him to drive his enemies before him and hear the lamentation of their women. Waitaminute...Fimir capture women, so I guess he'd be happy with something else.

[Thrawn]

Chaos warrior vs orc is more interesting, but in general, always kill the orc first.

With multiple heroes vs multiple monsters, it gets a little more complicated though. (For example, having the heavy hitter take the warrior, while someone lighter takes out the orc.)

[Count Mohawk]

So, after a few hours of crunching numbers in Excel, I have crafted a formula which will produce MSCs for any combination of monster Attack, Defend and Body Points, against any Hero, for all values of Attack, Defend and Body between 1 and 10. You can download the spreadsheet here, if you want it.
There are two issues with this spreadsheet, though. The first is that it only finds the MSC for one Hero vs monster situation at a time; ie, you have to write down the results manually. The other is more serious: although I am reasonably sure my calculations are correct, the MSC values I find from my spreadsheet do not match those found by thequester’s simulator. This indicates that either his simulator or my spreadsheet is inaccurate, since the Law of Really Large Numbers says that a sufficiently large set of data should trend towards the average. Here’s what I did:

I started by calculating the odds of rolling N skulls, shields or walruses (black shields for the uninitiated) out of some number of dice, and stored the results in a table, 1 < N < 10. Then, for each number of defend dice, I determined the odds of a Hero with N Attack dealing some amount of Body Point damage to a monster.

The formula for how many hits a monster can deal is as follows: if it survives the Hero’s attack, it attacks back. In numeric terms:

E(# of hits) = P(Monster takes 0 damage) x (1 Hit + E(# of hits)) + P(Monster takes 1 damage, but lives) x (1 Hit + E(# of hits with 1 less BP)) + P(Monster takes 2 damage, but lives) x (1 Hit + E(# of hits with 2 less BP)) + …

Which simplifies to:

E(# of hits at starting BP) = [P(Monster takes 0 damage) + sum of (P(Monster takes N damage, but lives) x (E(# of hits at N less than maximum BP); N > 1)] / (1 – P(Monster takes 0 damage))

From there, multiply this number by the expected damage from one monster attack with the given Attack and Defend parameters to get the MSC.

Finally, a short table of MSCs. Heroes are assumed to have 2 Attack and 2 Defend.

Code: Select all

                    Thequester   Count Mohawk
Goblin              0.6          0.3
Skeleton            0.7          0.4
Zombie              0.8          0.5
Orc                 1.3          0.7
Fimir (EU)          1.4          0.9
Fimir (US)          2.9          2.2
Mummy (EU)          1.7          1.1
Mummy (US)          3.3          2.7
Chaos Warrior (EU)  1.7          1.1
Chaos Warrior (US)  7.3          6.4
Gargoyle (EU)       2.4          1.7
Gargoyle (US)       8.4          7.5

Thoughts? Who is right – Thequester, or I?

[torilen]

I still need to read a lot of these new posts, and I think all the discussion is great.

But, I would like to say one thing, and I hope I don't come off as TOO judgmental.

Thequester's stuff works really well because the simulator works out things as it would actually happen.
Yes, it is just one hero vs one monster, but if you look back through the discussion, this has been taken
care of...how to add in more heroes and more monsters and come up with the proper number.

Yes, one might have to do it manually, but it is minor calculations and not really a big deal to work out.

That said...I would have serious reservations in using such a mathematical formula that count mowhawk
has come up with. I, for one, cannot figure it out from a quick glance, which means I'm not going to use it
on a general basis anyhow.

But more importantly, I SERIOUSLY doubt that the people who wrote heroquest used anything coming close to
a formula such as that. And as such, there is no reason why we should, either. Heroquest is very simple, and
I would bet money that the designers created without THAT much effort.

Count mohawk - again, I hope I'm not coming off as too critical. I, as do the rest of us, appreciate all comers
to any discussion. But remember, heroquest is very simple - that's why so many of us like it. And I would guess
that such simplicity went into the design of the game. There is no need to bring calculus and other higher maths
to the table.

[Count Mohawk]

Well, of course there's no need for high-level calculus for a game like HeroQuest. People build quests and quest packs all the time without referencing fancy-shmancy charts and graphs to make certain the sequence of events features a gently-rising difficulty curve. I am, however, the kind of guy who likes to 'solve' problems like this as a form of entertainment. I appreciate your point of view, though, which I will temper by posing as rebuttal, "where is the ideal balance between precision and simplicity?" That's a question that everyone will need to answer for him or herself.

On the subject of monster grading... due to the complexities of combat, it's not really feasible to determine the exact, perfect, most best value for each monster, but that doesn't mean we can't try to get an approximate understanding of the relationship between them. (For example, I will assert, without proof, that 1 Chaos Warrior is about equal to 3 Orcs.)

(Also, in case it comes off differently, I don't take any offense at your prior comment, torilen.)

[torilen]

Where is the ideal balance between precision and simplicity? Right at the point where calculus starts coming in for me.

you do have a point, though - that point is different for everybody. Take me for example - I came up with my own means of
judging how hard quests would be - using only the BP, AD, DD, and a few other things (when needed), and from what little bit of
testing I've been able to use, it seems to work just fine for me. Somewhat precision, as all monsters and heroes use those same
statistics, and the difference between them can typically change the tide of a battle - but very simple for me to use. It did require
a lot of manual written work, though.

Do make sure to check out the rest of this discussion closely, if you haven't already - as I stated before, there was some talk
about what to do with more than one monster/more than one hero and such. Your example - 1 chaos warrior equals 3 orcs -
I think something very similar to that was brought up, and if I remember correctly, might have been shot down.

I think this depends a lot on house rules though - as the basic rules state a hero and/or monster only gets one defend roll each turn.
So, that would have to be factored in.