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Anderas wrote:After several days of data crunching, now, i am pretty sure that count Mohawk's formula is wrong.
Hero AT DE Initiative Monster AT DE BP MSC Standard Deviation
Generic Hero 2 2 Monster Goblin EU/US/YeOlde 2 1 1 0,8 1,0
Generic Hero 2 2 Hero Goblin EU/US/YeOlde 2 1 1 0,3 0,7
E(Number of attacks Goblin makes against Hero) = P(Goblin survives Hero's attack) * (1 hit + E(Number of attacks Goblin makes against Hero)).
E(# of attacks Goblin makes vs Hero) = 0.3333 * (1 + E(# of attacks Goblin makes vs Hero))
E() = 0.3333 + (0.3333 * E())
0.6667 * E() = 0.3333
E() = 0.5000
Anderas wrote:Hey,
i am trying to do my own calculations now in Excel....
Anderas wrote:I found that it is a huge, huge, huge difference if the monster has the initiative or not. So much that a standard Goblin with 1 Body Point is costing you .8 Body points if he has the initiative; and he costs you .2 body points if the Hero has the initiative and strikes first. Other than many other small things, i think this really has to be included in your calculation of the Mission difficulty.
A wandering Monster (or a monster appearing because of a trap, because of a spell or other things) has the initiative, so it deals the high amount of damage. A Monster that is waiting for you in a room normally has the low value.
Anderas wrote:Did you think about the variance?...
The typical standard deviation I found so far was more or less around 2 for the higher results....
A Monster with 5.8 MSC might just deal between 3.8 and 7.8 damage as "entirely normal result" (68% propability); and he might deal between 1.8 and 9.8 damage as a result that is "not normal, but *lemony goodness* happens" (27% propability). Higher and lower results happen with ~4.5%; meaning they are possible but do not appear very often.
Meaning, if you use a calculated monster against a single hero, please take care that you keep some "security distance" between the Hero's life points and the Monster's MSC. If you have a Hero with 6 Life points, rather use a MSC 3 Monster and send a second MSC 3 Monster if the first accidentally under-performs. Don give him one single all-or-nothing MSC 5 Monster, it's too risky - with two exceptions, of course: If the Hero has enough Potions of Healing, here we go; and if it is the Final Boss of your dungeon, he shall really be dangerous.
Anderas wrote:I did find a working and accurate formula to calculate single-bodypoint-Monsters without need of data crunching. Sadly, the same formula underperforms between 5% and 15% if i apply it to multi-bodypoint-Monsters, so i have still to work on it....
............. | Goblin | Skeleton | Zombie | Orc | Fimir | Mummy | Chaos Warrior | Gargoyle |
Avg. MSC | .35 | .41 | .48 | .78 | 1.75 | 2.0 | 4.4 | 5.25 |
Avg. x 20 | 7.0 | 8.1 | 9.6 | 15.6 | 35.0 | 40.0 | 88.0 | 105.0 |
Adj. MSC | .29 | .32 | .37 | .61 | 1.36 | 1.51 | 3.45 | 4.83 |
Adj. x 25 | 7.0 | 8.0 | 9.25 | 15.25 | 34.0 | 37.75 | 86.25 | 100.75 |
MCV | 7 | 8 | 9 | 16 | 36 | 40 | 90 | 99 |
Anderas wrote:Et voilá, here we are, we have the same result now
Anderas wrote:I think my math has rusted. I used a different angle of attack, but yours is convincing.
Why the 1+ in the Goblin Attack?
did you calculate that the goblin may survive two rounds with P(survive)^2 and three rounds with P(survive)^3? I did this for 100 rounds, added all the surviving parts of the goblin together and let them attack.
Anderas wrote:The probability of a specific amount of damage is not calculated and i won't restart it. But with the standard deviation you have a pretty good estimation. This is why i calculate it.
Anderas wrote:Hero: AT4 DE 6
Hero strikes first
Monster AT4 DE9 BP8
Average Monster Slaying Cost: 5,2
Standard Deviation: 3,4
Accounting Demons wrote:MSC = (Average damage per Monster attack) * (Average number of attacks Monster gets to make)
E(Average damage) is trivial to calculate. In this matchup we get a value of 0.5926.
E(# Monster attacks, N Body) = P(Monster takes 0 damage) * (1 + E(# Monster attacks, N body))
+ P(Monster takes 1 damage) * (1+ E(# Monster attacks, N-1 Body))
+ P(Monster takes 2 damage) * (1 + E(# Monster attacks, N-2 Body))
+ ...
+ P(Monster takes X damage) * (1 + E(# Monster attacks, N-X Body))
This can be simplified a little further, but we trust you get the point. By recursing the scenario backwards across monsters of equivalent A/D but lower Body, you can more easily build a chain of MSCs up to whatever Body level you wanted to start with.
Anderas wrote:Update - My Monstercruncher is calculating the last batch of monsters. Estimated time of calculation end is 23:30. It may be sooner as the strongest monster comes last - and i take a shortcut. If a monster ever manages to generate 100 BP of damage, three times, the calculation gets interrupted and the next Hero/Monster combination is calculated. No-one wants to see a Monster on the table that has the possibility of generating 100 BP of damage. My monsters are getting subsequently stronger and stronger, so the shortcut may be taken more and more often.
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