Combat math

[Nelphine]

Neither of which is quite accurate. Oh well. I'd say it's going to be high 98, around 98.8 or so. Oh well. I was close with my 99 theory. So I guess then you'd need 21 armor and +2 to defend to get the defense I consider a contender for reasonably invulnerable.

And 16 with +1 to defend is around what, 93 or so? Which is why I said you can get away with it, but it's not great, and requires a lot more work in terms of specific spells to back it up.

[crusader.mike]

> And 16 with +1 to defend is around what, 93 or so?

0.940223. All this assuming MoM correctly implements related RNG rolls. Which I bet it doesn't. Like 99.9% of games :-)


Funny thing:
Probability[x ==0, x\[Distributed]damaged[8, 0.3, 16, 0.3]] = 0.904213
Probability[x ==0, x\[Distributed]damaged[8, 0.4, 16, 0.4]] = 0.940223
Probability[x ==0, x\[Distributed]damaged[8, 0.5, 16, 0.5]] = 0.968043
Probability[x ==0, x\[Distributed]damaged[8, 0.6, 16, 0.6]] = 0.986787

i.e. for same atk/def increasing to-hit and to-def in unison causes defense to "take over".

also, if you expect that (atk * to-hit) vs (def * to-def) determines the outcome (these calcs "pit" 18 avg dam vs 24 avg defense):
Probability[x ==0, x\[Distributed]damaged[60, 0.3, 80, 0.3]] = 0.88504
Probability[x ==0, x\[Distributed]damaged[45, 0.4, 60, 0.4]] = 0.902576
Probability[x ==0, x\[Distributed]damaged[36, 0.5, 48, 0.5]] = 0.922172
Probability[x ==0, x\[Distributed]damaged[30, 0.6, 40, 0.6]] = 0.94376

[Nelphine]

Defense should take over with those rolls. There's twice as many rolls done for the defense, so the absolute amount of defense succes is going up twice as fast as the offense. Change both numbers to 8 and you shouldn't see that anymore. Same thing on the second set, just it isn't a doubling.

[crusader.mike]

Hmm... Probability of making zero damage does behave differently (because most of PMF is no longer squeezed into zero), but expected damage value still goes down

Code:

Expectation[x, x\[Distributed]damaged[60, 0.3, 80, 0.3]]
Expectation[x, x\[Distributed]damaged[45, 0.4, 60, 0.4]]
Expectation[x, x\[Distributed]damaged[36, 0.5, 48, 0.5]]
Expectation[x, x\[Distributed]damaged[30, 0.6, 40, 0.6]]

Expectation[x, x\[Distributed]damaged[80, 0.3, 60, 0.3]]
Expectation[x, x\[Distributed]damaged[60, 0.4, 45, 0.4]]
Expectation[x, x\[Distributed]damaged[48, 0.5, 36, 0.5]]
Expectation[x, x\[Distributed]damaged[40, 0.6, 30, 0.6]]

Result:

Code:

0.361537
0.279723
0.200902
0.127849

6.36154
6.27972
6.2009
6.12785

[teelaurila]

My hero in the example has +2 to defend (endurance and lucky).  Diminishing returns means that any armor past 15 ignores any bonuses to defend. So he has 15, 0.5 AND 5, 0.3.

Wait, what, so any +to-defend is ignored for armor points above 15?

Does this also work similarly for attack and to-hit?

[Seravy]

No, only To Defend.

[teelaurila]

20 armor and +2 to-defend certainly seems like overkill to most situations. Sure it's what you need if you want to use a single hero to wipe the board in the mid-game. I was thinking more along the lines of buffing a beetle or turtle or gargoyles so that it can really wreck about. Later on maybe stone giant. In the toughest fights it would need an army to backup, or you need 3 of them, but most fights it could do alone. So a bit different tank strategies we are talking about.

With a turtle+endurance+holy armor+prayer, with tactician, I did absolutely roll over every normal unit of lizardmen, and also of high elves except for elven lords and massed magicians. I was succesfully attacking cities with single turtles, but of course losing one isn't like losing a hero. I think I took a fortress, defended by magicians mostly, with ~5 turtles. So it seemed about 13-15 armor and +2 to-defend is good enough. The best halberdiers, turtles and magicians would attack at around 8/+1. I did take some damage against them, but nothing healing couldn't handle. Also I could usually carry through even if a dispel hit the endurance, as long as prayer was there.

One question would be: Do you must have Life to pull this off, or is Iron Skin enough?

[Nelphine]

Iron skin comes too late..it's amazing but you can't afford to wait that long before you get going.

[crusader.mike]

Neither of which is quite accurate. Oh well. I'd say it's going to be high 98, around 98.8 or so. Oh well. I was close with my 99 theory. So I guess then you'd need 21 armor and +2 to defend to get the defense I consider a contender for reasonably invulnerable.

Your gut feeling could be correct... I imagine due to RNG limitations actual PMF is more "tapered" on sides (i.e. goes to zero much faster) -- due to nature of typical RNG implementation (and the fact that all "independent" rolls share same RNG state) expected value could be in line with theoretical value (i.e. average damage lines up to expectations), but outliers -- not (e.g. chance to roll 10 or 9 zeroes out of 10 rolls can be zero as opposed to theoretical 0.01 or whatever it is). This means predicted 0.91 chance of 0 damage in reality might be 0.99 or 1 :-)

[Nelphine]

Sure but given that based on my in game experience I expected 20 armor +2 to defend to be 99.7 or so (and in reality it's more like 98.8) and 16 +1 to defend to come out around 95 (and reality is a little under 94) I think the RNG in CoM is actually pretty accurate.

Obviously I'm not saying the RNG is perfect, but experience seems to indicate it's close enough that actually using Wolfram for predictions isn't a waste of time.