As I said, I chose those weapons because my script was written for 1e and isn't limited in the number of times it will use a surge ability.  That means that if I had run the reanimate's attack, it would have come out exactly the same as the berserker's (since the only difference is that the reanimate can only spend a maximum of 1 surge).

There's not that much variability in the starting weapons.  The stats I calculated for the necromancer's attack are also basically the same as the disciple's iron mace, and only missing the surge damage from the spiritspeaker's oak staff or the wildlander's yew shortbow.  I think the two attacks I chose are reasonably representative of the range of options.

Maybe you saw the heroes get way luckier than this a few times - that doesn't make the numbers wrong, it just means that there's luck involved (there's also a long list of psychological reasons your impression may not be representative of even your own overall experience - in particular, people tend to remember the exceptional events and gloss over the ordinary ones).  I only calculated the average, perfect rolls would of course be far better (and with perfect rolls for the overlord it would take infinity attacks!).

I'm not modeling the entire game, but I'm modeling a decent chunk of it precisely.  I absolutely refuse to entertain counter-arguments based solely on anecdotes.

Though, seeing such a big difference between the ettins and the shadow dragons, I am suddenly wondering if our overlord could have used the act 2 card by mistake.  Can anyone confirm those stats?

The ancetodal evidence is pretty reasonable given the math.  The math says on average anywhere from 3.7 to 8.2 attacks to kill a master ettin depending on the strength of the attacks.  A group of 4 heroes has at least 8 actions so assuming they are focusing on nothing but attacking the master ettin killing it in 1 round is hardly surprising.  Throw in the use of skills to spike the ettin down and it would be more surprising if the ettin didn't die.  The OL's job of course is to make sure he doesn't end up in the circumstance where all 4 heroes can spend all their actions beating on his master ettin.  Might be trickier then it sounds with the use of fatigue moves but that's a different issue.

Side question for modeling the barbarian's attack.  Did it include the Rage starting ability?  I calculated a 12.3% chance for a barbarian to kill na ettin in 1 swing and 60.2% chance to kill it in two or less swings which seemed a little higher then what you were getting with Rage being the most likely difference. 

I agree that one-rounding an ettin looks completely plausible based on these numbers.  I was more referring to the anecdote about one-rounding a lieutenant with 15 wounds and black+grey defense, and hooliganj's vague claim that "basically, your numbers don't match what I've seen in play".

As I think I mentioned, I did not include any hero skills.  Partly because assuming that the berserker will use Rage on *every* attack seems rather disingenuous, and partly because I thought it would probably be more representative of hero attacks as a whole if I did not include it, since most classes do not have starting skills that add damage to their attacks.

Eh-hrm…seems I made a mistake entering the information for the gray defense dice.  All of those monsters are actually harder to kill than I listed.  Here's the updated stats, assuming there are no other mistakes:

Chipped Greataxe:

• Cave Spider (minion): 1.7 attacks
• Cave Spider (master): 2.5 attacks
• Cave Spider (4-hero group): 9.3 attacks
• Ettin (minion): 4.0 attacks
• Ettin (master): 6.0 attacks
• Ettin (4-hero group): 9.9 attacks
• Shadow Dragon (master): 15.4 attacks
• Lieutenant with 15 health and black+grey defense: 15.5 attacks

Reaper's Scythe:

• Cave Spider (minion): 2.9 attacks
• Cave Spider (master): 4.5 attacks
• Cave Spider (4-hero group): 16.0 attacks
• Ettin (minion): 9.8 attacks
• Ettin (master): 15.1 attacks
• Ettin (4-hero group): 24.9 attacks
• Shadow Dragon (master, from 2 spaces): 16.9 attacks
• Shadow Dragon (master, from 1 space): 25.9 attacks
• Lieutenant with 15 health and black+grey defense: 49.2 attacks

And just for grins, here's the Berserker using Rage on every attack:

• Cave Spider (minion): 1.4 attacks
• Cave Spider (master): 2.0 attacks
• Cave Spider (4-hero group): 7.6 attacks
• Ettin (minion): 2.8 attacks (12% chance to one-shot)
• Ettin (master): 4.1 attacks
• Ettin (4-hero group): 7.0 attacks
• Shadow Dragon (master): 10.2 attacks (64% chance to cause no harm at all)
• Lieutenant with 15 health and black+grey defense: 9.8 attacks

I'm having trouble following the math (or quite likely the game mechanics).  How are you calculating the average time to death?  Using purely averages I get 5.3 attacks for a chipped  greataxe to kill a normal ettin with no skills.

Red Die for Great Axe: Average 2.33 dam

Blue Die for Great Axe: Average 2 damage + 1/6 of attack missing

Total average great axe damage (red die+blue die)*attack hitting = 4.3*5/6 or 3.61

Gray Defense Die: 1.33 damage reduction or 2.66 for 2 gray die

Average Damage per attack: 3.61-2.66=.94

5 health at .94 damage per attack = 5/.94 = 5.29 attacks to kill an ettin.

Tons of other ways to calculate time to death of course and the scythe doing an average of negative damage would suggest another method might be more useful then the one used here something which accounts for the variance better then means.

Antistone's math isn't using Skills, but does include any bonus damage potentially gained from surge abilities on the weapon. The Chipped Greataxe can turn up to 2 surges into +1 damage each, which gets you the lower numbers. If you use your math on the Reaper's Scyth, which has no bonus damage, you'll probably get the same results as Antistone.

Ratcur said:

Or, in the case of Encounter 2 of the quest Castle Daerion, the Master Ettin respawns at the (either beginning or end of the OL's turn, I forget which), and a turn later (or less with Dash) is back wailing on the NPC whose death is the OL's victory condition, easily dealing between 5 and 7 damage a hit (or more with Frenzy), making that possible full turn that Heroes spent wailing on it for nothing.  And that's not to mention the open group, the zombies (number based on how well the OL did in Encounter 1), and the Lieutenant who are also causing trouble.

The average damage takes into account surges. 

Without surges the chipped great axe averages 2.16 for the red die and 1.6+1/6 of the attack missing for the blue die.

Dividing max health by average net damage doesn't give you an accurate answer, because it doesn't penalize for damage wasted on overkill (a 90% miss chance and a 10% chance to hit for 10 times the monster's max life does not mean that you kill it in an average of 1 attack).

And subtracting average defense from average damage rolled doesn't even give you the true average net damage dealt, for the same reason (sometimes defense exceeds rolled damage, in which case the extra defense is wasted).

Here's the algorithm I'm using (note: numbers are rounded for purposes of examples):

• List every possible combination of die rolls, and the probability of each.  For example "the blue die rolls 2 wounds and 3 range, the red die rolls 3 wounds and a surge, and the gray die rolls 1 shield" would be one possible combination, with a probability of (1/6)*(1/6)*(3/6) = 1/72
• Determine the amount of damage that will be done if that particular combination of results is rolled (in this example, 5 wounds after spending the surge and subtracting defense, but we cap that at the monster's maximum health, if lower)
• Use these results to build a table showing every total amount of damage it is possible to do with a single attack, and the probability of doing that amount of damage (e.g. 20% chance of a miss or zero net damage, 9% chance of 1 damage, 17% chance of 2 damage, 54% chance of one-shotting the cave spider) - basically, combine all the die rolls that produce the same net result, adding up their probabilities to get the total probability of that result
• From that, you can calculate the average number of attacks it would take to kill the spider if it only had one health remaining, ignoring attacks with no effect (so…1 attack)
• Using that, you can calculate the average number of attacks it would take to kill the spider if it had two health remaining, still ignoring attacks with no effect (.09 / 0.8 = 11% of hits deal 1 damage, which means that it dies in 1 + (the one-health number) attacks, while (.17 + .54) / .8 = 89% of hits kill it outright (1 attack), for a weighted average of 1.11 attacks)
• Using that, calculate the average number of attacks if it had three health remaining (11% deal 1 damage, killing it in 1+1.11 attacks; .17 / .8 = 21% deal 2 damage, killing it in 1+1 attacks; .54 / .8 = 68% kill it in 1, for a weighted average of 1.33 attacks)
• And so on, up to the monster's maximum health
• But that was ignoring the attacks with no effect - actually, 20% of our attacks are completely wasted.  So now we need to divide by the fraction of effective attacks (80%), which gives us 1.33 / .8 = 1.67 attacks average for the entire process

As you can probably tell, that's a LOT of math, which is why I have a computer program do it.  But the number you get is not an estimate or an extrapolation, it's the actual exact average number of attacks (within the limits of floating point precision, and assuming there are no mistakes in my input data…)

Ratcur, I think you're not taking the effect of misses into account on the defense side - basically you are counting the defense as reducing damage even when the hero misses, and that brings down the average.

If you chart out the possible combinations of the dice involved (1 blue, 1 red, 2 grey, including surges as damage), the average result is 1.52 damage dealt.

My experience tells me that berserker heroes will often deal much more damage than that - but I will readily admit that my experience may not represent an average sample. Then again, I'm not the one who claimed a figure has broken stats based on a game or two. If nothing else, working out this math has taught me how good the Rage skill card really is - you can take 1 fatigue to raise the average damage to 2.26, a vast improvment.

edit: This was a simulpost. Antistone's math looks correct, as far as I can tell with a glance.

Antistone said:

Thank you. I've been going through this thread waiting for someone to actually address probability instead of averages.