If all units were to compete Wimbledon-style...

[Lord Ludwig]

I am really glad to have sparked such interest and calculations... I am almost tempted to actually draw a tournament table and see what comes out

I imagined from the start, as I said in the first post, that it likely would be a rock-scissor-paper issue between archdemon, black dragon and ancient ent, so that means maybe a round robin between all lvl 5 units would be better to give a "winner" than playoffs.

Another couple of thoughts:

1) I said that if the tournament was held at night the troll would be unbeatable. Obviously he would not, however, be undrawable, since many creatures can outrun him and would never get caught, even a tiny forest fairy for example;

2) what would happen if we threw in also the ancient phoenix and even the lvl 5 book of evil? The book is easily dispatched, but what is the intrinsic strength of it's spells without an "Amelie" behind it? Anyway I suppose it still would be no match for any lvl 5 and most lvl 4 units. But the ancient phoenix? In the campaign it's a more or less useless spell, but in a one-on-one contest I think it would rank quite high...

[DGDobrev]

Well, there it is

Calculations complete. At the "ceteris paribus" rule (meaning "all other things being equal"), the Ancient Ent wins.
EDIT: Just a small clarification: Wasp Swarm damage is 50-90 physical + 50-90 poison, so I've applied the resistance to the first part of the formula in the xls file. Forgot to comment it for better clarity

However, with a pinch of luck, the archdemon can win. All it takes is that 1% better crit chance to work properly and give him a slight edge over the Ancient Ent.

I've used the standpoint that Archdemons must attack straight away, since the damage provided by Wasp Swarm at a distance greater than 4 squares actually equals the Ancient Ent's average attack damage. As such, both parties must start exchanging blows straight away or the other will gain an advantage (for example, if the Archdemon waits or the Ancient Ent defends).

Everything is in the xls table

[Lord Ludwig]

Impressive analysis... so it could really go either way, but on average the AE should win more often.

[Lord Ludwig]

Another couple of things regarding AD-AE.

I suppose "halve" works on the number of enemy creatures, not on their overall health, right? If it was the second way round then the AD would have a good chance to halve the AE's health with one blow winning hands down.

On the other hand we are ignoring (rightly, because that would not be in the spirit of the "tournament") that an actual army with a single AD would provide no bonuses, but a single AE would actually have +1 morale. However, as I said, I think it's correct to leave this out.

[MaroonMaurader]

I think a few elements of that analysis probably should be changed.

1. The Ancient Ent's wasp swarm damage should also be effected by the difference between attack and defense, so it's not actually 63 on average (41 at range, actually).

2. Ignoring critical hits overly disadvantages the ancient ent - and here's why: the ancient ent does 100-140 damage. The Archdemon does 88-99 damage. So a critical hit for the ent does 210 damage, or 1.75 times its average damage. A critical hit for the archdemon does 149 damage, or 1.6 times it's average damage. So even though both crit at basically the same rate, the ancient ent benefits more from it.

3. Ancient ents get a +10 defense bonus from defending. So if the ancient ent simply sits there defending, it only takes about 75 damage when the archdemon attacks, and retaliates for about 63. So the Ancient Ent can actually just sit there defending and either stalemate or win with greater odds than if it takes initiative and launches attacks of its own. Over 6 rounds defending, the ancient ent would take about 2 critical hits and 10 regular (including counter-attacks) for about ~988 damage; it would give about 2 critical hits and 10 regular for about 850 damage (significant overkill).

4. Wasp Swarm cannot be retaliated. Ancient Ent should use it.

If the ancient ent and archdemon just sit there swinging at each other, every 2 turns the ancient ent has been hit 4 times (for about 408 damage), and has hit the archdemon 4 times (for about 252 damage). As DGDobrev showed, this ends in 7 rounds with ~74 health left to the ancient ent. And a noticeable portion of the time, due to random variations in damage and critical hits, the AD will even win.

If the archdemon just parks itself next to the ancient ent and starts swinging, but the ancient ent only uses it's abilities, then every 2 turns the ancient ent is hit twice (for about 204 damage), retaliates the archdemon twice (for about 126 damage), and hits it with a close-range wasp swarm once (for about 82 damage). So overall, the AE takes 204 damage and does 208 damage. So if they repeat this pattern for 6 rounds, then in the 7th round the archdemon hits, is retaliated, then gets hit by wasp swarm... the archdemon has done ~714 damage and has taken ~769 damage. The archdemon's chance of victory is less than one in a million in this case.

If the archdemon is a little smarter, it will make use of the "wait" option to park itself precisely 5 spaces away from the ancient ent every time the ancient ent is about to launch a wasp swarm, then close in to strike afterwards - in which case the ancient ent is only doing 167 damage per 2 combat rounds. If this pattern goes on for 9 rounds of combat, the Archdemon does about 918 damage and takes about 772 damage. Closer, but still fairly clearly a win for the Ancient Ent.

[DGDobrev]

1. I am uncertain whether attack and defense play a part in the use of abilities. This is why I left it out. I will read through the russian guide carefully and I'll do some research. However, if it does play a part, the wasp swarm damage will be:
(1/(1+(66-50)*0.0333))*((70*0.8 )+70)

2. That is quite right, but I think you miss that the crit modifier is 1.5, not 1.75, which puts the Ancient Ent's damage at the value I put in there (atk/def ratio is taken into account as you can see from the formula). I know that Jolly Roger from the gift bag improves crit damage by another 20%, but we're talking about pure stats here.
here's the formula I used:
=((1/(1+(66-50)*0.0333))*140)*1.5
everything's there - def/atk ratio, multiplier, etc.

3. That is a good point.

4. Wasp swarm is a ranged attack. Can you use in against an enemy that is right in front of the ent? I haven't seen the AI do it, so I surmise it is impossible (otherwise the AI should have used it because the AI always chooses the higher damage attack).
- waiting puts the AD at a disadvantage, because the Ancient ent will always retaliate to the AD's attack, while in the meantime he will take damage from wasp swarm, even if it's lower.

[ivra]

Regarding: "3. Ancient ents get a +10 defense bonus from defending. So if the ancient ent simply sits there defending..."

I thought the Defend command only lasted out the current round. So it makes no sense to defend if your initiative is lower than the opponent. If the opponent waits for some reason, then defend works. How does the defend command work? Does it last out the current round only or does it last all until it is the defending unit's turn to act again next round?

[MaroonMaurader]

I think we have a non-disagreement about critical damage. I merely meant to say that the ratio between critical damage and average damage is not fixed across units (unlike the ratio between critical and maximum); the ancient ent's critical does 1.75 times its average while the AD's critical does 1.6 times its average. Your formula for figuring out the ancient ent's critical damage is precisely right, and gives a more precise value for the specific situation of an ancient ent fighting an arch-demon than my general statement that a critical does a base of 210 damage before resistances, attack, and defense are considered.

I did forget about the adjacent-enemy restriction on wasp swarm, and you're absolutely correct - it makes my suggestion about wasp swarm simply incorrect.

Defense lasts until the unit's next turn. I'm not sure how that works with abilities that give multiple turns in one round, but that's not really relevant here.

And, because I was curious, I went and checked what the archdemons odds actually are in a straight-up punching match by writing a short script to simulate 10,000 of them (including rolling for damage and critical). The ent won 7,804; the demon 2,196. When the ents took the defensive and forced the archdemons to attack, the archdemons won precisely one match out of 10,000.

So it looks at first glance like the ancient ents have a major edge... which means the archdemons would be happy with a draw, and are free to take delaying tactics of their own: sitting next to the ents and defending, getting a +6 defense boost. Now the ents can't defend, or else the match ends in a draw... and the ents would like to have more than a 50% success rate out of this. When the archdemons do that, their odds of victory go up to 35%.

But it gets even better - suppose the archdemons just sit there defending themselves, UNTIL they have good odds of killing the ents with their next attack; then instead of waiting to counterattack they take the initiative and strike first. Now the demon's odds of winning rise up to 63%.

To summarize:
If the archdemons defend, and the ents defend, it's a draw. 50% success for each.
If the archdemons defend (intelligently), and the ents attack, the archdemons win 63% of matches.
If the archdemons attack, and the ents defend, the archdemons win 0.01% of matches.
If the archdemons attack, and the ents attack, the archdemons win 22% of matches.

So obviously the archdemons should start every match on the defensive. However, the ents need not respond by defending as well. The ents know that even if they get one or two unlucky attacks, the archdemons will still accept a draw; on the other hand if they get a string of lucky attacks they might win. So the ents would be well-served to attack for a little while, and if things go poorly call it off, take the defensive, and accept a stalemate. So if both players are playing optimally, you would expect well over 63% of the matches to end in draws (I don't know the exact number, but I'd guess around 80%), and the remainder to be victories for the ents.

If you change the scoring, you change behaviors and results of course. You could make it zero-sum (a victory for the ents gives the ents one point and takes one from the demons, and vice versa), you could make draws worthless, or any of a number of other creative scoring techniques... which is why it's so hard for me to say who actually "wins" this matchup and by how much. But if you forced me to guess what the outcome would be, I'd predict stalemate (neither side willing to attack, so both sit next to each other defending for eternity).

[lauvhk]

All the defend/use ability analysis are based on player knowledge. For all Ents (both ancient and normal), the AI will never defend, use normal attack when the opposing unit is within reach and only use special when the enemy is out of reach. So while the Ancient Ent Wasp Swarm is a range attack that cannot be retaliated, the AI will never use it if you park something next to it.

(In case you have doubts, I would suggest starting a new game and play through the tutorial. The last battle involve two normal Ents in separate stack. Place your paladin in different hexes to see different actions from them.)

While Ancient Ent can defeat the Archdemon, it would be interesting to see how it deals with the Cyclops. I will leave it to the number crunching players.

[tetleytea]

I tend to view it differently. The demoness has the best backhand, but Knights have a killer circular forehand swing. Vampires have the best serve. Demonologists and Gorguls are pretty good at pressing the net and volleying close-up shots, but that is more suited for doubles play.