Tuesday, 19 May 2015

Impossible: Why It's Not Impossible

Last Post I talked about why Impossible difficulty is so hard in King's Bounty. If two armies walk to the middle of the arena and fight it out then the one with five times the strength of the other is going to win. I'd say they have a high probability of winning, but it's a little beyond probability. If I'm a master tactician and manage to get my five stacks of guys to all attack one of their stacks while their other four stacks linger in the back, I still lose brutally.

So why is Impossible not literally impossible? There are several reasons:

Attack and Defense
Last time I simplified creature combat to ignore attack and defense, but you can't actually ignore those things. Each unit has an attack and a defense score. If the attacker's attack is higher than the defender's defense then damage is multiplied by 1 + (difference / 30) to a maximum of 3. If defense is higher then damage is divided instead.

For example, a black dragon has 2500 leadership, 1000 health and hits for 110-130. Peasants have 5 leadership, 6 health and hit for 1-2. If you put 500 peasants together to get 2500 leadership then you have 3000 health and 500-1000 damage. That doesn't make dragons sound good. But a dragon has 70 attack and defense and the peasants have only 1, so the dragon actually does triple damage to the peasants and takes only one third. Now that's still not great and the dragon loses in a stand up fight, on average about 840 peasants survive the fight - peasants are actually the second strongest unit I've found in terms of raw fighting power per leadership.

What helps you the player is that your hero has attack and defense scores that are added to all of your troops. These are affected by your skills and by your equipment. So when you start you get a weapon with +1 attack, giving your troops an average of a 3.3% damage edge over enemy troops of the same kind. Late in the game you might, depending on your class, have attack and defense scores ranging from 15 to 30 or even 40. Add 30 attack and defense to your 10 zombies from last time and they beat the 17 zombies with 6 of your zombies remaining. That's an extreme example, but even 5 points of attack and defense effectively scale that 70% army difference down to a 45% difference, which is a lot more manageable.

Spells
You can cast one spell every round, limited by your mana. If you start as the vampire you begin with both Slow, which reduces one unit's speed by 1 for 2 rounds for 5 mana, and Poison Skull, which does 45-155 damage for 5 mana and has a 30% chance of poisoning the target.

Back to those zombies, if you can do 100 spell damage to the enemy stack every turn of the fight then your zombies win with 5 zombies left.

That's better and worse than it sounds. It's better because you can be doing that damage before your zombies even meet their zombies. In fact, with low speed units like zombies you can probably spend your entire mana bar blasting them before you ever have to fight them in melee. Similarly, spells can target ranged units without actually having to get next to hem. Plus, while damage spells are nice, spells like Slow can control a battlefield and keep an enemy unit out of the fight for a long time.

On the other hand, it's not your 10 zombies against their 17. It's more like your 10 zombies times five vs. their 17 times five. Now you have run out your entire mana bar and you haven't even killed one of their overpowered stacks. Still, I'd better think spells are the key to victory if I've chosen to try Impossible difficulty on the mage class.

Rage
In addition to spells, you have rage abilities. You get rage during combat by dealing and receiving damage. Rage abilities are a lot like spells, but there are only 9 different ones and they get more powerful as your familiar levels up.

What makes rage abilities special, when compared to spells, is that they often allow you to deal with enemy units in ways that kind of ignore how powerful they are. Chief among these is Jealousy, which let's you make an enemy unit go uncontrolled, attacking friend and foe alike - usually friend since their foes are all the way across the arena still. Jealousy certainly has restrictions on how it is used, but it does not depend on the leadership of the stack. You can sometimes use jealousy to turn the enemy's most powerful stack against them. There are also two abilities that kill a percentage of the troops in a stack, which is nice as an equalizer; and an ability that makes a small number of hexes impassible, which gives you get tactical options.

On Impossible difficulty, rage earned from combat is halved, but I still anticipate rage playing a very significant role in make the impossible possible.

Better Units
If it's all zombies vs. zombies then the side with more zombies is just going to win. Attack, defense, spells and rage can equalize the fight, but in the end zombies just crack each others' heads. Units in King's Bounty, however, are much more complicated than that.

When I said above that peasants beat black dragons, that would be true on a map with only two hexes. But in reality the black dragon wins every time. While peasants have an initiative of 3 and a speed of 2, the black dragon has an initiative of 6 and a speed of 8. The dragon can also fly. Basically, the peasants will never get to even attack the dragon unless the dragon allows that to happen. Of course if the dragon attacks the peasants they still get to counterattack. However, every three rounds the dragon has the ability to move up to it's full speed and deal 110-140 damage to everything it flies over with an 80% chance on inflicting the burning condition. That does not allow counter attacks. So if you put 1 black dragon up against a stack of 1 million peasants then 48000 rounds of combat later the dragon would emerge victorious.

There are several ways that units are better than other ones. Obviously having more initiative more speed and a way to attack without being counter attacked is a sure victory. |A less obvious way to be better is hidden in the black dragon example, and that is large health pools. The peasants have to do 1000 damage to win but the entire time they are dealing damage the black dragon is doing full damage back. The black dragon has to do 3000 damage to win, but wen it's done 300 damage, it's reduced the peasant's attack strength by 10%. In fact, if the attack and defense calculations didn't cap at 3 and the dragon was allowed to use all 69 points of advantage is has it would win against the 500 peasants. However, if you pit 1000 dragons against 500,000 peasants then then dragons only manage to defeat about a third of the peasants before dying in a straight fight, because with that number of creatures the advantage from having a high health pool is neutralized. In the early game, having aunit with a large number of hit points is very useful.

There are also a variety of abilities that allow you to control fights in other ways.

Next time I'll move beyond the abstract and start talking about the specific things I did to get through the impossible very early game.

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