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Author Topic: Mage Wars: a Reductionist Perspective  (Read 1556 times)

Sailor Vulcan

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Mage Wars: a Reductionist Perspective
« on: September 30, 2015, 08:59:31 PM »
Something I've thought of before is that The Mage wars game state at any point could probably be represented by a (ridiculously long) sum of resource conversions/exchanges, with positive values for one player's stuff and negative values for the other player's stuff. It would be really complicated, but you could theoretically describe it using the main resources only plus a couple other things.

The starting resources for every game of Mage wars are innate Mage stats and abilities, including spellbook points, life, channeling and starting mana supply.

All the cards in your spellbook cost spellbook points to include. Although it might be easier to understand if you represent the Mage as having two kinds of spellbook resources: the maximum spellbook points for your Mage, and the amount of spellbook points worth of cards removed from your book during the game--sort of like damage and life.

Additionally all creatures effectively have an action-regeneration stat. Similar to the channeling stat, which can give a creature a certain amount of mana each round, creatures gain a certain number of actions each round during the reset phase.

Just like a familiar has an action that can only be used to cast certain kinds of spells, mages have a second quick action that can only be used for a certain kind of spell. This extra quick action is the quickcast action as we know. A Mage could be described as gaining a quickcast action every reset phase, and losing all quickcast actions they have left at the end of every round.

Someone else (reddawn I think) wrote an article once on here somewhere describing different orders of resources in Mage wars. Or maybe it was just in a reply to deckbuilder's article on resources. They basically said that there were different orders of resources based on what you convert into what.

I would say that the Mage and their innate stats and abilities are 0th order resources. It could also be argued that the arena itself is a neutrally controlled 0th order resource, if you want to think about trying your hand at arena design using the battlegrounds tile zones. So are orb guardians and v'tar orbs in domination mode. Since mages are creatures, they gain actions every reset phase. The mages' ability to gain actions during the reset phase is a 0th order resource as well. So is your mage's starting position.

1st order resources include the cards in yours and your opponent's spellbook, your respective mana supplies (excluding the starting 10 mana that each Mage has) your mage's action and quickcast action, and the mages' positions after they gain actions during the reset phase which can be used for moving.

Anything that your Mage has the innate ability to use an action for is a second order resource. This includes spells (as distinct from the cards or abilities you use to cast them which are 0th order), non-spell attacks (as distinct from the abilities on your mage ability card that allows you to use said attacks), changes in position and guard markers.

Third order resources are things that are converted from second order resources. This includes all non-Mage objects that aren't map features. Objects, strangely enough are not necessarily a single resource in and of themselves but rather are a collection of resources, and the exact resource composition of an object depends on the object. All other resources in a single object besides cards are tied to a single card by definition.

One resource I haven't talked about yet are resource conversion limiters and catalysts. Things that limit what resources can be converted to what other resources, or dictate when a particular resource conversion takes place. These include mana costs, levels, types, subtypes, some abilities and even some of the rules in the rule book and codex.

For instance, here is one way to gain an action outside of the reset phase:

1. spend a card from your spellbook (1st order)
2. that card has the name "rouse the beast" (limiter)
3. turn over a quickcast marker (catalyst) 4. spend your mage's quickcast action (1st order)
5. Spend mana (0th/1st order)
6. That mana is equal to a level (limiter)
7. That level is attached to the same card as the ability to gain actions during the reset phase (this is a limiter which checks for the presence of a limiter and a catalyst that are tied to a 1st order resource by another limiter.)
8. That card must be in the arena (limiter that checks for a limiter that ties the card to a 0th order resource)
9. Gain one action.


The players' decisions are also a resource. They're resource conversion limiters, although they are the only resource that is converted from real resources outside the game.

An entire game of Mage Wars could be reduced to in-game resources, in-game resource conversions/exchanges, and units of in-game time. Everything that exists in the game is made of these things. In Mage Wars, a "creature" is a conceptual abbreviation of a collection of in-game resources that include the ability to gain actions during the reset phase and the ability to spend actions during the action stage. At the surface level we see an object, a single unit, even though it's not a single unit. Rather it is a collection of smaller parts that we refer to using a single word.

However, this would be a very complicated way to represent and talk about the game, so generally we will conceptually condense and abbreviate these components when writing or talking about them. In fact, the human brain naturally isn't very good at thinking about Mage wars in such precise and extended terms, let alone everything else. Our brains have to abbreviate or approximate these things most of the time because we simply don't have enough neurons to represent things as they really are without abbreviations or approximations. Of course, the brain isn't a single unit either...

Try to see what other examples of this you can find outside of Mage Wars. I think you'll be surprised by how many there are.

And there you have it. I just used Mage Wars to explain reductionist philosophy. I'm guessing this might end up being one of the least controversial attempts to explain it, ever, though perhaps I'm being overconfident.

What do you think? Did you like it?

(I originally put this in the strategy and tactics section by mistake before I realized where I was ultimately going with it. Sorry about that.)
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ringkichard

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Re: Mage Wars: a Reductionist Perspective
« Reply #1 on: October 01, 2015, 01:24:31 AM »
Did someone say "Reductionist"? :D

One important characteristic of Mage Wars is that it's periodic, and non-linear. If your mage has 10 channeling, something with a mana cost of 11 is much more difficult to cast than something that costs 10.

(The following is being written at 2:00am, on my phone, working from memory. Errors abound no doubt!)

Or consider creature damage: the expected lifespan of a number of defending creatures D, being attacked by some number of attacking creatures A, is a *compounding step function* dependent on As' attack dice and piercing, and Ds' health and armor, population sizes and number of rounds. If we assume efficient elimination of targets, mean rolls, and that there is only one species of attacker, and only one species of defender, perfect attack targeting, simultaneous attacks, more attackers than defenders, and ignoring initiative, we can represent the number of rounds the defenders will live as a system of equations:

total_damage_dealt_at_end_of_round(n)=damage_reduced_by_armor(attack_dice,armor_minus_piercing)*attacker_population_at_end_of_round(n-1)+ total_damage_dealt_at_end_of_round(n-1)

defender_population_at_end_of_round(n)= int(total_damage_dealt_at_end_of_round(n)/defender_health)

where there is also another symmetrical pair of equations governing how quickly defenders kill attackers (i.e. the attacker and defender roles are reversed).

damage_reduced_by_armor(attack,armor) is a function that calculates the mean damage of an attack, given the number of dice in the attack and the armor value. This is actually a pain to calculate, and I'm using a lookup table for this part of the calculation.

The key to the system is the int() function at the end of the 2nd equation (and its symmetrical twin) that allows a damaged, but not killed, creature to attack at full strength. This means that the attacker's advantage doesn't compound as quickly as one might think, because the defender hits back with an extra creature most rounds.

It's a headache to calculate even this small part of the game with this simplified model. A full system acurately describing all game factors would probably take me hundreds of hours more of work to implement and debug.

It's been slow going :)
« Last Edit: October 01, 2015, 01:28:51 AM by ringkichard »
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Sailor Vulcan

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Mage Wars: a Reductionist Perspective
« Reply #2 on: October 01, 2015, 08:32:40 AM »
Did someone say "Reductionist"? :D

One important characteristic of Mage Wars is that it's periodic, and non-linear. If your mage has 10 channeling, something with a mana cost of 11 is much more difficult to cast than something that costs 10.

(The following is being written at 2:00am, on my phone, working from memory. Errors abound no doubt!)

Or consider creature damage: the expected lifespan of a number of defending creatures D, being attacked by some number of attacking creatures A, is a *compounding step function* dependent on As' attack dice and piercing, and Ds' health and armor, population sizes and number of rounds. If we assume efficient elimination of targets, mean rolls, and that there is only one species of attacker, and only one species of defender, perfect attack targeting, simultaneous attacks, more attackers than defenders, and ignoring initiative, we can represent the number of rounds the defenders will live as a system of equations:

total_damage_dealt_at_end_of_round(n)=damage_reduced_by_armor(attack_dice,armor_minus_piercing)*attacker_population_at_end_of_round(n-1)+ total_damage_dealt_at_end_of_round(n-1)

defender_population_at_end_of_round(n)= int(total_damage_dealt_at_end_of_round(n)/defender_health)

where there is also another symmetrical pair of equations governing how quickly defenders kill attackers (i.e. the attacker and defender roles are reversed).

damage_reduced_by_armor(attack,armor) is a function that calculates the mean damage of an attack, given the number of dice in the attack and the armor value. This is actually a pain to calculate, and I'm using a lookup table for this part of the calculation.

The key to the system is the int() function at the end of the 2nd equation (and its symmetrical twin) that allows a damaged, but not killed, creature to attack at full strength. This means that the attacker's advantage doesn't compound as quickly as one might think, because the defender hits back with an extra creature most rounds.

It's a headache to calculate even this small part of the game with this simplified model. A full system acurately describing all game factors would probably take me hundreds of hours more of work to implement and debug.

It's been slow going :)

Well yes. A complex system is made of many simpler parts. It's like the difference between writing the expression (10*10)+(10*10), and writing 10+10+10+10+... until you've written that twenty times.

But multiplication isn't really something separate from addition. Saying that 10+10+10+10=40 is exactly the same thing as saying 10*4=40. 10*4=40 is just an abbreviated form. It's simpler to write or think about, but it's still just shorthand for something bigger and more complex.

The target line is a limit on what resources can be converted to what other resources in the presence of what catalysts at what time. A mage's starting life is a 0th order resource, but life in general is also a limiter on a catalyst in the rule book. The catalyst is the effect that causes you to lose a collection of resources which includes action-spending and action-gaining abilities. The limiter is the effect that makes it so that this only happens when a certain amount of damage has been added to that collection of resources, or in other words, life.

Attacks, actions and life are all different resources. All life does is limit a resource-elimination catalyst by a quantity of a resource called "damage" included in that collection of resources. It just so happens that oftentimes that collection of resources includes an attack ability. How much damage an attack could put somewhere on average if it was indefinitely available is not relevant to that, because damage is a resource that gets put in the collection of resources which we refer to as the "defender", not the collection of resources we call the "attacker". The concept of approximate mean damage potential which you are referring to is only an emergent property; it's a shorthand for a complex series of exchanges in which friendly life and positioning indirectly limits enemy damage. (In fact I would say that "positioning"as a resource is just a sum of ranges, where "range" is a limiter that prevents some resource exchanges  from occurring. All ranges are relative to each other, which is why we need to use zones as a sort of two-dimensional x-axis. Just like how on a coordinate plane you would use axises to define the coordinates everywhere else.
« Last Edit: October 01, 2015, 08:36:52 AM by Sailor Vulcan »
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I am Sailor Vulcan! Champion of justice and reason! And yes, I am already aware my uniform is considered flashy, unprofessional, and borderline sexually provocative for my species by most intelligent lifeforms. I did not choose this outfit. Shut up.