I still don't get what your formula is supposed to gives. The final result represent what? And I can use it for what purpose?
The one variable on the left hand side of the equation represents the final game state. I haven't thought of any definite applications yet, although I imagine this equation might be useful for making AI mage wars opponents. However, the notation would have to be altered to distinguish between friendly and enemy resources. Please reread my OP. I've made multiple corrections to it.
Also, I should probably mention that the equation is harder to read on tapatalk since it does not support superscripts and subscripts.
If you're being serious with this, maybe you should explain how you came up with the gibberish equation in your OP.
First of all, did you even attempt to read the equation and understand what it says? Or did you just see a bunch of mathematical and logical symbols and think "gibberish". I spent HOURS working on this equation. I've defined ALL of my terms. I've corrected all the errors I've managed to find so far. The only thing in there that I'm not sure of is my use of averages per round when it comes to mana gained from the channeling phase and activations gained from the reset phase.
No one has bothered actually commenting on the actual content of the equation. Everyone's just glanced at it and said "GIBBERISH!" without even READING THE EQUATION. Otherwise I would be reading critiques on the actual mathematical logic that I used. Not a single person has actually pointed out any particular flaws in the equation, only the fact that it's an equation. Keep in mind I worked very hard on this. And I DID explain how I came up with this equation, but in case it's not clear, I will repeat myself in greater detail.
I realized that most things in the game of Mage Wars is a resource or a conversion of resources. After that realization I started jotting down my ideas for what the formula for a single direct conversion of resources might be in Mage Wars. (By direct I mean that all of the resources being converted are only converted once.) I already knew that most resource conversions in mage wars include a cost (negative values) and a gain (positive values). However, I did not know the mathematical symbol for and/or, to indicate the choice between resources for each conversion. I vaguely remembered an algebra class where we learned that all possible solutions for the unknown variable in an equation could be written in a list like this:
x={x
1, x
2, x
3,...}
So I thought that the list separated by commas indicated that any of those x values were possible solutions for x. However, x
1 could not be the solution
simultaneously to x
2, since they were in different places on the coordinate plane. Therefore, I thought a list separated by commas was the equivalent of saying "and/or" between every value on the list. I'm starting to see that a lot of people don't know that notation, or that notation is wrong. That's what I used at first before I started to realize that:
{-m, -a, -p, -t, -d, -l}+{m, a, p, t, d, l}
The variables used here are the main resource categories described in Deckbuilder's article on resources. I thought any resources that I had to account for could all fall under these categories, or would be "placeholders" that would convert to one of these types of resources, like channeling to mana. After that I was struck by another epiphany. If I could multiply this expression for resource conversion in mage wars by the number of times it occurred in the game, I might be able to figure out an equation for all resource conversions in the game. I realized that nearly all if not all chains of resource conversions started with actions and activated abilities
[{-m, -a, -p, -t, -d, -l}+{m, a, p, t, d, l}]*[r*a]
where r=total # of rounds in the game.
Then I realized I had made a mistake. Not all resource conversions were voluntary by one player or the other, even though most chains of resource conversions started off that way. Some resource conversions triggered without anyone choosing to activate them.
[{-m, -a, -p, -t, -d, -l, -tr}+{m, a, p, t, d, l, tr}]*[r*(a+tr)]
(tr=trigger)
I then realized that there were some chains of resource conversions that started with a trigger rather than an activation. They were the free mana and actions triggered during the channeling and reset phases, whose values were equal to the channeling stat and the number of objects with the creature type.
r
|total|*(m
(cavg/r)+(a
reset)
avg/rI remembered an article I read once on these forums about resources (not Deckbuilder's) in which resources were described by "order". They described the mage as the first order resource, spellbook points as second order resources, mana and actions as third order, and so on until mage-damage, which is the final order resource.
Eventually I started to realize that it wasn't just most things in the game that could be considered a resource. It was absolutely everything, and by everything I mean everything, including the turn phases. I wasn't sure how to put it all in a single equation because of the great, great diversity of resources in the game, but then I figured I could probably just divide it into categories like Deckbuilder did. Deckbuilder's resource article didn't cover everything. For instance, it didn't cover most traits, it didn't cover turn phases, it didn't cover attack rolls, or armor, or defenses. It also didn't cover creatures as separate resources from their actions, in spite of the fact that a single creature is not a single action, but rather something that generates actions during the reset phase. And it wasn't just creature actions that were generated during the reset phase, but also activated abilities.
I tried categorizing resources a bunch of different ways until I settled on the current variables. At one point I tried using "tra" for traits, but I realized that didn't work very well, and it would overlap with some of the other resource categories too much. I also made sure to include 0 as a resource in the equation, since sometimes you could pay some resources and get nothing out of it (like if the target ceases to be valid), or you might gain something for free (like a free action, or a vine marker during deploy if you're a druid).
Then I realized three big mistakes that I had missed earlier. Firstly, I forgot to include the starting point for all these conversions, the initial game state: g
iThe second huge mistake I made was having spellbook points be the variable on the left side of the equation. I realized spellbook points were included in the initial game state, and spellbook points didn't account for all resources in the game. Particularly, it didn't account for the neutral resources and the mages themselves. I finally realized that what I was calculating wasn't merely the paths a game could take--that was just the right side of the equation. The whole thing actually equaled the final game state: g
fThe third BIG, BIG mistake I made was that I had forgotten to take variation between resource conversions into account. The way everything was written at this point, every resource conversion would have to be completely identical for the equation to be true. Through trial and error, I eventually figured it out:
∑[(-s
n∨-c
n∨-m
n∨-o
n∨-a
n∨-tr
n∨-p
n∨-t
n∨-d
n∨-l
n∨0
n∨-stp
n∨-ph
n∨-stg
n∨-r
currentn)+(s
n, c
n, m
n, o
n, a
n, tr
n, p
n, t
n, d
n, l
n, 0
n, stp
n, ph
n, stg
n, r
currentn)]
And now for the full equation (or at least the latest version):
g
final=g
i+r
|total|*(m
(cavg/r)+(a
reset)
avg/r+∑[(-s
n∨-c
n∨-m
n∨-o
n∨-a
n∨-tr
n∨-p
n∨-t
n∨-d
n∨-l
n∨0
n∨-stp
n∨-ph
n∨-stg
n∨-r
currentn)+(s
n, c
n, m
n, o
n, a
n, tr
n, p
n, t
n, d
n, l
n, 0
n, stp
n, ph
n, stg
n, r
currentn)]*[r
|total|*(a+tr)
avg/r]
I still need to find out whether it works to multiply averages per round of the mana gained from channeling and actions gained from the reset phase by the total number of current-round periods in the game. (for the purposes of this equation, there is only ever one current round at any time. Starting a round is adding a round, and ending a round is subtracting a round.)
I'm also debating whether to make a separate resource category for dice, since their values are partially determined by chance, which is different from any other resource in the game.
And now I just realized two things that I didn't notice before:
1. There are exactly two game components that are not resources, but affect usage of resources: initiative and card text.
2. Since I'm using the summation symbol, and because the total resources in the game doesn't always stay constant (since you can pay a resource cost to lower your opponent's resources rather than increasing your own, which means that the value of g CAN decrease overall)...that means I can condense the equation even more:
gf=gi+r|total|*(m(cavg/r)+(areset)avg/r+∑(sn∨cn∨mn∨on∨an∨trn∨pn∨tn∨dn∨ln∨0n∨stpn∨phn∨stgn∨rcurrentn)*(r|total|*(a+tr)avg/r)where:
s=spellbook points
g=the totality of all resources in the game when r
current=0, AKA the gamestate. (g
i varies with the game mode, the number of players, what board you're using, and the mages chosen for the game.)
c=channeling
m=mana
o=objects
a=activations. (actions, activated ability uses, and non-mandatory enchantment revelations. In this equation a=0 at the end of every round, and the quantity of activations increases by the number of action markers, activated abilities and hidden non-mandatory enchantments on the board during the reset phase, as well as when someone casts "Rouse the Beast", etc.)
Tr=triggers (uses of triggered abilities, including mandatory enchantment revelations and all "passive" abilities like regenerate x, upkeep x, bleed, armor, aegis, resistance, immunity etc.)
p=position (summation of ranges between a single object to all other objects and spells that can affect or be affected by that object either directly or indirectly)
t=tempo
d=damage
l=life
reset=end of reset phase
i=initial
f=final
avg/r=average per round
stp=current step (The net value of this variable never exceeds 1. stp increases by 1 when a step begins and decreases by 1 when a step ends.)
ph=current phase (The net value of this variable never exceeds 1. ph increases by 1 when a phase begins and decreases by 1 when a phase ends.)
stg=current stage (The net value of this variable never exceeds 1. stg increases by 1 when a stage begins and decreases by 1 when a stage ends.)
r
current=current round (The net value of this variable never exceeds 1. r
current increases by 1 when a round begins, and decreases by 1 when a round ends.
r
|total|=the total number of times a round has been added by the end of the game
