I've discovered the Mage Wars equation (I think)

[Sailor Vulcan]

I might have discovered the Mage Wars equation. This equation describes all of the possible resource conversions of a single game. A lot of the resources have been chunked together because there wouldn't be enough room for them otherwise. Tell me if I've missed anything.

g_f=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)*(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

r=round

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 when r_current=0.

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What do you think?

[Lord0fWinter]

Can you perhaps give an example? Like work through the equation with a card, explaining where each number in the final equation comes from?

[Aylin]

Can you perhaps give an example? Like work through the equation with a card, explaining where each number in the final equation comes from?

Pretty sure he's just messing with you.

[IndyPendant]

This would have been a *perfect* April 1 post...; )

[Zuberi]

s=gi+r|total|*(mcavg/r+aresetavg/r)]+[{-c, -m, -o, -a, -tr, -p, -t, -d, -l, 0, -stp, -ph, -stg, -rcurrent}+{c, m, o, a, tr, p, t, d, l, 0, stp, ph, stg, rcurrent}]*[r|total|*(a+tr)avg/r]

Close. I recommend abandoning the search, for once you crack this code, your games shall devolve into inputting data into an algorithm and having the winner declared by the computer. This occurred on the show "The Adventure's of Pete and Pete" to the game Kick the Can.

[Sailor Vulcan]

Sorry, I noticed a few mistakes and corrected them. Not sure about whether it works to calculate anything as averages per round. Someone will have to check me on that. This doesn't calculate the winner, zuberi. It calculates all paths a game could take, not just the one to one mage's or another's victory. It does not calculate what you should do, only what you can do.

[Sailor Vulcan]

And this isn't a joke. I realized that every single thing that occurs in this game is resource management. There is nothing in this game that is not resource management. You can manage your own resources and to an extent your opponents' resources, and so can your opponents. Changing the phase can be considered a neutral resource management, where an end of phase is -ph and the beginning of a new phase is +ph.

Also, there are some constraints on the equation that I did not mention: card text. Card text is the thing that limits what we convert resources to. For instance, when you cast a hidden enchantment, you are spending mana to gain an object with a position and activation associated with it. You cannot spend that enchantment's activation to change its position. However, you can cast shift enchantment, converting an additional quantity of mana into a change in the position of the enchantment.

Also I just fixed another error in the equation. When you remove a card from your spellbook, you are spending spellbook points. When a card comes back to your spellbook, you are gaining spellbook points.

[Aylin]

And this isn't a joke.

I'm having a hard time believing this.

[Lord0fWinter]

Can you perhaps give an example? Like work through the equation with a card, explaining where each number in the final equation comes from?

Pretty sure he's just messing with you.

That's why I asked for an explanation I'm hesitant to believe it, but willing to listen to the reasoning and calculations behind it.

[Sailor Vulcan]

I've done a lot of explaining already, but if it wasn't clear...

We begin with the initial game state:

o=28 (this includes all zones, arena walls, and mages
s=120*number of mages
p(mages)=starting corners
p(walls and zones)=self explanatory
a=0
tr=0
m=10*the number of mages
c=combined channeling of all channelers
t=0 since no ones gained or lost any tempo yet
d=0.
l=combined life of all creatures and conjurations, in this case the mages.


Next, you add mana equal to the channeling stat of every round to the game state. You also add activations equal to the total number gained during each reset phase in the game. The notation for this part was ridiculously hard to figure out, so I ended up using mana gained from the average channeling per round, and the average number of activations gained per round. Next, I added the expression for a single most direct resource conversion multiplied by the product of the total number of rounds in the game and the summation of activations and triggers that occurred per round on average.


The expression for the most direct resource conversion has two parts: cost (- values) and gain (+values). Theoretically you could choose any number of costs and any number of gains, but the costs and gains are constrained by card text, as I explained above.

The s= at the beginning is another mistake I just caught. Spellbook points are included in the game state.

[Zuberi]

It calculates all paths a game could take

Is the answer 42?

[Sailor Vulcan]

It calculates all paths a game could take

Is the answer 42?

Of course not. This equation represents all the paths the game could take, not just one. Theoretically the game doesn't even need to have an end if the players aren't trying to convert all their resources to damage.  The part with the { , , ...} allows for many, many solutions, just for a single direct resource conversion. You can make such conversions as many times as there are activations in the game. The choice is yours.

[Aylin]

The expression for the most direct resource conversion has two parts: cost (- values) and gain (+values). Theoretically you could choose any number of costs and any number of gains, but the costs and gains are constrained by card text, as I explained above.

On the off chance you're being serious, you shouldn't use one variable to represent multiple things. Instead of 'a' and '-a' which is confusing as hell, you could use 'a' and 'A' instead.

As written, in your equation I would take the two vectors you have and simplify that to 0 since it's not clear what you're meaning. And I'm not even even sure you're wanting to use a vector!

[Sailor Vulcan]

I wasn't sure how to put "and/or" between every variable in the {}'s.

[Aylin]

I wasn't sure how to put "and/or" between every variable in the {}'s.

...what?