Scientific way to evaluate decks?

[Toge111]

There exists a way to calculate probability averages for many aspects of decks. It just takes enormous amount of work to do, but it is possible to give scientific answer to questions like how much quanta 10 tower deck produces on average game, or how many turns does it take for Ultimate Speed EM (http://elementscommunity.org/forum/index.php/topic,10563.0.html) deck to win without opposition.

The model works no doubt best for mono decks with simple damaging creatures and towers. It can answer questions like whether mono death mummy rush (http://elementscommunity.org/forum/index.php/topic,10503.0.html) or Shrieker rush (http://elementscommunity.org/forum/index.php/topic,482.0.html) is actually faster.

The model itself is pretty simple:
1. First we calculate average number of towers in opening hand (auto-mulligan included)
2. Creatures in opening hand = cards in opening hand - towers
3. Creature composition probability comes from deck composition.

Here we have determined average opening hand. Next phase is to play all towers and keep drawing one card at the time from deck.

Logic goes:
Get quanta -> play creatures -> creature damage / remaining health = turns to win.

Trick here is to start calculation from end towards start, because we want to minimize turns to win. There are no decimals! Excess damage should go to improve deck's reliability i.e. chance to draw the right things.

The math. Here's where I have to let you guys down. It's been several years since I studied probability math in high school. There are two big projects to undertake. One is to calculate average quanta on turn-to-turn basis. The other one is to calculate accumulating creature damage.

Quanta gain:
30 size deck with 10 pillars
Let's say average starting hand has 3 pillars
Turn 1: 0 quanta
Turn 2: 3 quanta (chance to draw pillar 7/23)

How to calculate the result depends whether or not the player draws pillar next turn, which in turn affects subsequent probabilities. It's possible to calculate these averages without infinitely complex probability tree, I just don't remember how.

[Ifailgood]

Calculating the QI is just as effective and much simpler.

[Toge111]

Calculating the QI is just as effective and much simpler.

- Much simpler, but once we get those two formulae down the game as we know it will be no more. It is a 'solution' for all simple decks. If you're not familiar with the term, check this wiki page: Solved game (http://en.wikipedia.org/wiki/Solved_game).

[kobisjeruk]

How to calculate the result depends whether or not the player draws pillar next turn, which in turn affects subsequent probabilities. It's possible to calculate these averages without infinitely complex probability tree, I just don't remember how.

unfortunately deck themselves by nature are complex and varied
how would you calculate poison rush? what about the presence of adrenaline, nightfall and other stat booster? how about creature generator? or pillarless deck? or deck with immolation/nova?

Much simpler, but once we get those two formulae down the game as we know it will be no more. It is a 'solution' for all simple decks.

good luck

[Toge111]

unfortunately deck themselves by nature are complex and varied
how would you calculate poison rush? what about the presence of adrenaline, nightfall and other stat booster? how about creature generator? or pillarless deck? or deck with immolation/nova?

- It's much easier in theory. Perhaps some mathematician could easily come up with formula for these things.

Poison is like having a creature(s) that deal X points of damage.
Adrenaline increases creature damage by pre-determined amount.
Nightfall is like creature whose attack is 1*N
Creature generator is an entity with progressively increasing damage output, same as lava golem.
Nova decks have same probabilistic principle for quanta gain as pillar decks.

[Toge111]

To be honest I'm a bit surprised this idea hasn't picked wind beneath its wings. Instead there's hundreds of threads petitioning whether one rush is better than another, with no one interested in facts? Hundreds of posts in threads that attempt to evaluate decks, with user relative results on small sample sizes. I guess non-scientific thinking is just that much easier.


... or am I the only adult playing a game meant for children?

[xdude]

To be honest I'm a bit surprised this idea hasn't picked wind beneath its wings. Instead there's hundreds of threads petitioning whether one rush is better than another, with no one interested in facts? Hundreds of posts in threads that attempt to evaluate decks, with user relative results on small sample sizes. I guess non-scientific thinking is just that much easier.


... or am I the only adult playing a game meant for children?

No, but, frankly, I don't think anybody cares enough to do all these calculations. Why don't you do it, instead of offending the community?

[Amilir]

There is another scientific way to evaluate decks:  Play them and analyze the results.  Not only would this be horrendously complicated, the data it gives is mostly useless.  People have found the speed of decks against opponents that don't play cards.  They did so by having a program run hundreds of games and total the results.  This was still not so helpful.  The current trend of playing decks under actual conditions is much more accurate and useful.  'Facts' can be found from actual data.  Theoretical analysis only goes so far.  Did you account for mummies being resistant to RT?  Did you account for (insert card here)?  One of the beautiful things about elements is the number of variables you have to account for.  If you only miss a couple, your error could easily be greater than that of a few hundred games of stats. 

The useful way to do this sort of thing would be to set up a program that plays decks against each other.  It's pretty feasible, though you'd probably need to rip zanz's AI, AND write your own.

[Sir Valimont]

Well Toge your proposed method is not a bad idea, but it should not be thought of as the best possible metric for deck choice. Surely it would be useful as you propose it nonetheless.

I would hesitate to use a term like "solved game" since the appropriate statistic for a round of Elements would also account for the opponent's cards and the opponent's AI in the case of non-PvP or would use some form of game theory for PvP itself.

Consider for example that an opponent with a Life rush deck would probably be easier to beat with a simple mono-Gravity, Fire or Aether deck whereas Life rush vs. Life rush is mostly based on luck.