The "Mana Curve": Throwing M:tG logic on it's head

[jmizzle7]

I was commenting on Jangoo's claim that damage-to-quanta was the determining factor, which is false. I obviously didn't address everything - only the point Jangoo was making. I was only speaking of the generic damage/quanta ratio, separate from the total value of the card. It should be obvious that a Phase Dragon is better than an Immortal because it deals more damage over time, which makes it a better investment, which is at the core of your original post.

[Jangoo]

Wisenheim reporting back for duty. 

I realized that seperating the "risk curve" from the "investment curve" (as it is dictated by the game-layout) doesn't do any good after all.

You miscalculated the dmg output Essence.

Immos

turn4: 25
turn5: 40
turn6: 60
turn7: 85
turn8: 110
turn9: 140 (6th Immo)
turn10: 170
turn11: 200
turn12: 230
turn13: 260

Dragons:

turn4: 20
turn5: 30 (cant afford the 2nd one yet)
turn6: 50 (2nd drag)
turn7: 70
turn8: 90 (cant afford the 3rd one yet)
turn9: 120 (3rd drag)
turn10: 150
turn11: 180
turn12: 220 (4th drag)
turn13: 260

So, on a streak of 13 turns the dragons finally manage to draw the Immos. (while the Immos hit the 100 and 200 dmg mark one turn earlier than the drags)

Now getting back to the circumstances of the game, the streak shown above is already well past the first 5 turns because you simply wont have 5 pillars in your starting hand;
more like 2-3 pillars on turn1, 3-4 on turn3, 4-5 on turn5 ...
This implies that playing an Immo probably even comes way earlier than the model streak above suggests, allowing him to build up dmg the dragon will realistically never catch up with.

In the theory of an infinite game of elements a dragon will certainly be the better investment.
In the actual environment of Elements, 18 turns are a long way to go and some 180 dmg output just might be enough to do the job ... which is why I still cant believe that dragons are superiour to Immos.

Coming back to the mana-curve in Mtg, there actually is something like this in Elements.
While quanta certainly dont get burnt after every turn I still have to calculate with them and I could still draw a "curve" as to how my quantum supplies will build up over time and adjust my deck accordingly.
The above model-streak suggests to me that Paul Sligh probably would have laughed in the face of dragon spamming opponents while sticking to the less amazing but much more suited to the quantum supply - Immos.

[Essence]

Perhaps I used the wrong example.   Let's look at the RoI from a SINGLE Immortal vs. a SINGLE dragon, which is the situation you're much more likely to be facing in-game.  Which should you play first in order to maximize your damage over time?

Turn   Quanta   Immortal-first damage      Dragon-first damage
1   5   0      0
2   10   5      0
3   15   10      10
4   20   15      20
5   25   30*      35*
6   30   45      50
      
* - the turn at which the other creature gets played


And so on.  The point is that while Immortals and Phase Dragons have the same cost/power ratio, the higher-power creature has better returns on your investment over time.  If you have a Phase Dragon and an Immortal in your opening hand (assuming no opponent intervention), the opponent will ALWAYS die first if you wait and play the Dragon first rather than playing the Immortal first and then the dragon.

That's why the concept of the "mana curve" is nonexistent in Elements: there is an active disadvantage to playing your cheaper, lower-power creatures first.  The only question you need to ask is about risk: is it more likely that if you play a cheap creature now, your opponent will waste a non-renewable resource to kill it (and thus your high-power creature will live to get through more later) -- or that delaying to play your high-power creature in a turn or two will allow your opponent to put up a defense that you aren't prepared to disrupt? 

[Jangoo]

Hm, that makes sense ... and then again not because the above example with multiple creatures is also credible.

I am totally confused by now as to which "model situation" is really suitable for this question and as to how long one can shuffle those model situations to prove certain points ...

Taking all the other circumstances (risk evaluation) into consideration will only make things worse, such as:

- Why take 6 immos when 3 drags do a better job? the immos would only clog up your deck
- having fewer dragons may result in not drawing any
- there is various shields ... against some immos are better, against some dragons
- realistic investment capacities: you wont be able to afford waiting for the dragon because you will need to spend quanta on a shield, on loboing enemy creatures etc ... or will you?

well, I am lost here ...

[Essence]

Thank you, Jangoo, you summed up the risk-investment dilemma pretty much perfectly.

[Jangoo]

Lol, well I am glad we talked about it. 

[jmizzle7]

Sometimes you just gotta talk it out, I guess.

[coinich]

If someone felt really strongly about it, they could use this: http://stattrek.com/Tables/Hypergeometric.aspx (http://stattrek.com/Tables/Hypergeometric.aspx) to calculate the average overall damage per card based on the probabilities of having those cards in a certain deck size.  Even calculate it vs electrum cost, though I think a couple Immortals is something even the newest players can afford within a short time of playing.

[yeehaw]

I feel obliged to point out something. Using a dragon first is only better when 5 free quantum or above is available per turn. Quite a convenient breaking point you have chosen there.

[Essence]

Not anything I chose deliberately, I just figured it was a pretty common amount to have available in the first few turns of a game.  Like you said, because the amount of quanta available generally goes up pretty quickly in the first several turns of a game, if anything pointing out the breaking point is another tick in favor of the dragon.

[yeehaw]

We are in agreement then. =) I feel the new alchemy cards like Stoneskin help to address the amount of quanta going up rapidly in mono decks. The huge amounts of quanta was the biggest reason why mono decks were by and large unviable besides rush/scaling.