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Thursday, August 13, 2009

What is this, Mana Curve?


I believe that the most overused, misused, and misunderstood concept in all of Magic: the Gathering is Mana-Curve. At base value, I have seen casual players and veterans alike, use the term Mana-Curve to simply describe the number of lands in a deck. Though this usage is wrong, in my opinion, it is sadly the most accurate , in comparison to other usages I have heard or read. I have heard Mana-Curve used in reference to the casting cost of creatures and spells in a deck. People have literally said, "The Mana-Curve of such and such card or cards is off in this deck." or "The cards in this sleigh deck are all above the curve." and my favorite, "That card in this deck throws the curve off." I believe that we intuitively call the pool of available mana, which varies turn by turn, a Mana-Curve, because we recognize that there is not generally a linear relationship, between turn and the available mana. In other words, we will almost always lay down a land on turns one and two (most players will take a mulligan if they do not have at least two lands in their opening hand), but the third land will usually come out on turns four or five. If we were to plot this trend, we would see a curve that starts to rise quickly, but slows in its ascent over time, a logarithmic curve.


I believe that we as a gaming community need to come up with, and use a more descriptive definition of this observation. I propose: Mana Availability Curve, defined as the functional relationship between the dependent variable of available mana to a single player, generated by any permanent owned by that player, within a given parameter of probability, for a given deck quantity and mana source quantity, per the independent variable of turn. This is a lengthy definition, but MAC is more complex than most players realize. If we were to plot Turn, T, on the x-axis, and the whole number value of Available Mana, M, on the y-axis, we would still need to plot the probability of N mana-sources per turn, P(T,M), on a z-axis, in order to relate the entire story. This three-dimensional plot is known as a hyper-geometric matrix (Prywes). By setting a given parameter of probability, 70% to 80% being reasonable according to Pyrwes, we can view a cross-section of the hyper-geometric matrix on a two-dimensional graph. On this plot, we will initially observe a curve that resembles either a step-function, or a diagonally oriented sine-curve. We can smooth out this curve by multiplying M by P(T,M). Presented here is the Mana Availability Curve of a sixty card deck, with twenty lands as the only mana-sources, where I have applied this treatment.




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