Mana curve

The "mana curve" is the application of mana optimization theory to deck construction. By organizing the cards that are to go into a deck by their casting cost, a player can see how likely they will be able to optimally utilize each turn's mana (i.e., to play a card or cards with a casting cost or costs with a total equal to the mana available on that turn). In order for a deck to curve out properly it must also maintain color balance.

Basic curves
Use of statistical analysis leads to the four following basic curves which vary based on deck size, format, and play/draw. Assuming that there is no mana acceleration or card drawing. No assumption is made as to what the spells themselves are except that their value is proportional to their cost. Another assumption is that one play per turn is desirable. In all of these cases except "40 Cards, Play first," the final mana cost has received a doubled number because it is expected that you will miss the subsequent land drop and that it is therefore desired to draw a second of the prior part of the curve because enough land to make said land drop prevents enough spells to make every spell drop. See 60 cards, draw first for an example calculation.

60 Cards, play first

9 at one, 8 at two, 8 at three (One added here to make 60 cards), 11 at four, 24 Land.

60 cards, draw first

8 at one, 7 at two, 6 at three, 5 at four, 9 at five, 25 Land.

40 Cards, play first

6 at one, 5 at two, 4 at three, 4 at four, 4 at five, 17 Land.

40 Cards, draw first

5 at one, 4 at two, 4 at three, 4 at four, 6 at five, 17 Land.

Simulation
Computer simulation can create mana curves by a process known as evolution.

Natural mana curves and artificial mana curves differ in that artificial mana curves have a bias for playing fewer lands. This bias can be achieved by using the number of lands in a deck as a tie-breaker during evolution. Since simulations are able to create thousands of simulated draws it is summarize outcomes.

The key to the curves given here is:

{Land One-drop Two-drop Three-drop Four-drop : turn4%kill turn5%kill... : # games total# turns}

Natural mana curve [sic]:

27 12 13 05 03:3446 5519 1034 1 0 0:Finished 10000 games in 57590 turns

Artificial mana curves [sic]:

22 12 12 14 00:1978 6893 647 243 127 35:Finished 10000 games in 60117 turns

24 12 12 08 04:2608 6537 526 183 88 31:Finished 10000 games in 58811 turns. RDW mana curve

24 24 04 04 04:1228 7389 1163 149 31 12:Finished 10000 games in 60552 turns

This is the mana curve from a red deck wins! It has to be noted that the turns it kills are not identical to practice, since the fetchlands have been replaced by basic lands.