-------------------------------------------- "Let's do the Numbers - Part I, Mana Ratios" -------------------------------------------- One of the least talked about, but most theoretically important part of MTG is the numbers. MTG is at a very basic level, and from a certain viewpoint, all about numbers. Perhaps the subject is too dry or analytical for some tastes, but the numbers are worth delving into for the intermediate player looking to hone their deck building skills, and even for the expert player looking to refine and analyze a deck to the "Nth" degree. The numbers that are presented here revolve around mana ratio's and expected number of land drawn on a given turn. Let's look at the first chart: "Probability of having at least X number of land(s) (Lx) in the initial z number of cards (Cz) given n lands in a 60 card deck:" L1:C7 L2:C8 L3:C9 n=16 90.06% 69.12% 53.45% n=17 91.68% 72.91% 58.58% n=18 93.02% 76.40% 63.45% n=19 94.18% 79.56% 68.00% n=20 95.17% 82.42% 72.24% n=21 96.02% 84.98% 76.10% n=22 96.72% 87.22% 79.62% n=23 97.34% 89.24% 82.73% n=24 97.82% 90.98% 85.52% n=25 98.26% 92.51% 87.94% n=26 98.61% 93.82% 90.04% The above chart may look a little daunting, so I'll use Jay Schneider's "Sligh Assualt" (SA) Deck from June '98 to illustrate it's use. The SA deck has 22 land (18 Mountains and 4 Wastelands) so we'll look at an abbreviated chart concentrating on the number of mountains in the deck (18) and total land (22): L1:C7 L2:C8 L3:C9 n=18 93.02% 76.40% 63.45% n=22 96.72% 87.22% 79.62% This tells me many things: 1. The SA deck has a 93.02% chance of drawing at least one mountain in the initial draw of 7 cards (Cross section of n=18 and L1:C7). a. The SA deck will be forced into a "No-Mountain mulligan" about 1 in 14 games (7% of the time). b. Considering an average tourney to be six rounds, and an average round to be 2.5 matches, we get a figure of 15 games per tourey. So the SA deck will forced to "No-Mountain mulligan" about once per touney. 2. When going first, the SA will have at least three land (three or more) on the third turn (9 cards) about 80% of the time (Cross section of n=22 and L3:C9), and will have at least three mountains on the third turn about 63% of the time (Cross section of n=18 and L3:C9). a. The SA deck will have the necessary mana to make a third turn play such as Sandstalker, Lancer, or Scroll activation 4 in 5 games. b. The SA deck will have the necessary mana to make a third turn play such as Ball Lightning or Seismic Assault 2 in 3 games. Decks can be analyzed in many ways. The next table is a bit simpler, geared towards showing how quickly a deck will reach a minimum mana of two by the third turn (if going first): "Probability to have at least two lands in the initial 9 cards given n lands in a 60 card deck:" n=16 76.02% n=17 79.52% n=18 82.62% n=19 85.36% n=20 87.74% n=21 89.81% n=22 91.62% n=23 93.14% n=24 94.45% n=25 95.53% n=26 96.44% Taking as example "Cuneo Blue" (CB) from the June "Decks to Beat" we start with a base of 24 land, 16 which produce blue mana and eight colorless. Assuming that CB needs at least 2 mana on turn 3 (to be set-up to Counterspell, Impulse, or play a Mind Stone) we can consult the above chart and see that CB will have the necessary land 94.45% of the time. One corollary is that CB will have to discard (assuming the player took a one land hand rather than mulliganing) about 1 in 20 games, or less than once per tournament. If someone took the CB deck and tweaked it so that it had 2 less land (a total of 22 land now), the percentage drops to 91.62%, and the "Discard on third turn" ratio jumps up to a much worse 1 in 11 games, or almost *TWICE* as often. The above examples are simplified, as there are many cards that are typically used in decks that will skew these numbers, e.g. Dark Ritual, Mox Diamond, Svyelunite Temple, Birds of Paradise, etc. Still, these charts are a good reference for basic deck construction, and a tool that can be expanded and used for further exploration and contemplation of "The Numbers". -Frank Kusumoto