In the previous post, as well as in Karsten Frank's analysis, there is a subtle nuance that we have to touch upon. In both his article and in my initial post we assumed that we can read off the table the number of lands that is required for a spell like Anger of the Gods by looking at double-casting spells on turn 3. But, the table doesn't show that -- it shows the number of colored lands required for casting a CC spell on turn 3, assuming we have enough lands (i.e. 2 lands on turn 3). This is not the same!
It turns out that casting a 1CC spell on turn 3 requires less colored sources than casting a CC spell on turn 3. This sounds absolutely crazy at first, but remember the first assumption, that we have enough lands to cast them in the first place. Consider for a second, that we want 0% color-failure in a 24-land 60-card deck. To have no color failures on turn 2 means that we need to have 24 colored mana. On turn 3, you might think that we can allow non-colored mana, but that is wrong since we are comparing against the chance of having enough lands and that includes the chance of having only 2 lands on turn 3 - in which case there is a non-zero chance that one of them is the off-colored mana source.
In other words, the pre-condition "have enough lands to be able to cast the spell" over-inflates the colored-land tables that we have presented, and it may be more useful to make a table consisting of the required number of lands in order to avoid color-failures for each of the consecutive spells. So, for instance, a table comprising C, 1C, 2C, 3C, 4C, 5C and 6C for single-colored spells and a table CC, 1CC, 2CC, 3CC, 4CC, 5CC for double-colored spells and so on, given at the first turn you can cast them:
| Spell Type | C | 1C | 2C | 3C | 4C | 5C | 6C |
|---|---|---|---|---|---|---|---|
| 90.00% | 14 | 13 | 11 | 9 | 8 | 7 | 6 |
As you can see, this is quite different from the previous table. For double-colored spells:
| Spell Type | - | CC | 1CC | 2CC | 3CC | 4CC | 5CC |
|---|---|---|---|---|---|---|---|
| 90.00% | - | 20 | 17 | 15 | 13 | 11 | 10 |
And finally for triple-colored spells
| Spell Type | - | - | CCC | 1CCC | 2CCC | 3CCC | 4CCC |
|---|---|---|---|---|---|---|---|
| 90.00% | - | - | 22 | 19 | 17 | 15 | 13 |
From this, we can revise our numbers for Anger of the Gods, which requires 17 out of 24 red sources, and Cryptic Command that requires 19 blue sources out of 24.
For completeness, here's a few variations:
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16/40 -- 1 2 3 4 5 6 7
C 9 8 7 6 5 4 4 3
CC 13 12 10 9 7 7 6 5
CCC 15 13 11 10 9 8 7 6
CCCC 16 14 12 11 10 9 8 7
17/40 -- 1 2 3 4 5 6 7
C 10 9 7 6 5 5 4 4
CC 14 12 10 9 8 7 6 5
CCC 16 14 12 11 9 8 8 7
CCCC 16 15 13 12 10 9 9 8
18/40 -- 1 2 3 4 5 6 7
C 10 9 8 7 6 5 4 4
CC 14 12 11 9 8 7 7 6
CCC 16 14 13 11 10 9 8 7
CCCC 17 15 14 12 11 10 9 8
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22/60 -- 1 2 3 4 5 6 7
C 13 12 10 9 7 6 6 5
CC 19 16 14 12 10 9 8 7
CCC 21 18 16 14 12 11 10 9
CCCC 21 19 17 15 14 12 11 10
23/60 -- 1 2 3 4 5 6 7
C 14 12 10 9 8 7 6 5
CC 20 17 14 12 11 10 9 8
CCC 22 19 16 15 13 12 10 10
CCCC 22 20 18 16 14 13 12 11
24/60 -- 1 2 3 4 5 6 7
C 14 13 11 9 8 7 6 5
CC 20 17 15 13 11 10 9 8
CCC 22 19 17 15 13 12 11 10
CCCC 23 21 18 17 15 14 12 11
25/60 -- 1 2 3 4 5 6 7
C 14 13 11 9 8 7 6 6
CC 21 18 15 13 12 10 9 8
CCC 23 20 18 16 14 13 11 10
CCCC 24 21 19 17 16 14 13 12
26/60 -- 1 2 3 4 5 6 7
C 15 13 11 10 8 7 7 6
CC 21 18 16 14 12 11 10 9
CCC 24 21 18 16 15 13 12 11
CCCC 25 22 20 18 16 15 13 12
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