Arithmetic you can move
Two calculators that turn the deck you actually play into dates. Put in your lands, your colours, your curve and whether you are on the play; get back the turn a card really arrives and the mana your deck never spends — every figure moving as you change the deck, with the working shown underneath it.
The calculators
Calculator
Mana and the Turn
The turn you can count on casting a card of each cost — not the turn its mana cost suggests. It works out, for any amount of mana, the first turn you hold that many lands at least half the time, and shows the whole table of chances behind the answer.
Move the lands between fifteen and nineteen, take the play or the draw, add cheap mana sources, and watch the dates move. That is the whole argument about what “too expensive” means: a number you can check instead of a verdict.
And now with the colours in it. Split your lands between two colours, give the cost its coloured pips, and it answers for that card: the turn it really arrives, and whether it was the mana or the colour that kept it waiting. A grid of every cost against every turn sits above it, so the whole ladder is on one screen.
The arithmetic behind Mana. The drill that uses it is Casting Speed. Open the calculator →
Calculator
The Wasted Mana Calculator
The other half of the same question. Not when one card can be cast, but what a whole deck does with the mana it makes: how much goes unspent each turn out to turn fifteen, how many of your spells you actually cast, and how many are still stuck in your hand at the end.
Set a count at each cost and the extremes tell on themselves. By turn 10 a deck of nothing but two-drops has wasted 24.9 mana and a deck of nothing but six-drops 24.8 — the same figure, for opposite reasons. The cheap one has run out of cards (0.2 spells left in hand); the dear one is holding 6.2 it cannot deploy. The page names which of the two faults it is, in a sentence computed from the same run.
The arithmetic behind Mana, and behind the deck questions in Casting Speed. Open the calculator →
How they answer
One of them is solved and the other is dealt, because the two questions are not the same shape. “When can I cast a six-drop” is a question about one card: the chance that six of the cards you have seen — seven to start, one a turn, one more on the draw — are lands. That has an exact answer, and the calculator computes it rather than sampling it.
“How much mana does my deck waste by turn ten” depends on the order the cards arrived in and on what you have already cast, so there is nothing to solve: the deck is dealt 4,000 times from a fixed shuffle, and the same deck always gives the same figure.
Both are the same code the chapters and the drills use. The turn the chapter prints, the turn the drill marks you against and the turn the calculator shows are one calculation in one file — so they cannot disagree, and when the arithmetic is corrected all three move together.
And what they are not. There is no opponent in either of them, no mulligan, no card drawn beyond the one a turn, and no judgement about what a card does once it is cast. The deck that wastes the least mana over fifteen turns has almost no cheap spells and would lose to any fast start. Least waste is not the best deck; these answer “when” and “how much”, and leave “is it worth it” to you.
The drills live on the exercises page, and the chapter these two belong to is Mana.
