Manabase+

The engine

Your deck is shuffled and played out as a goldfish, turn by turn: 6,000 games for a 60-card deck, 4,000 for 90 or more, on the play and on the draw, in the background so the page never freezes. The example the page opens on plays 2,000 games, so a first visit isn't kept busy; any list you paste or deck you open plays the full count. Mulligans follow Frank Karsten's keep rules with the London mulligan: keep seven with 2 to 5 lands, six with 2 to 4, five with 1 to 4, and always keep four. In multiplayer and Brawl the first mulligan is free (rule 103.5c), and a 99-card deck sends back a two-land seven only while that free mulligan is left. King Goldfish uses the same keep rules.

At the start of each turn it asks every spell: with what's already out, fast mana in hand, and a land drop from your hand that pays for it (picked in hindsight, as Karsten's method assumes), could you be cast now? Then it develops: a land (a tapped one when that turn's mana isn't needed, and the color the deck wants most), rocks and creatures, ramp, Treasure, and cantrips while short on lands. Rituals and free mana are saved for the turn that needs them. In decks of 90 or more cards, a two-land seven goes back while a mulligan is still cheap.

What each number means

Colors right: in the games where you have enough mana on the spell's turn, how often you can also pay its colors, counting every source. Lands only: the same question with every nonland source switched off, which is Frank Karsten's measure. On curve: the share of all games where you can cast it on the turn equal to its mana value. The bar to clear is Karsten's:

colors right = games castable / games with enough mana

bar = 89% + turn, up to 99%

What each source adds: the same shuffled games replayed with one kind of source switched off (the first 60% of them), so the difference is the source, not luck.

Land count

The report prints the deck's land count, the figure from Frank Karsten's 2022 regression for its curve, and the signed difference between the two:

60 cards: 19.59 + 1.90 x average mana value - 0.28 x cheap draw or ramp spells

99 or 100 cards: 31.42 + 3.13 x average mana value - 0.28 x cheap draw or ramp spells

Cheap means mana value 2 or less. A deck of 38 to 42 cards is set against the Limited standard of 17 lands.

Draw odds

Exact, not simulated: the hypergeometric chance to see at least one copy by a turn.

P(at least one) = 1 - C(N - K, n) / C(N, n)

N is the deck size, K the copies, n the cards seen by then (7, plus one per turn, minus one on the play). With tutors, K counts the tutors too.

Land and mana swap test

Every nonbasic land legal in the format (and inside the commander's colors) is screened. The ones that make two or more of the colors your spells ask for, counting a fetchland by what it can find in this deck, get a screening score, and the 24 with the highest score (30 for 99-card decks) are played out, plus up to eight mana rocks and creatures at three mana or less: the ones with the lowest EDHREC rank, legal here and not already in the deck. Each is swapped in for one land, on the very same shuffles as the deck as it is, so the difference is the swap and nothing else. When a swap brings a land with basic types (a shock or surveil land), fetchlands already in the deck count it as something they can find.

screening score = 10 x (share of the spells' colored mana symbols its colors cover) x untapped factor + 0.4 if a fetchland in the deck can find it - 0.3 if the deck already runs a copy - min(1, EDHREC rank / 40,000)

The untapped factor is 1 for a land that always enters untapped, 0.97 for a fastland (0.85 in 99-card decks), 0.94 for a checkland, 0.9 for a slowland (0.96 in 99-card decks) and 0.72 for a land that always enters tapped. The land taken out is the basic whose color has the most sources for each mana symbol asking for it; with no basics, the land that makes the fewest of the colors your spells ask for. The list is sorted by the change on the measure you pick, largest first; ties go to the larger change on curve, then to lands without a hidden cost, then to lands that enter untapped more often, then to the lower EDHREC rank.

Shuffles and ranges. The deck as it is plays 6,000 shuffles (4,000 for 90 cards or more); each tested swap plays the first 2,000 of those same shuffles (1,000 for 90 or more). The deck is put in one order first (copies merged, cards by name) and every shuffle gets its own seed from the card names and its number, so the same deck pasted in any order plays the same games, and a deck with one card swapped plays the very same shuffles with that one card changed: its change is paired, game for game. Shuffles run in batches of 100. A figure's 95% range comes from how much it varies from batch to batch, and a change's from how much the paired change varies from batch to batch:

range = figure +/- t x sd(batch figures) / sqrt(batches), with t from Student's t at batches - 1 degrees of freedom (about 2.09 for 20 batches)

Points are percentage points across the deck's spells, every copy counted (the report's headline counts each card once, however many copies). A figure is shown to one decimal, and a change shown beside its before and after figures is the difference of those two shown figures.

Measured one after another. Up to three land swaps in sequence. A swap is eligible when the lower end of its change's 95% range is above zero; the eligible land with the largest change is measured again on all the deck's shuffles against the deck before it and kept only if that range is above zero too. Each later swap is found the same way on the deck the swaps before it made, among the eight eligible lands with the largest changes in the first list, so a fetchland and the dual it finds are measured together. Every before and after figure is measured, and the deck after one swap is the deck before the next, on the same shuffles, so each after figure is the next before figure. Lands with a cost these games can't see are named on their row and left out of the sequence: life every time they tap (City of Brass, Mana Confluence), a gift to the opponent, colors borrowed from other lands (Reflecting Pool), or a color an opponent picks. In formats with a commander the sequence keeps the life-per-tap lands. Each swap has an apply button, which puts in that swap and the ones above it; each row of the list has one too. Limited is not tested: its lands come from your pool.

Checks and limits

Checked when it was built: its lands-only numbers came within two points of the site's first engine on three test decks (a two-color 60-card deck, an Esper deck full of taplands, and a 99-card Commander deck). That first engine matches Karsten's published numbers: 14 sources for a one-drop in 60 cards gives 91.6%, against his target of about 90%. It is a goldfish: nobody kills your mana creatures, so in real games a deck with many mana creatures casts on time a little less often than these numbers. Cards that get cheaper during a game (convoke, delve, affinity) are measured at printed cost; variable mana counts at its smallest amount.

The swap test in Decks

In a deck's stats tab in Decks, test legal lands and mana runs the same test on the deck: every land legal in the deck's format and colors is screened, the ones with the highest screening score are swapped in for one land and played out on the same shuffles, and up to three swaps are measured one after another, with fetchlands and the duals they find measured together. Each apply button puts its swaps in as one step that Ctrl Z undoes. Here on Manabase+ an apply button changes the list as it is in the box, typing included, and measures it again; Ctrl Z, or the undo on the notice, puts the box back exactly as it was. A saved deck is only changed in Decks, where it removes the copy with the least you added to it (no note or category first).

Sources

• Frank Karsten, "How Many Sources Do You Need to Consistently Cast Your Spells? A 2022 Update" (ChannelFireball, 2022): the bar and the lands-only method.
• Frank Karsten's land-count regression (2022): the land count for a given curve.
• Mana abilities read from each card's rules text; legality from Scryfall.

A hand you'd keep, and combo odds

Exact multivariate hypergeometric sums: the library is cut into pieces by which of your groups each card is in, so overlapping groups count once. After a London mulligan to six, the card put on the bottom is the one that keeps the rule, if any does. For combo odds, a tutor in hand stands in for one missing piece; mana, timing and mulligans are left out.