King Goldfish

Live odds

Each card in your hand shows whether your untapped lands and the mana in your pool, plus a land drop if you haven't made one, can pay for it now. If not, it shows the chance your lands can pay for it on its turn (its mana value, or next turn if that has passed), from 1,000 shuffles of what's left in your library: one land a turn from your hand and draws, lands that enter tapped played first, then on that turn a land that pays for it. The shuffles are seeded from the game, so the same position always shows the same numbers.

odds = shuffles where the lands pay its cost on turn T / 1,000

Lands only, as in Frank Karsten's tables: mana rocks, creatures and rituals aren't counted, so decks with them cast on time more often than the chips show. Fetchlands count as the colors they can find in your deck; taplands, fastlands, slowlands and checklands enter tapped by the usual rules. Every chip is the same color, with a pale bar as long as its percent; no cutoff colors a chance.

Multiplayer rules

Commander and Oathbreaker decks play by the multiplayer rules: the first mulligan is free (Comprehensive Rules 103.5c, which also makes it free in any Brawl game), and everyone draws on turn one, on the play too (103.8c).

This hand against random hands

Your hand is played out 1,000 times with the rest of the deck shuffled (after a mulligan, the cards you put on the bottom stay on the bottom), next to 1,000 random hands of the same size and 1,000 of one card fewer, which is the hand a mulligan gives (a fresh seven when the first mulligan is free). Each game plays the land that lets it spend the most that turn (a land that enters tapped goes first when it costs nothing), then casts the most mana's worth of spells the lands can pay for. Split cards and Rooms count the half you cast.

mana used by turn 4 = mana value cast on turns 1 to 4 (at most 1 + 2 + 3 + 4 = 10)

The page shows this hand's mana used by turn 4 next to the random hands, and the difference to the hand a mulligan gives, with that difference's 95% range from the spread of the games on each side:

difference range = d +/- 1.96 x sqrt(s1^2/1,000 + s2^2/1,000), where d is the difference and s1, s2 the standard deviations of mana used

Also shown, with the same difference in percentage points: the chance of three lands by turn 3, four by turn 4, and being stuck on two. No threshold turns the numbers into a call; the matchup and the plan are yours to weigh.

The deck over a thousand games

The same games from random hands, with Frank Karsten's mulligan rules (keep seven with 2 to 5 lands, six with 2 to 4, five with 1 to 4) and the London mulligan's bottom cards chosen to leave about 43% lands.

Shuffles and seeds

Every game is dealt by a seeded shuffle (the mulberry32 generator), so the same seed and deck deal the same game: replay it, or share the seed. A card you force into the opening hand is taken from the library first, and the rest of the hand is dealt as usual.

Two decks on one device

Two decks on one device: each player keeps a hand in turn, then you take turns; between turns a cover hides the table until the next player says who they are, so each sees only their own hand. Both life totals are counted; a new turn starts a new undo history. The game is kept on this device as you play: a reload brings it back on the hand-off screen, never on a hand, and Leave two decks has an undo.

The board's extras

The board's extras: tokens (named, with power and toughness, tapped or not), counters of any kind (+1/+1 and -1/-1 cancel in pairs, rule 704.5q), a two-faced card's other face, face down, and attaching; a permanent that leaves the battlefield takes none of these with it (rule 400.7), and an Aura attached to it goes to the graveyard (rule 704.5m) while Equipment stays, unattached.

Sources

• Frank Karsten, "How Many Sources Do You Need to Consistently Cast Your Spells? A 2022 Update" (ChannelFireball, 2022): lands-only castability and the mulligan rules.
• Land colors read from each land's rules text; card data as on the other pages.
• Feature requests on Moxfield's public boards: #2277 (a guaranteed opening card), #145 (seed replay), #123 (a touch-friendly mana pool), #984 (cards from outside the deck), #1131 (an action log with undo).

Version against version, and the land count

Both lists play Matchup Lab's goldfish games from the same seeds. The cards they share sit in the same places and each changed card takes the place of the one it replaced, so game N of one version and game N of the other start from the same shuffle (common random numbers), and differences come from the lists, not luck. The 95% range is the normal interval on the per-game differences (unpaired, and said so, when the lists differ in size). The land count moves by up to three, swapping the land and spells the page names; screwed is fewer than 3 lands among the cards seen by turn 3, on curve is a land for each of turns 1 to 4, flooded is 7 or more lands among the cards seen by turn 6.