MTG Mulligan Probability Calculator
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MTG Mulligan Probability Calculator
Calculate the probability of having at least a certain number of key cards (e.g., lands, combo pieces) in your opening hand, accounting for multiple mulligans using the London Mulligan rule.
Deck Size (cards)
Number of Key Cards in Deck
Minimum Copies Wanted in Hand
Maximum Copies Wanted in Hand (0 = no max)
Number of Mulligans Taken (0–3)
On the Play? (draws 7, not 8)
Yes (on the play) No (on the draw)
Calculate Results will appear here.
function mtgHypergeometric(N, K, n, k) { // P(X = k) = C(K,k)*C(N-K,n-k)/C(N,n) function logFactorial(x) { if (x a) return -Infinity; if (b === 0 || b === a) return 0; return logFactorial(a) - logFactorial(b) - logFactorial(a - b); } var logP = logComb(K, k) + logComb(N - K, n - k) - logComb(N, n); return Math.exp(logP); }
function mtgHypergeoCDF(N, K, n, minK, maxK) { // P(minK Please fill in all fields with valid numbers.'; return; } if (N 250) { resultDiv.innerHTML = 'Deck size must be between 40 and 250.'; return; } if (K N) { resultDiv.innerHTML = 'Key cards must be between 1 and deck size.'; return; } if (minCopies 7) { resultDiv.innerHTML = 'Minimum copies must be between 1 and 7.'; return; } if (maxCopies !== 0 && maxCopies Maximum copies must be 0 (no max) or >= minimum copies.'; return; } if (mulligans 3) { resultDiv.innerHTML = 'Mulligans must be between 0 and 3.'; return; }
var effectiveMax = (maxCopies === 0) ? 7 : maxCopies;
// London Mulligan: after m mulligans, you draw 7 cards and keep (7 - m) // You bottom (m) cards after drawing 7 each time. // For probability purposes: you see 7 cards each mulligan attempt. // The probability of a "good" hand on attempt i (0-indexed) is: // P(good | see 7 cards from remaining deck) using hypergeometric // We model: each mulligan you draw 7 from the full deck (shuffled fresh). // P(keep on first draw) = P(good in 7) // P(keep after 1 mulligan) = P(bad in 7) * P(good in 7 with 6 kept) // After m mulligans, hand size = 7 - m
// P(good hand of size h) = P(minCopies 0) ? ' (forced keep)' : ''; tableRows += '' + '' + label + forced + '' + '' + row.handSize + '' + '' + (row.pReach * 100).toFixed(2) + '%' + '' + (row.pGood * 100).toFixed(2) + '%' + '' + (row.pKeepGood * 100).toFixed(2) + '%' + ''; }
var maxLabel = (maxCopies === 0) ? '7' : maxCopies; var playLabel = (onPlay === 1) ? 'on the play' : 'on the draw';
resultDiv.innerHTML = '### Results ' + 'Configuration: ' + N + '-card deck, ' + K + ' key cards, want ' + minCopies + '–' + maxLabel + ' in hand, ' + mulligans + ' mulligan(s) allowed, ' + playLabel + '.
' + '' + '' + 'Attempt' + 'Hand Size' + 'P(Reach)' + 'P(Good Hand)' + 'P(Keep Good)' + '' + tableRows + '' + 'Total probability of a satisfactory hand: ' + (totalGood * 100).toFixed(2) + '%
' + 'Probability of an unsatisfactory hand: ' + ((1 - totalGood) * 100).toFixed(2) + '%
'; }
#### Formula
Each draw uses the Hypergeometric Distribution:
P(X = k) = C(K, k) × C(N−K, n−k) / C(N, n)
- N = deck size
- K = number of key cards in deck
- n = hand size drawn (7 − mulligans taken)
- k = number of key cards in hand
A hand is "good" if minCopies ≤ X ≤ maxCopies.
Under the London Mulligan, after m mulligans you draw 7 cards and keep 7−m (bottoming m cards). For probability modeling, each attempt is treated as drawing from a freshly shuffled full deck of size n = 7−m.
Total probability of a good hand:
P(good) = Σi=0..m [ P(bad)i × P(good | hand size 7−i) ]
where P(bad)i is the probability of reaching attempt i (all prior hands were bad).
#### Assumptions & References
- Uses the London Mulligan rule (draw 7, keep 7−m, bottom m cards), introduced in Magic: The Gathering in 2019.
- Setting Maximum Copies = 0 means no upper limit (you just want at least the minimum).
- References: Frank Karsten, How Many Lands Do You Need to Consistently Hit Your Land Drops? (Channel Fireball, 2022); Hypergeometric distribution (Wikipedia).
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