MTG Card Draw Probability Calculator

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MTG Card Draw Probability Calculator

Calculate the probability of drawing at least a certain number of specific cards from your deck using the hypergeometric distribution.

Deck Size (N)

Total number of cards in your deck (Standard: 60, Commander: 99)

Copies of Card in Deck (K)

How many copies of the target card are in your deck

Cards Drawn (n)

Number of cards drawn (opening hand = 7, after 1 draw = 8, etc.)

Desired Copies in Hand (k)

Minimum number of copies you want to draw

Calculate Probability Enter values and click Calculate.

function mtgLogFactorial(n) { if (n n) return -Infinity; if (k === 0 || k === n) return 0; return mtgLogFactorial(n) - mtgLogFactorial(k) - mtgLogFactorial(n - k); }

function mtgHypergeomExact(N, K, n, k) { // P(X = k) = C(K,k) * C(N-K, n-k) / C(N,n) var logP = mtgLogComb(K, k) + mtgLogComb(N - K, n - k) - mtgLogComb(N, n); return Math.exp(logP); }

function mtgHypergeomAtLeast(N, K, n, k) { // P(X >= k) = sum from i=k to min(K,n) of P(X=i) var prob = 0; var maxK = Math.min(K, n); for (var i = k; i Please fill in all fields with valid numbers.'; return; } if (N Deck size must be at least 1.'; return; } if (K Copies in deck must be at least 1.'; return; } if (n Cards drawn must be at least 1.'; return; } if (k Desired copies must be at least 1.'; return; } if (K > N) { resultDiv.innerHTML = 'Copies in deck cannot exceed deck size.'; return; } if (n > N) { resultDiv.innerHTML = 'Cards drawn cannot exceed deck size.'; return; } if (k > K) { resultDiv.innerHTML = 'Desired copies cannot exceed copies in deck.'; return; } if (k > n) { resultDiv.innerHTML = 'Desired copies cannot exceed cards drawn.'; return; }

var probAtLeast = mtgHypergeomAtLeast(N, K, n, k); var probExact = mtgHypergeomExact(N, K, n, k); var probZero = mtgHypergeomExact(N, K, n, 0); var expectedValue = n * (K / N);

var pct = (probAtLeast * 100).toFixed(2); var pctExact = (probExact * 100).toFixed(2); var pctMiss = (probZero * 100).toFixed(2);

var breakdown = ''; var maxK = Math.min(K, n); for (var i = 0; i ' + i + '' + p + '%'; }

resultDiv.innerHTML = '### Results ' + 'P(drawing at least ' + k + ' cop' + (k===1?'y':'ies') + ' in ' + n + ' cards): ' + '' + pct + '%

' + 'P(drawing exactly ' + k + ' cop' + (k===1?'y':'ies') + '): ' + pctExact + '%

' + 'P(drawing zero copies): ' + pctMiss + '%

' + 'Expected copies in hand: ' + expectedValue.toFixed(3) + '

' + '#### Full Distribution (P(X = i)) ' + '' + 'Copies Drawn (i)' + 'Probability' + '' + breakdown + ''; }

#### Formula

This calculator uses the Hypergeometric Distribution:

P(X = k) = C(K, k) × C(N−K, n−k) / C(N, n)

P(X ≥ k) = ∑i=kmin(K,n) P(X = i)

Where:

Logarithms of factorials are used internally to avoid numerical overflow for large deck sizes.

#### Assumptions & References

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References

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