Calculate the hypergeometric distribution rate for drawing specific cards in your deck.
Understanding MTG Probability Rates
In Magic: The Gathering, deck consistency is determined by the mathematical "rate" at which you draw specific resources. Whether you are trying to calculate the probability of hitting your land drops or the likelihood of drawing a specific win condition in your opening hand, the Hypergeometric Distribution is the standard tool used by pro players.
How the Calculation Works
This calculator determines the statistical likelihood of drawing a specific number of "successes" (the cards you want) from a finite population (your deck) without replacement. This is different from simple percentage math because every card drawn changes the "rate" of the remaining cards in the deck.
Realistic Example: Opening Hand Lands
Deck Size: 60
Successes in Deck: 24 (Lands)
Sample Size: 7 (Opening Hand)
Min Wanted: 2
Using these inputs, the calculator will show you the rate at which you can expect to see at least 2 lands in your starting seven cards.
Optimization Tips
To improve your draw rates, consider the following deck-building principles:
The Rule of 9: In a 60-card deck, running 4 copies of 9 different cards provides the highest consistency for a specific strategy.
Mana Sinks: If your land draw rate is high (over 26 lands), ensure you have cards that can utilize extra mana in the late game.
Cantrips: Cards like "Opt" or "Consider" effectively reduce your total deck size, increasing the rate of finding key pieces.
function calculateMTGRate() {
var N = parseInt(document.getElementById('deckSize').value);
var K = parseInt(document.getElementById('successInDeck').value);
var n = parseInt(document.getElementById('sampleSize').value);
var kMin = parseInt(document.getElementById('minSuccess').value);
var resultDiv = document.getElementById('mtg-result');
var resultText = document.getElementById('mtg-result-text');
if (isNaN(N) || isNaN(K) || isNaN(n) || isNaN(kMin)) {
alert("Please enter valid numbers in all fields.");
return;
}
if (K > N || n > N || kMin > n || kMin > K) {
resultDiv.style.display = "block";
resultText.innerHTML = "Error: Input values are logically impossible (e.g., drawing more successes than exist in the deck).";
return;
}
function combinations(n, k) {
if (k n) return 0;
if (k === 0 || k === n) return 1;
if (k > n / 2) k = n – k;
var res = 1;
for (var i = 1; i <= k; i++) {
res = res * (n – i + 1) / i;
}
return res;
}
function hypergeometric(k, N, K, n) {
return (combinations(K, k) * combinations(N – K, n – k)) / combinations(N, n);
}
var totalProbability = 0;
for (var i = kMin; i <= Math.min(n, K); i++) {
totalProbability += hypergeometric(i, N, K, n);
}
var percentage = (totalProbability * 100).toFixed(2);
resultDiv.style.display = "block";
resultText.innerHTML = "The probability rate of drawing at least " + kMin + " target card(s) is: " + percentage + "%This calculation assumes no cards have been removed from the deck prior to this sample.";
}