Best Lottery Calculator

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Best Lottery Calculator

Calculate your odds of winning and the Expected Value (EV) of any lottery game.

Results

How to Use the Lottery Probability Calculator

Calculating the odds of winning the lottery involves complex combinatorics. Our calculator simplifies this by using the standard combination formula. To get started, you need to know the specific rules of the lottery you are playing.

  • Main Pool: The total count of numbers available to choose from (e.g., in Powerball, this is 69).
  • Numbers to Pick: How many numbers you must select on your ticket (e.g., 5).
  • Bonus Pool: If the game has a "Powerball" or "Mega Ball," enter the total range of that pool (e.g., 26). If there is no bonus ball, enter 0.
  • Jackpot Amount: The current advertised prize. This is used to calculate the Expected Value.

Understanding the Math: Combinations Formula

The probability of winning is determined by the number of possible ways to choose k numbers from a set of n numbers. The formula is expressed as:

C(n, k) = n! / [k! * (n – k)!]

If there is a bonus ball, we multiply the result of the main pool combination by the combination of the bonus pool. For a standard 5/69 + 1/26 game, the total combinations are 292,201,338.

What is Expected Value (EV)?

Expected Value tells you the "fairness" of a bet. In lottery terms, if the EV is positive (greater than $0.00 after subtracting the ticket cost), it technically means the ticket is worth more than you paid for it. However, because lotteries are high-variance, a positive EV does not guarantee a win.

Game Format Odds of Jackpot
Powerball 5/69 + 1/26 1 in 292,201,338
Mega Millions 5/70 + 1/25 1 in 302,575,350
EuroMillions 5/50 + 2/12 1 in 139,838,160

Why Taxes and Annuities Matter

Our calculator provides a raw Expected Value based on the gross jackpot. In reality, your "Real EV" would be lower due to federal and state taxes, and the difference between the cash value and the advertised annuity jackpot. Always play responsibly and view the lottery as entertainment, not an investment strategy.

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 Math.round(res); } function calculateLottery() { var n = parseInt(document.getElementById('mainPool').value); var k = parseInt(document.getElementById('pickCount').value); var m = parseInt(document.getElementById('bonusPool').value); var z = parseInt(document.getElementById('bonusPick').value); var cost = parseFloat(document.getElementById('ticketCost').value); var jackpot = parseFloat(document.getElementById('jackpotAmount').value); if (isNaN(n) || isNaN(k) || n <= 0 || k n) { alert("Please enter valid numbers for the main pool (n must be greater than k)."); return; } var mainCombos = combinations(n, k); var bonusCombos = 1; if (!isNaN(m) && !isNaN(z) && m > 0 && z > 0) { bonusCombos = combinations(m, z); } var totalOdds = mainCombos * bonusCombos; var probability = (1 / totalOdds) * 100; // Expected Value = (Jackpot * Probability) – Cost var rawEV = (jackpot / totalOdds) – cost; // Display results document.getElementById('lotteryResult').style.display = 'block'; document.getElementById('oddsDisplay').innerHTML = "Odds of Winning: 1 in " + totalOdds.toLocaleString(); document.getElementById('probDisplay').innerHTML = "Probability: " + probability.toFixed(10) + "%"; var evElement = document.getElementById('evDisplay'); var expElement = document.getElementById('evExplanation'); evElement.innerHTML = "Expected Value (EV): $" + rawEV.toFixed(2); if (rawEV > 0) { evElement.className = "res-val ev-positive"; expElement.innerHTML = "This game has a positive Expected Value based on the current jackpot. Note: This does not account for taxes or prize sharing."; } else { evElement.className = "res-val ev-negative"; expElement.innerHTML = "This game has a negative Expected Value. Statistically, for every dollar spent, you are expected to lose money."; } // Smooth scroll to result document.getElementById('lotteryResult').scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }

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