Lottery Win Probability Calculator
Calculate your chance of winning when drawn tickets are not put back (sampling without replacement) — in other words, the probability of winning within a given number of draws.
Just enter the number of draws, winning tickets, and losing tickets, and it works out the probability for each draw along with the formula.
This tool has been used … times.
📖 How to Use
STEP 1 — Enter the draw conditions
Enter how many times you can draw in “Number of draws”, and the ticket counts in “Winning tickets” and “Losing tickets”.
Change the values with the +/− buttons or by typing directly.
Change the values with the +/− buttons or by typing directly.
STEP 2 — Calculate the probability
Press “Calculate” and the win probability appears with an animation.
You can also review the probability and formula for each individual draw.
You can also review the probability and formula for each individual draw.
⚠️ This tool calculates for the “without replacement” method (drawn tickets are not put back). The result differs from cases where tickets are returned each time (constant probability, like gacha). For the with-replacement case, use the Probability Calculator.
ℹ️ How It Works
When drawn tickets are not put back, you calculate the win probability on each draw and add them up to get the total win probability.
Example: 3 draws, 1 winning ticket, 9 losing tickets:
- Winning on draw 1: 1/10 = 10%
- Winning on draw 2: 9/10 × 1/9 = 10%
- Winning on draw 3: 9/10 × 8/9 × 1/8 = 10%
- Total win probability (sum): 30%