Lottery Win Simulator | Visualize Expected Value & Payout Ratio with Monte Carlo
Based on the prize table of Japan's Year-End Jumbo Lottery, calculate the exact expected value and payout ratio, then run a Monte Carlo simulation for any ticket count and see the spread of outcomes as a histogram. Free tool.
Prize Table (Japan Year-End Jumbo Lottery)
| Rank | Winners | Prize Amount |
|---|---|---|
| 1st Prize | 1 | 700,000,000 yen |
| 1st Prize Adjacent | 2 | 150,000,000 yen |
| 1st Prize Group Difference | 9 | 100,000 yen |
| 2nd Prize | 1 | 100,000,000 yen |
| 3rd Prize | 3 | 1,000,000 yen |
| 4th Prize | 100 | 100,000 yen |
| 5th Prize | 2,000 | 10,000 yen |
| 6th Prize | 100,000 | 3,000 yen |
| 7th Prize | 1,000,000 | 300 yen |
* The figures above are representative values based on the standard prize structure of Japan's Year-End Jumbo Lottery. Actual prize amounts and winner counts are announced officially for each drawing and may vary slightly.
Based on this prize table, the total prize pool for one unit of 10,000,000 tickets is 1,733,900,000 yen. For a ticket priced at 300 yen, the expected value is about 173.4 yen — a payout ratio of roughly 57.8%. In other words, on average you only get back a bit more than half of what you spend.
What Is the Lottery Win Simulator?
Talk about the lottery usually fixates on one thing: the chance of winning hundreds of millions of yen. But the actual shape of what comes back to buyers looks nothing like that headline number. This tool starts from the prize table of Japan's Year-End Jumbo Lottery (年末ジャンボ), works out the exact expected value and payout ratio, and then runs a Monte Carlo simulation that repeats a "buy this many tickets" attempt many times over, plotting the spread of outcomes as a histogram.
The real story is in the shape of that distribution. The overwhelming majority of attempts land on the loss side, while only a rare few spike far into positive territory. That lopsidedness is the whole point — it is invisible if you only look at the average. The simulation itself relies on pseudo-random numbers and does not predict any real drawing; it exists purely to make the underlying probabilities tangible.
How to Use This Simulator
- Check the expected value in the prize table The expected value and payout ratio, calculated from the winner counts and amounts per rank, are shown first — this tells you how much comes back on average per yen spent.
- Enter how many tickets you plan to buy Specify how many tickets to buy in a single attempt. Using a realistic number gives you a distribution that matches what you are actually considering.
- Read the shape of the histogram The horizontal axis is the net result and the vertical axis is the number of attempts. Notice where the bulk of outcomes cluster and how thin the positive-side tail is.
- Re-run it to see how consistent the shape is Each run uses a new random sequence, so individual numbers shift. Try running it several times to confirm the overall shape stays similar.
Tips for getting more out of it
- The more tickets you buy, the closer your average result converges to the overall payout ratio (about 58%) — but that never means you come out ahead. This is the law of large numbers: more trials converge toward the expected value, not above it.
- Notice how most attempts cluster on the "net loss" side of the histogram, with only a rare few spiking far to the right (a big win). This lopsided shape is characteristic of lotteries.
- Every time you click "Re-run Simulation," a new random sequence is used, so the result changes slightly. Try running it several times to see how the overall shape of the distribution stays consistent even as individual outcomes vary.
- This tool's payout ratio (about 58%) is notably lower than government-authorized racing (roughly 75%) or pachinko (roughly 80-85%) in Japan — useful context when comparing the economics of different forms of gambling.
Ways to Use This Simulator
Decide on a budget before you buy
Run the number of tickets you're actually considering and see the average result and win rate. That turns a gut feeling into a number you can budget against.
Understand the difference between expected value and distribution
Two situations with the same average can feel completely different depending on the shape of the distribution. This is a clear, concrete example for learning basic probability.
Compare payout ratios across forms of gambling
Lining up the lottery's payout ratio against government-authorized racing or pachinko makes the different design philosophies visible as numbers, not impressions.
See the law of large numbers in action
Increase the ticket count and watch the average result drift toward the expected value. It's a hands-on way to feel how trial count and convergence relate.
Probability & Expected Value Terms
- Expected value
- The average amount you get back per attempt. It is calculated by multiplying each prize amount by its probability and summing the results.
- Payout ratio
- The share of your spending that comes back on average. It equals the expected value divided by the ticket price — around 58% for this lottery.
- Monte Carlo method
- A technique that repeats a random trial a large number of times and studies the resulting distribution. It is used for problems that are hard to solve with a formula alone.
- Law of large numbers
- The principle that the average outcome converges toward the expected value as the number of trials grows. It is also why buying more tickets never shrinks your expected loss.
- Histogram
- A chart that shows how many results fall into each value range as bar heights. It reveals where outcomes cluster at a glance.
- Skewed distribution
- A distribution that isn't symmetric and instead has a long tail on one side. The lottery's distribution has an extremely long tail stretching toward the positive side.
Frequently Asked Questions
Side Note — Why Is the Lottery's Payout Ratio So Low?
Japan's lotteries are issued under the Lottery Ticket Act (当せん金付証票法), which caps the total prize payout as a fixed share of ticket sales. The remainder funds public projects run by the issuing prefectures and municipalities — welfare, education, disaster prevention — along with printing and administrative costs. In other words, a low payout ratio is a deliberate feature of the system, not an accident, which is why lotteries pay out less than most other forms of gambling.
Government-authorized racing (horse racing, bicycle racing, and similar) typically returns around 75% of stakes, and pachinko/pachi-slot machines are often estimated at around 80-85%. Compared to these, the lottery's payout ratio (roughly 58% for the Year-End Jumbo) is clearly on the low side. What the lottery offers instead is a uniquely accessible bet: a ticket costs only a few hundred yen, yet the top prize can reach into the hundreds of millions — a "low risk, low probability, extremely high jackpot" design found nowhere else.
Lottery winnings are entirely exempt from income and residence tax in Japan (Lottery Ticket Act, Article 13). The idea is that the tax burden is effectively already built into the price of the ticket, so winners receive the full prize amount — a notable advantage compared with other one-time windfalls, such as sweepstakes prizes, which are typically taxable.