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.
Tips
- 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.
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.