1. Expected Value: The Average Return per 300 Yen Lottery Ticket
For games like lotteries, you can find the average return per ticket by dividing the total prize money by the number of tickets sold. This figure is called the expected value. It does not mean you get this amount back every time you buy a ticket; rather, it is the average if you bought many tickets.
According to data for fiscal year 2024, 46.5% of lottery sales are allocated to prize money [3]. If you multiply 300 yen by 0.465, you get 139.5 yen. This means the average return per ticket is about 140 yen, which is roughly 160 yen less than the cost of the ticket.
If you buy 10 tickets, you spend 3,000 yen, and the average return would be about 1,395 yen. However, this is a national average. The return rate for specific lotteries, such as the year-end Jumbo, may differ slightly from this figure.
2. The Chance of Winning the Jumbo Lottery Top Prize: 1 in 20 Million
The year-end Jumbo Lottery is sold in units of 200 sets, or 20 million tickets, with one top prize per unit [2]. Therefore, the probability of winning the top prize is 1 in 20 million.
If the total sales are 138 billion yen and there are 23 units, there are 460 million tickets in total. Since there are 23 top prizes, dividing 23 by 460 million still results in 1 in 20 million. This agrees with the per-unit calculation: one top prize for every 20 million tickets.
To help visualize this large number, consider this example: If you stack 20 million sheets of paper, each 0.1 millimeters thick, the pile would be about 2 kilometers (about 1.2 miles) high. Only one sheet in that pile is the winner. Alternatively, if you tried once every day, it would take an average of 20 million days, or about 55,000 years.
The figure of 1 in 20 million is calculated from official ticket counts. It is not a probability explicitly written on the official page, but derived from the data.
3. The Law That Caps Lottery Prize Money at 50% of Sales
Article 5 of the Prize-Bearing Ticket Act states that, as a rule, the total prize money must be 50% or less of the total sales [1]. However, for additional prize lotteries, extra prize money can be added. The calculations in this article assume a standard lottery. Even if the return rate were exactly 50%, the average return on a 300 yen ticket would be 150 yen, which is still less than the purchase price.
According to the Ministry of Internal Affairs and Communications, the return rate for lotteries in fiscal year 2008 was 45.7%. This is much lower than public sports betting, such as boat racing (74.8%), bicycle racing (75.0%), and horse racing (74.1%) [6]. Because these figures are from an older fiscal year, they cannot be used for current comparisons.
The law sets a general cap on the share of sales that can be paid out as prizes, and public documents record return rates.
4. Where Lottery Sales Money Goes: Prizes, Public Funds, and Costs
For fiscal year 2024, the breakdown of lottery sales was: 46.5% for prize money, 36.2% for revenue, 16.0% for printing and sales commissions, and 1.3% for social contribution publicity [3]. Total national sales were approximately 759.8 billion yen, distributed according to these percentages.
The revenue is what is left of sales after prizes and expenses; according to Wakayama Prefecture, it is about 40% of sales. It is paid to the prefectures and designated cities that issue the tickets, and is used for roads, rivers, educational facilities, child-rearing support, elderly welfare, and cultural and sports promotion [5].
Tokyo plans to use about 60.4 billion yen for public works and other projects in fiscal year 2025. This includes about 21.3 billion yen for child-rearing promotion grants and about 6.6 billion yen for park development [4]. Tokyo’s chart classifies expenses and commissions as 17.4%, which is a different categorization method compared to Mie Prefecture’s 16.0% plus 1.3%. Figures from different fiscal years or with different classifications should not be mixed for comparison.
5. Why People Overestimate Very Small Chances of Winning
Psychologists Kahneman and Tversky stated in their 1979 paper on Prospect Theory that people sometimes treat very small probabilities as heavier in their judgments than they actually are. They wrote that this may increase the appeal of insurance and gambling [7].
The phrase "may contribute to" is important. The paper does not say that this is the only reason people buy lottery tickets. Other motivations, such as enjoyment, the time spent dreaming, or the desire to support public funds, may exist, but this article’s sources do not verify them.
The probability of 1 in 20 million is hard to grasp intuitively. By calculating the numbers yourself, you can see that the average return of about 140 yen is less than the ticket price.
6. Try the Lottery Calculations Yourself With Paper and Pencil
With paper and pencil, try these two calculations: 300 yen multiplied by 0.465 (the average per ticket) and 460 million divided by 23 (the denominator for the top prize probability). You can verify the meaning of the numbers with your own hands.
For a deeper look, read Article 5 of the Prize-Bearing Ticket Act, the Ministry of Internal Affairs and Communications document on effective return rates, local government explanations of how lottery revenue is used, and the original Kahneman and Tversky paper. Note that numbers change depending on the fiscal year.
【Safety Note】This article does not recommend purchasing tickets. Decide how to spend money in consultation with your family.