Lottery commentary

type

According to the official website, the public lottery includes the "National Self-Governance Lottery" that is sold nationwide, and the "Block There are two types of lotteries.

Public lottery official website→https://www.takarakuji-official.jp/schedule/top.html

There are lottery, lottery, bingo, numbers, Kisekae Ku-chan, Quick One, etc., but in the story, we use the jumbo lottery of the "National Autonomous Lottery".

jumbo lottery

schedule

Jumbo lotteries are released five times a year, roughly according to the schedule below.

Valentine Jumbo Lottery Released: February
Dream Jumbo Lottery Sale: April to May
Summer Jumbo Lottery Release: July
Halloween Jumbo Release: October
Year-end Jumbo Release: November

Jumbo Lottery Details

As a prerequisite knowledge, I will talk about groups and numbers.

set, number, unit

When you buy a lottery ticket, numbers such as 99 pairs, 111111, etc. are drawn on the right side, and those pairs and numbers are set as winning numbers.



Depending on the type of lottery, there may be 100 or 200 pairs, and in the case of the year-end jumbo, 200 pairs from 01 to 200 will be sold.→200 ways
number from 100000 to 199999 →100,000 ways

And in the year-end jumbo, one unit is a set of this set and number (200 sets x 100,000 = 20 million sheets). Since 23 units (23 first prize winners) were released at the end of the year jumbo in 2022, there can be up to 23 people with the same group and number set all over Japan (※ if all are sold) ).

In summary, 200 x 100,000 x 23 units = 460 million copies will be sold.

before and after awards

It refers to the one that has only one number different from 1st class. In the case of last year's year-end jumbo, you will receive a prize of 150 million yen even in the front and rear prizes.

81 group No. 128386 ← Front and back prize (150 million yen)
81 group No. 128387 ← 1st prize (700 million yen)
81 group No. 128388 ← Front and back prize (150 million yen)

Year-end jumbo lottery winnings and number of winnings

1st prize 700 million yen 23 prizes (1 in 20,000,000 chance of winning)
Around 1st prize 150 million yen 46 pieces
1st class difference 100,000 yen 4,577 pieces
2nd prize 10 million yen 92 bottles
3rd prize 1 million yen 920 bottles
4th prize 50,000 yen 46,000 bottles
5th prize 10,000 yen 1,380,000 bottles
6th grade 3,000 yen 4,600,000 bottles
7th prize 300 yen 46,000,000 bottles

Out of the above 460 million tickets, 52,031,658 will be the number of winning tickets.

Expected value

Based on the above, let's find the expected value of last year's 945th year-end jumbo lottery. *This time, we assume that all 460 million copies have been sold.

700000000×23 + 150000000×46 + 100000×4577 + 10000000×92 + 1000000×920 + 50000×46000 + 10000×1380000 + 3000×4600000 + 300×46000000

If you divide the above by 460 million, the expected value per sheet will be 149.995 yen.
On average, you will receive 149.995 yen per 300 yen per ticket, so about half

1/2, 1/4, 1/8 And it is expected that the more you buy, the more you buy, the more your assets will be halved.