Receipt Lottery Ticket
When I learned that receipts are lottery tickets in Taiwan, I wondered if you could win the lottery by making a bunch of small purchases. This obviously wouldn't work, right? I don't think these thoughts are that uncommon either. I have a friend who told me they would sometimes split up their purchases so that they would get more receipts. How do we figure out how much a lottery ticket should be worth?
Expected value. You just multiply the chances of winning by how much you'll win.
There are 8 digits in a receipt lottery ticket. Therefore your odds of winning are 1 in a hundred million.
So we can multiply the amount of each prize by it's probability to get the expected value of a receipt for a given prize. You can then add up all of the individual expected values for each prize to get the total expected value of the receipt.
I've made a table below for doing these calculations for each prize amount.
| Prize | Winning Amount (NTD) | # to match | # of Tickets | Expected Value of Prize |
|---|---|---|---|---|
| Special | $10,000,000 | 8 | 1 | 0.1 |
| Grand | $2,000,000 | 8 | 1 | 0.02 |
| Regular | $200,000 | 8 | 3 | 0.006 |
| 2nd | $40,000 | 7 | 30 - 3 = 27 | 0.0108 |
| 3rd | $10,000 | 6 | 300 - 30 = 270 | 0.027 |
| 4th | $4,000 | 5 | 3000 - 300 = 2700 | 0.108 |
| Subtotal | 0.2718 | |||
| 5th | $1,000 | 4 | 30000 - 3000 = 27,000 | 0.27 |
| 6th | $200 | 3 | 300000 - 30000 = 270,000 | 0.54 |
| Additional | $200 | 3 | X * 100,000 | 0.2 * X |
| Total | 1.2818 | |||
Note the X in the Additional row is a variable. Some months there are multiple additional prizes and some there are none.
But wait — that's before tax. There's a 20% lottery tax that's applied to receipts that win more than $1000 NTD. Therefore the expected value actually becomes $1.25444 NTD after taxes.
In theory yes. In practice probably not. I searched for the lowest cost item I could find at 7-11. It is a $2 NTD funeral envelope. My theory is 7-11 is offering it essentially at-cost as an act of good will. Even that item isn't priced low enough. For this type of scheme to work you'd you'd have to find an item for sale for $1 NTD.
You could make some money by making lots of $1 NTD purchases (about $ 0.2 NTD per receipt). But once you price in the time and effort spent making the purchases as well as checking all of the receipts it's probably not worth it.
The cool thing is if you have hundreds of tickets piled up you should scan them. You can think of each one worth about $1.2 NTD. So what are you waiting for? Check your receipts. You can even check them by using apps to scan them.