Lottery Principle:
Lottery organisations like Singapore Pools raises money because on average the cost of each ticket is more than the return of it. For example, the cost of a ticket is $1 and the return of it by winning something (including all the prizes) is 50 cents. On average, one loses 50 cents for every ticket he buys.
In 1992, some investors noticed that the Virginia Lottery violated this principle. The lottery involved picking 6 numbers from 1 to 44. They are C(44, 6) - a combination, or 7,059,052 ways (about 7 million) of choosing 6 numbers from a group of 44. The jackpot was $27 million, and with the 2nd, 3rd, 4th prizes included, the pot grew close to $28 millmion, or $27,918,561 to be exact. Therefore, each ticket has an approximate value of $28m / 7m = $4 (or $3.95). However, the cost of each ticket was just $1. To put simply, if one buys all the more than 7 million different combintions, he will have a net profit of $21 million ($28m pot - $7m cost).
The Australian investors quickly found 2,500 small investors in Australia, New Zealand, Europe and the United States willing to put up an average of $3,000 each. If the scheme works, each will have an average net profit of about $10,000.
Risks in the scheme:
1. They were not the only ones buying the tickets; they would have to share the winning pot.
(However, the statistics was on their side: in the 170 times the lottery had been held, there were 120 times with no winners, only 40 times with a single winner and just 10 times with two winners. The expected return is 120/170 *$28m + 40/170*$14m + 10/170*$9m = $23m, or more than $3 per ticket, net profit $2 per ticket on average.)
2. Time for filling in the slips. Each slip was good for 5 tickets. They had 1.4 milion slips to fill out.
As they only had 72 hours before the deadline, they hired grocery-store employees working on shifts to sell as many tickets as possible. In the end, they own managed to purchase 5 million out of more than 7 millions, 0r 70%.
3. Payment for the tickets bought. Luckily, some chain store accepted back checks for 2.4 million tickets, or about 50% of the tickets they bought.
4. Time for checking the prizes. This was not really a problem as the lottery gave 1 ~ 3 months of collecting the prizes won. It was just hard searching work. It took them days to come forward with the winning tickets.
5. Legal or illegal: Luckily, the officials concluded that they had no valid reason to deny the group's winning.
Really interesting and exciting true story!
Lottery organisations like Singapore Pools raises money because on average the cost of each ticket is more than the return of it. For example, the cost of a ticket is $1 and the return of it by winning something (including all the prizes) is 50 cents. On average, one loses 50 cents for every ticket he buys.
In 1992, some investors noticed that the Virginia Lottery violated this principle. The lottery involved picking 6 numbers from 1 to 44. They are C(44, 6) - a combination, or 7,059,052 ways (about 7 million) of choosing 6 numbers from a group of 44. The jackpot was $27 million, and with the 2nd, 3rd, 4th prizes included, the pot grew close to $28 millmion, or $27,918,561 to be exact. Therefore, each ticket has an approximate value of $28m / 7m = $4 (or $3.95). However, the cost of each ticket was just $1. To put simply, if one buys all the more than 7 million different combintions, he will have a net profit of $21 million ($28m pot - $7m cost).
The Australian investors quickly found 2,500 small investors in Australia, New Zealand, Europe and the United States willing to put up an average of $3,000 each. If the scheme works, each will have an average net profit of about $10,000.
Risks in the scheme:
1. They were not the only ones buying the tickets; they would have to share the winning pot.
(However, the statistics was on their side: in the 170 times the lottery had been held, there were 120 times with no winners, only 40 times with a single winner and just 10 times with two winners. The expected return is 120/170 *$28m + 40/170*$14m + 10/170*$9m = $23m, or more than $3 per ticket, net profit $2 per ticket on average.)
2. Time for filling in the slips. Each slip was good for 5 tickets. They had 1.4 milion slips to fill out.
As they only had 72 hours before the deadline, they hired grocery-store employees working on shifts to sell as many tickets as possible. In the end, they own managed to purchase 5 million out of more than 7 millions, 0r 70%.
3. Payment for the tickets bought. Luckily, some chain store accepted back checks for 2.4 million tickets, or about 50% of the tickets they bought.
4. Time for checking the prizes. This was not really a problem as the lottery gave 1 ~ 3 months of collecting the prizes won. It was just hard searching work. It took them days to come forward with the winning tickets.
5. Legal or illegal: Luckily, the officials concluded that they had no valid reason to deny the group's winning.
Really interesting and exciting true story!
Warning: The golden rule is NEVER EVER GAMBLE!
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TOTO: Choose 6 numbers from 1 to 45.
(1) How many different combinations are there? Ans: 8,145,060.
(2) Each combination (6 numbers) costs 50 cents. How much does one pay for all combinations? Ans: $4,072,530.
(3) This coming TOTO jackpot is $5,500,000 (estimated).
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