Some lucky Singaporeans are expected to welcome the year of the dog with a fat bank account.
TL;DR: We wanted to hack the TOTO Hong Bao Draw with math. Here’s what we found out
- To have a 100% chance of winning the TOTO Jackpot, you will need to buy 13,983,816 Ordinary TOTO tickets.
- 54 ordinary tickets are all it takes to at least win something.
- I have 4 times higher chance of spotting a UFO today than striking Jackpot with 1 TOTO ticket.
Singaporean’s Guide on how to TOTO
In the game of TOTO, one has to purchase a set of 6 numbers, selected from 1 to 49.
Types of TOTO bet and the cost of each type of bet:
|Types of Bet||Cost||Description|
|Quick Pick||$1||The computer to select 6 number at random.|
|Ordinary Bet||$1||TOTO ticket buyer selects 6 numbers from 1 to 49.|
|System 7||$7||TOTO ticket buyer selects 7 numbers from 1 to 49.|
|System 8||$28||TOTO ticket buyer selects 8 numbers from 1 to 49.|
|System 9||$84||TOTO ticket buyer selects 9 numbers from 1 to 49.|
|System 10||$210||TOTO ticket buyer selects 10 numbers from 1 to 49.|
|System 11||$462||TOTO ticket buyer selects 11 numbers from 1 to 49.|
|System 12||$924||TOTO ticket buyer selects 12 numbers from 1 to 49.|
|System Roll||$44||TOTO ticket buyer only selects 5 numbers from 1 to 49. The 6th number is any of the guaranteed winning numbers.|
Payouts of TOTO prize:
|Group||Prize Money||Winning Numbers Matched|
(or known as 'Jackpot')
|38% of prize pool|
(minimum: $1 million or the amount stated)
|All 6 numbers|
|2||8% of prize pool||5 numbers + additional number|
|3||5.5% of prize pool||5 numbers|
|4||3% of prize pool||4 numbers + additional number|
|6||$25||3 numbers + additional number|
What is my chance of winning TOTO?
|Prize||TOTO odds of winning|
|1 in 13,983,816|
|Group 2||1 in 2,330,636|
|Group 3||1 in 55,491|
|Group 4||1 in 22,197|
|Group 5||1 in 1,083|
|Group 6||1 in 812|
|Group 7||1 in 61|
source: Interactive Mathematics
For every dollar we spend getting a TOTO ticket, we are risking it by subjecting ourselves to the probability of winning something.
How much do I need to spend to at least win something?
To calculate the probability of winning at least some money, we sum up all the above-mentioned probability to derive at 0.0186. Which works out to be about 1 in 53.76.
This means that one needs to at least fork out $53.76, about 54 TOTO tickets to at least win some money.
Editor’s note: You can use this fraction calculator here.
Sounds good? Think again.
- For Group 5, Group 6 and Group 7, the payout is $50, $25 and $10 respectively.
- Hence, winning any of the group will result in you losing money given that the cost price is at $53.76.
- Only by winning at least a Group 4 will the “investment” makes economic sense.
How much to win at least a Group 4 then?
- Assuming we use the same data of the Hong Bao Draw in the year 2017, there are 2,516 Group 4 winners bagging $346 each.
- We now turn a blind eye to anything Group 5 and below, we calculate to see how much we need to put in to win a Group 4 at least.
- The odds of winning a Group 4 at least turns out to be 1 in 3,932.51.
- This means that we need to put in at least $3,932.51 for a chance to win at least $346, which again, is not worth it.
The ultimate chart you need to illustrate the never-ending pursuit of quick wealth (based on 2017’s result):
|Group||How much you need to buy?||How much you win?|
(based on 2017's Draw)
|2||$1,997,688||$89,083 or more||- $1,908,605 or less|
|3||$53,991.25||$1,514 or more||-$52,477.24 or less|
|4||$3,932.51||$346 or more||- $3,586.51 or less|
|5||$849.12||$50 or more||- $799.12 or less|
|6||$415.07||$25 or more||- $290.07 or less|
|7||$53.76||$10 or more||- $43.76 or less|
The above chart shows that in order for a sure win, one needs to put in so much more money to compensate the risks and the odds.
- In order for one to win at least a Group 2, he needs to put in close to $2 million. The returns? A possible change of winning $89,083 or maybe, $3 million.
Data is based on Hong Bao Draw 2017’s statistics:
source: Today Online
To illustrate the low probability of winning a TOTO, we lay out the odds of some life events for reference:
- Odds of spotting a UFO today: 1/3,000,000
- Odds of a Royal Flush in poker on the first 5 cards: 1/ 649,740
- Odds of winning an Olympic medal: 1/662,000
- Odds of dating a supermodel: 1/88,000
- Odds of being murdered: 1/18,000
- Odds of winning an Academy Award: 1/11,500
This means that I have a 4 times higher chance of spotting a UFO today than striking Jackpot with my TOTO ticket.
Extra Reading: Are TOTO winnings subjected to tax?
Should you win the Jackpot this Hong Bao Draw, here’s a fun fact:
- As winnings from betting is a windfall and do not come from an income nature, it is not subjected to Income Tax.