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We wanted to hack the TOTO Hong Bao Draw with statistics. Here’s what we found out!

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 BetCostDescription
Quick Pick$1The computer to select 6 number at random.
Ordinary Bet$1TOTO ticket buyer selects 6 numbers from 1 to 49.
System 7$7TOTO ticket buyer selects 7 numbers from 1 to 49.
System 8$28TOTO ticket buyer selects 8 numbers from 1 to 49.
System 9$84TOTO ticket buyer selects 9 numbers from 1 to 49.
System 10$210TOTO ticket buyer selects 10 numbers from 1 to 49.
System 11$462TOTO ticket buyer selects 11 numbers from 1 to 49.
System 12$924TOTO ticket buyer selects 12 numbers from 1 to 49.
System Roll$44TOTO ticket buyer only selects 5 numbers from 1 to 49. The 6th number is any of the guaranteed winning numbers.

Payouts of TOTO prize:

GroupPrize MoneyWinning Numbers Matched
1
(or known as 'Jackpot')
38% of prize pool
(minimum: $1 million or the amount stated)
All 6 numbers
28% of prize pool5 numbers + additional number
35.5% of prize pool5 numbers
43% of prize pool4 numbers + additional number
5$504 numbers
6$253 numbers + additional number
7$10 3 numbers

What is my chance of winning TOTO?

PrizeTOTO odds of winning
Group 1
(Jackpot)
1 in 13,983,816
Group 21 in 2,330,636
Group 31 in 55,491
Group 41 in 22,197
Group 51 in 1,083
Group 61 in 812
Group 71 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):

GroupHow much you need to buy?How much you win?
(based on 2017's Draw)
Profit/Loss
1
(Jackpot)
$13,983,816$3,000,413 - $10,983,403
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.
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