One of the biggest annual prizes available is typically during the TOTO Reunion Draw around Chinese New Year – when the Group 1 prize is at least $5 million. This year, the Reunion Draw, which closes on 24 Jan 2025 at 9 pm, will be worth at least $10.8 million.
While we agree that it might be fun to buy “hope” (as we ourselves buy the odd ticket ourselves), it is also true that Singaporeans are better off abstaining from TOTO bets altogether. So, it could be acceptable to stake a few dollars if you’re in for the thrill, but you should never pour large amounts of money on a regular basis hoping to become an overnight millionaire.
In the long-run, you will always lose money. Here’s why.
Read Also: What Happens If You Find A Winning Toto Ticket?
Recap Of The TOTO Rules
For those who don’t know how to play TOTO, here is quick summary of the key rules.
1) You pick at least 6 numbers between 1 and 49, paying a minimum of $1. You can also choose to pick more numbers, up to 12 numbers, and pay more for a better chance of having a winning set of numbers.
2) During each draw, 6 Winning Numbers and 1 Additional Number are drawn.
3) If your chosen numbers match at least 3 of the Winning Numbers, you win a prize. The amount you receive depends on how many of your chosen numbers match the Winning Numbers.
4) Another important caveat is that if more than 1 winner in Groups 1 to 4, prizes will be divided equally among all winners of the group. The prize amounts for Groups 5 to 7 are fixed.
Source: Singapore Pools
The jackpot sum (i.e. Group 1 prize) will be a minimum of $1 million, and has a snowball feature – which means prize amounts can grow if there are no winners. If there are still no Group 1 winners after 3 consecutive draws, a cascade draw takes place. If there is no Group 1 Prize winner on the cascade draw (i.e. the 4th consecutive draw), the Jackpot amount cascades to the next Prize Group winners to share equally.
What Are The Odds Of Winning The TOTO Jackpot (Group 1)?
When you play TOTO, you do so in hopes of winning the eye-watering top prize. But what are your odds of doing so? To answer this question, we dusted off our copy of Schaum’s and refreshed our knowledge on Permutations and Combinations.
We need to match all 6 numbers from a possible list of 49. Since the numbers don’t repeat, there is only 1 possible combination that will yield us the top prize.
Thus, C(49, 6) = 1/13,983,816
In other words, the odds of winning are about 1 in 14 million.
To say these are extremely poor odds would be an understatement. Then again, we humans are bad at gauging immensely unlikely events. One way to think about how much value your $1 lottery ticket has is to calculate its Net Present Value.
Net Present Value Of A $1 TOTO Ticket
The actual odds and prize value can only be calculated once sales closes, since 54% of sales in each draw would be added to the existing prize pool.
For this calculation, we assume that the prize pool is $28,421,052 – based on $10.8 million being 38% of the prize pool and the Group 1 prize value. We also assume we only buy 1 TOTO ticket and ignore other players for now. In other words, this is how much your TOTO ticket is worth if you were the only one playing.
| Group | Odds of Winning | Prize Value | Odds x Prize Value |
| 1 | 1 in 13,987,816 | $10,800,000 | $0.77 |
| 2 | 1 in 2,330,636 | $2,273,684 | $0.98 |
| 3 | 1 in 55,491 | $1,563,157 | $28.17 |
| 4 | 1 in 22,197 | $852,631 | $38.41 |
| 5 | 1 in 1,083 | $50 | $0.05 |
| 6 | 1 in 812 | $25 | $0.03 |
| 7 | 1 in 61 | $10 | $0.16 |
| Present Value | $68.57 | ||
If we multiply the probability of winning by the prize money and sum up the total probable winnings, we will have a Present Value of $68.57. Pretty decent for spending just $1 to buy our TOTO ticket?
Obviously, though, Singapore Pools does not operate the draw just for you to win. When you consider other players and how they affect your winnings, your TOTO ticket’s Net Present Value looks very different.
Net Present Value Of A $1 TOTO Ticket (Based On Historical Number Of Winners)
If you recall, the prize money in Group 1, 2, 3 & 4 will be split in the event that there are multiple winners for each group.
Again, it is impossible to calculate the expected value because there is no way to know for certain how many winners there will be in each category. We can, however, use the average of the number of winners from each group in past Hong Bao Draws.
If we take into account that there may be multiple winners, and calculate the present value of our TOTO ticket based on average number of winners in the past 8 years, we get a very different conclusion:
| Group | Odds of Winning | Prize Value | Actual Winning (Account For Average Number of Winners in Past Years) | Odds x Prize Value |
| 1 | 1 in 13,987,816 | $10,800,000 | $2,700,000 | $0.19 |
| 2 | 1 in 2,330,636 | $2,273,684 | $87,449 | $0.04 |
| 3 | 1 in 55,491 | $1,563,157 | $1,544 | $0.03 |
| 4 | 1 in 22,197 | $852,631 | $321 | $0.01 |
| 5 | 1 in 1,083 | $50 | $0.05 | |
| 6 | 1 in 812 | $25 | $0.03 | |
| 7 | 1 in 61 | $10 | $0.16 | |
| Present Value | $0.51 | |||
The expected value has been significantly reduced to $0.51. In other words, we should expect to lose half our money when we buy a TOTO ticket.
This makes it very clear why it doesn’t make statistical sense to play TOTO. Thus, the real winner of every draw remains Singapore Pools.
Have Fun Responsibly
On a lighter note, the participation in TOTO betting should be one of leisure and a topic with friends and family, especially during the festive Hong Bao draw. However, if you are thinking about it as a get-rich-quick scheme by pouring substantial savings into TOTO draws, we’ve shown you why you will unlikely be successful.
Let’s exercise a Responsible Play mentality and treat TOTO (or any other form of gambling) as a recreational activity and never as a get-rich-quick-scheme or form of “investment”.
The post The Math Behind TOTO – Here’s Why It (Statistically) Doesn’t Make Financial Sense To Play appeared first on DollarsAndSense.sg.
