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How to Predict and Win Singapore TOTO with Mathematics

In the Singapore game of TOTO, 6 numbers plus one “additional” number are drawn at random from the numbers 1 to 49. In the Ordinary game, players spend $1 and they choose 6 numbers in the hope of becoming instant millionaires. Yet, what are the odds of winning the lucky numbers for Singapore TOTO? Tropika Club investigates if we can predict and win Singapore TOTO with mathematics. This article is adapted from Interactive Mathematics (source).

singapore toto mathematics

No Time to Read? Here’s a Snappy Summary of This Article

  • What is Singapore TOTO? It is a lottery game where players choose six numbers from 1 to 49 and hope to match the winning numbers drawn at random. Players can also make system entries to increase their chances of winning.
  • How to Win at Toto? The prize pool for each draw is 54% of the net amount of total stake collection. There are seven groups of prizes based on how many numbers the player matches, with group 1 being the jackpot prize. The odds of winning vary depending on the type of entry and the number of combinations.
  • Let’s look at TOTO winning Odds. The odds of winning group 1 with an ordinary entry are 1 in 13,983,816. The odds of winning group 6 with a system 12 entry are 1 in 15. The odds of winning any prize with an ordinary entry are 1 in 54.
  • System Entries Changes of Winning TOTO Group 6 with System 12 A system 12 entry allows the player to choose 12 numbers and generate all possible combinations of six numbers from them. This gives the player 924 chances of winning group 6, which requires matching three numbers plus the additional number.
  • Which are the “Best” TOTO Numbers? There is no definitive answer to this question, as every number has an equal chance of being drawn. However, some people may use various strategies to pick their numbers, such as using hot and cold numbers, lucky numbers, birthdays, anniversaries, etc.

What is Singapore TOTO?

As explained in the Singapore Pools website, to participate in the TOTO Game, the Participant has to either place a Bet through the Account Betting System or buy a Ticket at the Outlet. Details on how to place Bets and buy Tickets are set out in the TOTO Game Rules (Remote Betting) and TOTO Game Rules (Outlet Betting) respectively.

  • The Stake payable for each set of six (6) numbers selected for every draw shall be one (1) dollar. The Stake for a Ticket and/or Bet shall be no less than one (1) dollar.
  • Save as expressly provided in the Rules and/or the Account Opening and Operating Terms and Conditions, Stakes paid to the Company in respect of Bets shall not be refundable to the Participants.
  • An intending Participant may participate in the TOTO Game by making an Ordinary Entry whereby the Participant purchases a set of six (6) numbers from a total of forty-nine (49) numbers available for selection in the Game.
  • An intending Participant may participate in the Game by making a System Entry whereby the Participant purchases all possible combinations of sets of six (6) numbers from a selection of five (5) numbers with the sixth (6th) number from each of the remaining forty four (44) numbers of the total of forty-nine (49) numbers available for selection in the Game; and/or
  • all possible combinations of sets of six (6) numbers from a selection of seven (7) to twelve (12) numbers out of the total of forty-nine (49) numbers available for selection in the Game.

An intending Participant may choose to make one or more of the abovementioned System Entries as follows:-

  • System Roll for a selection of five (5) numbers as described in Rule 5.2(a)
  • System 7 for a selection of seven (7) numbers
  • System 8 for a selection of eight (8) numbers
  • System 9 for a selection of nine (9) numbers
  • System 10 for a selection of ten (10) numbers
  • System 11 for a selection of eleven (11) numbers
  • System 12 for a selection of twelve (12) numbers

How to Win at Toto?

There shall be a prize pool available for distribution of prizes which may be won for each draw (“Prize Pool”). The Prize Pool shall be an amount equal to fifty-four per cent (54%) of the net amount of total stake collection of that draw less the Goods and Services Tax thereon. Allocations shall be made to seven (7) groups of prizes based on the number of winning numbers matched in the following manner. There shall be a minimum guaranteed pool amount of $1,000,000 for the Jackpot Prize for each draw (“the Minimum Guaranteed Amount”). In the event that the Jackpot Prize amount plus any “snowballed” amount(s) (collectively, the “Prize Amount”) is less than the Minimum Guaranteed Amount, the Prize Amount shall be increased by the Company to the Minimum Guaranteed Amount, and paid out to and shared equally among the total number of winning shares of the Jackpot Prize.

As per the information provided in the web search result [1], the winning numbers for TOTO, a popular lottery game in Singapore, are randomly drawn every Monday and Thursday at 6.30pm. To play TOTO, you need to choose at least six numbers between 1 and 49, and the cost of playing a single game is $1, inclusive of GST.

It’s important to note that winning at TOTO, like any lottery game, is largely based on chance and luck. There are no guaranteed strategies or methods to win the game. However, some people may use different techniques, such as selecting numbers based on important dates, significant events or patterns, to increase their chances of winning. It’s important to keep in mind that these methods do not necessarily improve the odds of winning, and playing responsibly is always recommended.

In summary, winning at Singapore TOTO is largely based on luck and chance, and there are no guaranteed methods to win the game. If you choose to play, it’s important to do so responsibly and within your means.

Let’s look at TOTO winning Odds.

Recall (from the Combinations section) that the number of ways in which r objects can be selected from a set of n objects, where repetition is not allowed, is given by:

We can write (and type) the left hand side more conveniently as C(n,r).

Now let’s look at the probabilities for each prize.

Group 1 (Choose all 6)

The odds of winning the top Group 1 prize are C (49,6)). That is:

That is, there are 13,983,816 ways of choosing 6 numbers from 49 numbers but there is only one correct combination.

So there is 1 chance in 13,983,816 of getting the Group 1 prize.

This means we have to buy almost 14 million tickets (at a cost of $14 million) before we can confidently say we will probably win the top prize…

Group 2 (5 + additional)

Odds:

Explanation: We chose 5 of the 6 winning numbers [C(6,5)], and chose the correct “additional” number from the \displaystyle{43}43 remaining numbers that did not win anything [C(43,1)].

There is 1 change in 43 that we chose the additional number, so multiply by 1 / 43.

So there is 1 chance in 2,330,636 of getting the Group 2 prize.

Group 3 (5 correct)

Odds:

We chose 5 of the 6 winning numbers and chose 1 number from the 43 remaining numbers that did not win. In the Group 3 prize, we cannot include the “additional” number, so we need to multiply by the probability of the remaining43 numbers not containing the additional number which is 1 – 1/43 = 42/43 ​.

So there is 1 chance in 55,491 of getting the Group 3 prize.

Group 4 (4 + additional)

Odds:

We chose 4 of the 6 winning numbers [C(6,4)], and chose 2 numbers from the 43 remaining numbers that did not win anything [C(43,2)]. But we chose 6 numbers originally, so there are2 chances in 43 that we chose the additional number, so multiply by 2/43.

So there is 1 chance in 22,197 of getting the Group 4 prize.

Group 5 (4 correct)

Odds:

We chose 4 of the 6 winning numbers and chose 2 numbers from the 43 remaining numbers that did not win. Once again, we need to consider the probability of the additional number not being one of our 2 remaining (non-winning) numbers. This probability is 1 – 2/43 = 41/43​. So we multiply by 41/43.

So there is 1 chance in 1,083 of getting the Group 5 prize.

Group 6 (3 + additional)

Odds:

We chose 3 of the 6 winning numbers [C(6,3)], and choose 3 numbers from the43 remaining numbers that did not win anything [C(43,3)]. But we chose 6 numbers originally so there are3 chances in 43 that we chose the additional number, so multiply by 3/43​.

So there is 1 chance in 812 of getting the Group 6 prize.

Group 7 (3 correct)

Odds:

We chose 3 of the 6 winning numbers and chose 3 numbers from the 43 remaining numbers that did not win. Again, we need to consider the probability of the additional number not being one of our 3 remaining (non-winning) numbers. This probability is1 – 3/43 = 40/43​. So we multiply by 40/43​.

So there is 1 chance in 61 of getting the Group 7 prize.

Odds of Getting Any Prize:

Total probability of getting any prize is simply the sum of all the probabilities for Group 1 to Group 6 prizes:

Read Also:

Top Winning Singapore Pools Outlets for 4D and Toto

System Entries

In most Lotto and Toto games, you can buy a “System”. Your chances of winning increase, but of course, you pay more as well. For example:

System 7 means you choose 7 numbers (instead of the usual 6). This gives you 7 times the chance of winning (so it costs 7 times as much), since it is equivalent to buying 7 different 6-number games, or C(7,6). Say you chose 1, 3, 5, 7, 9, 11, 13 as your 7 numbers. You have the following 7 ways of winning if the 6 winning numbers happened to be:

1 3 5 7 9 11
3 5 7 9 11 13
1 5 7 9 11 13
1 3 7 9 11 13
1 3 5 9 11 13
1 3 5 7 11 13
1 3 5 7 9 13

System 8 means you choose 8 numbers and it gives you the equivalent of 28 ordinary bet combinations, so costs 28 times as much, or C(8,6).

Similarly, System 9 gives you C(9,6)=84 ordinary bet combinations, System 10 gives C(10,6)=210 ordinary combinations, System 11 gives C(11,6)=462 combinations and System 12 (the maximum in the Singapore game) gives \C(12,6)=924 combinations. The probability of winning with a System 12 is 924 times the probability of winning when you buy 1 game, that is:

Changes of Winning TOTO Group 6 with System 12

Reader David wrote in to ask about the probability of winning a Group 6 prize when you buy a System 12. He asked what happens when the probability appears to be greater than 1. What he means is this: For a Group 6 prize, the probability is 1 in 812, so (it appears) a System 12 will give you 924 chances in 812 or 1.138 chances – greater than 1! However, this refers to the high chance in relation to your 12 chosen numbers – not to the total 49 possible numbers.

It just means you can be “almost certain” to get a Group 6 prize when you buy a System 12.

In fact, you would expect to win 924 / 321 = 2.88 (almost 3) prizes of some sort.

If you win a Group 6 prize with a System 12, you actually get 28 Group 6 shares (28 × $25 = $700) and because you have 3 correct numbers as well, you get 56 Group 7 shares (56 × $10 = $560) so your total prize amount is $1,260 (or a “profit” of $1260 – $924 = $336). Don’t believe anyone who says any strategy is a “sure thing”. The only sure thing is the “house” (or in many cases, the government) are the real winners.

Which are the “Best” TOTO Numbers?

Of course, there are no “best” numbers, but it’s interesting to see which ones occur most frequently.

The number with highest frequency (40, at 101 times) has come out 1.7 times as often as the lowest frequency number (45, at 58 times).

The data for the above chart comes from the Toto number frequency chart (at Singapore Pools site.)

Conclusion

In conclusion, Singapore TOTO is a popular lottery game that offers players a chance to win millions of dollars by matching six numbers from 1 to 49. The game has different types of entries and prizes, and the odds of winning depend on the number of combinations and matches. There is no sure way to predict the winning numbers, but some players may use various methods to select their numbers based on statistics, personal preferences, or superstitions. Whether you play TOTO for fun or for fortune, remember to gamble responsibly and enjoy the game. Good luck!🍀

FAQ

Frequently Asked Questions (FAQs)

  • Q: How can I buy a TOTO ticket or place a bet online?
    • A: You can buy a TOTO ticket or place a bet online through the Singapore Pools website or mobile app. You will need to register for an account and verify your identity before you can start playing. You can also check the results and claim your prizes online. For more details, please visit the Singapore Pools website1.
  • Q: How much can I win from TOTO?
    • A: The amount you can win from TOTO depends on the prize group, the prize pool, and the number of winners for each group. The prize pool for each draw is 54% of the net amount of total stake collection. The prize groups are as follows1:Prize GroupNumbers MatchedPrize Amount1 (Jackpot)6 numbers38% of prize pool25 numbers + additional number8% of prize pool35 numbers5.5% of prize pool44 numbers + additional number3% of prize pool54 numbers$50 per winning combination63 numbers + additional number$25 per winning combination73 numbers$10 per winning combination
    • The minimum guaranteed amount for the jackpot prize is $1 million. If there is more than one winner for any prize group, the prize amount will be shared equally among the winners.
  • Q: How can I increase my chances of winning TOTO?
    • A: There is no sure way to increase your chances of winning TOTO, as every number has an equal chance of being drawn. However, some players may use various strategies to select their numbers, such as using hot and cold numbers, lucky numbers, birthdays, anniversaries, etc. Another way to increase your chances of winning is to make a system entry, which allows you to choose more than six numbers and generate all possible combinations of six numbers from them. This will give you more chances of matching the winning numbers, but it will also cost you more.
  • Q: How can I check the results and claim my prizes for TOTO?
    • A: You can check the results for TOTO on the Singapore Pools website or mobile app, or through various media channels such as newspapers, radio, and television. You can also scan your ticket at any Singapore Pools outlet or authorized retailer to check if you have won. If you have bought your ticket or placed your bet online, you can also check your transaction history on your account. To claim your prizes, you can either do it online or at any Singapore Pools branch, depending on the amount you have won. For more details, please visit the Singapore Pools website1.

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