In the past week, there was a big TOTO draw with a top prize of around $11million.
For those who don’t know what it is, here is a short summary:
Toto is lottery game hosted by Singapore Pools - Singapore’s only legal lottery provider. In this game, you pick 6 numbers between 1 and 49. If your 6 numbers match the 6 numbers that are drawn out, you will win the top prize of that draw. If there is no winner, the prize money will be accumulated to the next draw. This prize money will keep accumulating until someone wins. The cost per ticket is $1. There are more complicated versions you can buy but they do cost more.
In the recent Chinese New Year, the grand prize accumulated was $16million. 2 people won that.
Now that you have understood the game, how do you pick the best numbers? That is (literally) the million dollar question.
Mathematical Best Numbers
The math is not in your favour for this. The people at Singapore Pools made sure of that. Or else, why only 49 numbers?
tldr: If you rely on this, it is only logical you do not play this game.
But for those who want to see the numbers, here it is:
10,068,347,520 combinations of 6 numbers between 1 and 49 - that is over 10 billion different combinations. For simplicity of calculations, we will use 10 billion.
Let’s set the following assumptions:
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This draw has a grand prize of $10million (also for simplicity of calculations)
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You only bought 1 ticket
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Numbers are chose at “random” - we define random here VERY loosely
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We are going for the top prize only
Your expected value of returns will be the following:
E(X) = 10,000,000 x (1/10,000,000,000) = $0.001
That is a 10th of a cent. Considering you spent $1 on the ticket, you actually lose $0.999. Some of you will tell me, “99.9cents only”. But look at it this way. If a bank ask you to give them money with a risk of you losing 99.9% of it will you do it? You probably will withdraw your money quickly.
Disclaimer: The calculations here assume that you are going of the top prize only. There are second, third and forth depending on how many numbers you get right. There is also and additional 7th number drawn. The game gets really complicated really quickly. In any case, they still don’t give you ANY mathematical advantage over the house (in this case Singapore Pools).
So… Now that you know the mathematics, why are there people still playing this? The reason is rather simple. People are usually not driven by logic but by emotions. They do not see the 99.9% loss. They see the “有买有希望” (loosely translated to “Have buy then have hope”). Spend $1 to have a chance for $10million not bad what.
Ways other people get the best numbers
With 10 billion combinations of numbers to choose from, how in the world can I get the best numbers? Everyone have their own ideas on how to get the best number. This is what I call “Feel good numbers”.
Feel good numbers - Numbers that makes you feel good because you cannot decide so you let someone else decide
Some may seem like a joke. However, there are people that actually do it!!! And I don’t want to be a wet blanket. So I shall not go into why all of them do not work.
1. Random number generator
Go to any random number generator. Assuming the system Singapore Pools uses is random, hope that your generator is equally random to the Singapore Pools one and they might spit out the same numbers. There are actually tons of telegram bots and websites designed to do this. Some even analyse past data to try to get the best numbers (Spoiler alert: Does not work).
Singapore Pools themselves also know this hence they have a “Quickpick” system that helps you randomly choose 6 numbers.
2. Buy at the “lucky” stores
Not all outlets are made the same. Buying your numbers at some outlets makes your numbers superior. The website below shows the frequency of winner that bought from those outlets.
3. See past results
Some people have this idea that if the number came out the previous draw, it will not come out again. It sort of makes sense. What are the odds that 2 draws give the exact same number given 10billion combinations? You can see the past results in the following website:
4. Ask their pets to pick
For those with pets, place 49 numbers in front of them and get them to pick. They can be the next Paul the Octopus.
5. Get numbers from your surroundings
As you walk to the booth to buy your ticket, look around you. How many people are on the lift down? What is the first car plate number you see when you go to the store? Numbers are everywhere. You just need to find them.
6. Go to the temple
Go to the temple and pray. Listen closely for any noise. You might just hear some numbers. For the Chinese temple, after you burn the joss sticks and place it in the pot, look at how the smoke moves. You might actually see something. Or even better, buy the number first, then go to the temple and ask that these numbers be chosen. Definitely makes it a better number.
Conclusion
Armed with all that knowledge, I wish you all the best and if you win, please donate some… to me! hahaha
With all that said and knowing all the math, I still played the game. Obviously I did not win. But I felt good. Spending money, for me at least, is not always about the best ROI. If you treat this as a game, it’s no different from spending money to watch a movie or a concert.
Till the day I win, I will continue to work hard doing something I love.
To quote one of my favourite Instagram comics - Stay woke salary man.
Others
In the above discussion, I mentioned “What are the odds that 2 draws give the exact same number given 10billion combinations?” Sounds convincing. However, there is actually a reason why this assumption is wrong. The draws are independent of each other. Meaning the result of the first will not affect the result of the second in any way. The probability of the number reappearing is still 1/49. That probability did not change. So it is a fresh 10billion combination you need to choose from every time.