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4D and TOTO: How The Odds Are Against You

Updated: May 28, 2022

If there was one pastime in Singapore that transcended generational gaps, overcame dialectal differences, and even bonded PAP and WP supporters, it’s buying 4D and TOTO.

After all, the lottery is so easy to play! And it even comes with an element of fun. You only need $1 and a stroke of luck to strike it rich, wait, scratch that, hit millions of dollars!

So, it’s no surprise that so many Singaporeans buy 4D and TOTO.

Plus, what’s there to lose? A measly $1 is nothing compared to a chance to enjoy early retirement.

Except that’s not true.

You’re actually losing more than you think for every $1 you spend buying 4D or TOTO.

Before we get to that, let’s first understand how 4D and TOTO work.

How to play 4D

To play the 4D, or 4-Digits lottery, as the name explains it, you select a four-digit number from 0000 to 9999. The minimum amount required is $1.

Say you select “0298” you can place either a Big bet or a Small bet on this number.

If you choose a Small bet, you win a prize if “0298” appears in the top three prize categories. If you choose Big bet, you win a prize if “0298” appears in any of the five prize categories as follows:

There will be 1 prize for each of the top three categories, 10 prizes for Starter, and 10 prizes for Consolation.

How to play TOTO

There are three types of bets in TOTO: Ordinary Entry, System Entry and System Roll. The simplest is Ordinary Entry where you pick six numbers between 1 and 49. Again, the minimum bet is $1.

6 Winning Numbers and 1 Additional Number will be drawn during each draw. If your chosen numbers match at least three of the Winning Numbers, you win a prize.

The amount you win depends on how many numbers match the Winning Numbers.

If your numbers match all six of the Winning Numbers, you hit the TOTO jackpot, i.e., a million dollars minimally (Prize Group 1).

If there are two or more winners in Groups 1 to 4, the prize amount will be equally divided among the winners in each Prize Group. For Groups 5 to 7, the prize amounts are fixed, much like the prize structure in 4D.

Now that you understand how 4D and TOTO work, you must be thinking that surely there have to be certain numbers that appear more frequently throughout the years. And yes, you’re right!

There are historical records of which TOTO numbers, or 4D numbers, have appeared frequently over the years.

Here are the Top 10 most frequently drawn 4D numbers:

TOTO Winning Number Frequency

We also charted out a graph that shows which TOTO number historically gets frequently drawn as one of the Winning Numbers. The number 40 has the highest frequency (117 times) out of all numbers.

Data based on the frequency chart available at Singaporepools website

But even with this data on TOTO’s historical results, the chances of winning the jackpot are extremely low. The chances are actually so minuscule, that you might be better off aiming to be the President of Singapore.

No, really, we are not joking.

Let’s take a look at the statistics and probability to back this claim.

What are the odds of winning the TOTO Jackpot?

The odds of winning the TOTO jackpot can be calculated using 1 over C(49,6) which gives you 1 in 13,983, 816. The probability is about 1 in 14 million.

To become the President of Singapore, if we ignore the age criterion and take the whole citizen population into the calculation, you have a 1 in 3,500,000 chance. That’s 1 in 3.5 million.

To give some perspective, this means you are:

The description of the odds being “extremely low” now comes across as an understatement, doesn’t it?

What about the odds of winning 4D?

In 4D, a total of 23 numbers will be drawn, which means a total of 23 prizes will be given out. Say we take the bet that covers more prize categories, i.e. Big bet, the probability of winning 4D is 23 in 10,000.

While it definitely paints a more optimistic picture compared to TOTO, in reality, it’s still a pretty low probability.

In fact, if you do a breakdown of the Expected Value, you’ll discover that on top of the low probability, you’re actually losing money for every $1 spent.

Expected Value is basically a statistical term that refers to the return you would expect from buying 4D.

For every $1 you spend on a Small bet, your expected return is $0.58. You lose $0.42.

For every $1 you spend on a big bet, your expected return is $0.66. You lose $0.34.

Simply put, every $1 spent is $1 that could have gone into your retirement savings.

Investment: A Better Alternative

A financially smarter alternative is to put your accumulated lottery spending into investment. If you have no knowledge of investments, a safe first step is to begin investing in Exchange-Traded Funds, or ETFs, such as Straits Times Index (STI index) or S&P 500.

Compared to 4D and TOTO, investing in stocks at least guarantees a higher probability of getting returns.

Let’s do the math, shall we?

Take for example you spend a minimum of $7 a week on 4D and/or TOTO, you would have spent $364 in a year. This may seem like an inconsequential amount but it accumulates to $7,280 in 20 years, with no guaranteed winnings.

If you take this same amount and invest in the STI index, which has an average annualised return of 9%, in 20 years you would get $20, 767.70. You would have earned $13,517.70 from investing.

Take this same amount and invest in S&P 500, which has an average annualised return of 10.67%, in 20 years you would get $24, 903.64. You would have earned $17, 673.64 from investing. Not so inconsequential anymore, right?

Assuming you don’t win the lottery, this is what your investments could look like in 20 years:


Straits Times Index

S&P 500

Total Investment over 20 years




Value of Investments over 20 years




Net Profit/Loss




In other words, investing in lotteries is a much higher risk activity. If you’re unsure about your risk profile, feel free to check out our risk profile calculator!

How do I start investing?

Everyone needs to start somewhere and the sooner they do, the better!

If you have yet to embark on your investment journey and have no idea where to start, it would be smart to work with a financial professional.

Contrary to their reputation for pushy sales tactics, financial advisers help new investors cut through the noise. They can arrange your investments and build a financial plan that helps ensure you will meet your financial goals in a sustainable manner.

With regards to investment planning, they do the following:

  • Identify your current life stage

  • Identify your goals, needs and wants

  • Find out how much you will need for each need, wants, and goals

  • Plan how you can achieve these goals

  • Build and optimise your financial investments

To help you take control of your personal finance, Techiya offers a free comprehensive and personal financial assessment worth over $200 for individuals, don’t miss out on this!

Why do people continue to buy 4D/TOTO?

When it comes down to the nitty-gritty mathematical workings of Singapore’s 4D and TOTO, the odds are stacked against us. And for most people, an investment might just be the wiser choice.

It’s a wonder then why anyone would buy 4D or TOTO.

Perhaps it’s that sense of hope that one day that 1 in 14 million might be you.

Maybe it’s that ‘gut feeling’ that today is the day fortune is smiling upon me.

Maybe it’s that addictive thrill of discovering you were one number away from winning 4D.

According to a study made by The Association of Consumer Research, it states that the promise of wealth from playing the lottery serves those who strongly fantasize about being rich, and gives the illusion that purchasing the lottery is a low-cost fantasy. The “near-misses” then further feed the sensation-seeking traits of some lottery players.

In other words, what keeps the lottery going is the fantasy of making it rich through winning the lottery. Having a visual fantasy of what your life is could activate a part in your brain where emotions override logic and math.

And those who are more prone to fantasizing about becoming rich may find themselves addicted to purchasing lotteries.


Now that you’ve some knowledge about the mechanisms behind lottery addiction, you can start to rein this in by learning not to be swayed by your fantasies.

At any rate, it is undeniable that investment cannot replace the element of fun in 4D and TOTO. Likewise, the reverse holds true: playing 4D and TOTO cannot be a substitute for investment.

Now that we know the statistical workings of 4D and TOTO, perhaps we could still enjoy playing the lottery as a recreational activity, a form of entertainment we indulge in once or twice a year.



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