The Math behind Toto and 4D in Singapore


"Investing" in the Lottery? The Math behind Toto and 4D in Singapore
By Ryan Ong in Featured Post, Frugal Living | Oct 20, 2011 4 Comments
Big Sweep, 4D, Toto…so many ways to win. And on top of that, a ticket
is just a few dollars. Even if you have a snowball's chance in a
microwave, that small investment is worth the potential payoff right?
Besides, there are systems you can use to improve your odds. There are
whole books about it. In this article, I talk to some serious lottery
players. Then I examine the numbers behind it.

The paper road to dissapointment.

Winning Punters

I found some punters who claim to have won it big in the lottery.
Coincidentally, one of them I meet every morning:
Ellice (pronounced 'Alice') Kwong is a housewife, with two children in
JC. I run into her at the MRT station every morning, where she
invariably comments on my having five of the same shirt. She tells me
"I not sure how much I spend also. You ask me also I don't remember.
Maybe $60 one month. $20 for 4D, $40 for Toto. I think should be more
than most people spend. But you know I got win so many times! Four
times already. If my luck is good just play lah."
Dominic Wang is another serious punter. He's a former house mover, who
now deals in light fixtures. He says:
"I spend around $50, maybe more. I think with the right system, it's
quite possible to win. I've won twice myself, once I won over $3000. I
think as long as you know what you are doing, you don't go and
randomly tikam-tikam*, the odds are not as bad as most people think."
*Tikam-tikam – Roadside gambling game, very popular in the '60s. The
irony is noted.

Who says it's hard to live on luck? Rubbish.

Not-so-Lucky Punters

But most of the lottery lovers I spoke too have an entirely different
Jerome Quok is a Mass Communications student, who moonlights as a
short order cook. He tells me he spends:
"At most $10 a month. Maybe less. I don't really go with the mindset
that I will win. It's just for the excitement when I check the
results. It's more like entertainment than an actual investment. I
only ever won once, and it was something pathetic. Less than $100."
I said "it's still money," but Jerome said the win was after playing
regularly for four or five years.
Aaron Siew is one of those friends I love to hate. He's does
typesetting for brochures and magazines. While he comes over to steal
borrow more DVDs, I ask about his Toto obsession:
"I guess I spend about $20 a month. I promised that I will win Toto at
least once in my life. It's a 'must do before I die' thing. I don't
care even if it's consolation prize, so long as I win at least once in
my life. I've never won ANY lucky draw or anything before."
I asked if that wasn't a good reason not to buy Toto. But he suggested
I dip my head in a bucket three times and pull it out twice, then he
I asked Jenna McCormick, who lives two floors below me. She's a
housewife, with one child in Primary school.
"I think Louisa (her mother-in-law) has a bad influence on me. When
she buys, I'll buy. That's about $20 a month, but some months I don't
buy at all. I don't really understand the different systems, she
(Louisa) will tell me how to colour the slots in. I won once, it was a
few hundred dollars. So I split it with her and we had a big party at
Pizza Hut, and my share was all gone after that!"

"Your pizza. That'll be $1,200 over a five year period."

Investment vs. Payoff

Of the 12 people I spoke to, only one has actually seen a return on
his investment. Here is a cost / benefit comparison:
Claimed Investment(Refers to total investment over five years) Claimed
Payoff(Refers to total winnings over five year years) Profit / Loss
Dominic Wang $3000 $4500 (+) $1500
Ellice Kwong $3600 $2,500 (-) $1100
Jenna McCormick $1,200 $500. After splitting with fellow punter, $250 (-) $950
Jerome Quok $600 $60 (-) $540
Aaron Siew $1,200 $0 (ha ha!) (-) $1200

To put it in perspective, think about the last investment scheme you
saw. How would you react if someone showed you a scheme where, after
five years, your reward would be somewhere between $1500 and negative
If you reckon it's a great deal, drop me an e-mail. I've got a special
investment scheme you'll love.

Singapore Sweep
1st Prize
(Or Group 1 for Toto)
1 in 8,145,060
1 in 10,000
1 in 3,200,000
2nd Prize
(Or Group 2 for Toto)
1 in 1,357,510
1 in 10,000
1 in 3,200,000
3rd Prize
(Or Group 3 for Toto)
1 in 35,724
1 in 10,000
1 in 3,200,000

Just for the sake of reference, the odds of getting a Royal Flush in
Poker, on the first 5 cards, is around 650,000 to 1. So with the
exception of 4D, you might be better off just playing Poker. Or
betting on the PGA tour. The odds of a pro-golfer getting a
hole-in-one are 5000 to 1, around seven times more likely than winning
Group 3 Toto.

More probable than me winning 4D.

Pros and Cons

These are the upsides of investing in the lottery:
Ad-Hoc Payments – If you don't have enough, just don't play that
month. This means you need less planning and discipline than if you
used a regular investment scheme.
Affordability – Assuming you don't get obsessed, you won't feel the
pinch of the lottery. The amount spent is small, unlike the monthly
payments on an investment scheme.
Easy – No forms to sign, or documents to produce. Just buy a ticket, that's it.
Fun – Some people use the lottery as a way to relieve stress or tension.
And the downsides:
Negative Growth - The longer you play the lottery, the more you
actually lose. In almost all cases, there is a negative return on
High Improbability - The odds of winning a prize, even enough to just
break even, is very low.
Unpredictable Payouts - Some forms of lottery, like Toto, vary the
prize money based on the number of winners. That means there's no way
to accurately determine the potential winnings.
So there you have it: the only check you're going to get is a reality
check. Highly improbable wins, with a worse Return on Investment than
any financial plan on Earth. Which leaves one to wonder: would people
actually invest more in banks if the advisers just threw up their arms
and said: "Who knows? Just give us the money and we'll randomly pay it

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