# How to win at the \$10m Hong Bao Toto

## Stepping up to bet is a losing proposition, but if you must, avoid the commonly chosen numbers

Chinese New Year is when Chinese Singaporeans give red packets to one another, but a good number hope to get a hongbao of their own as well - from Singapore Pools.

I'm talking, of course, about the lottery operator's annual Hong Bao Toto Draw, which dangles a \$10 million top prize to entice gamblers.

The draw is on Feb 14 this year and it has become a national tradition as snaking lines form outside each betting outlet in the frenzied days before the big draw.

Even people who don't normally play the lottery get enticed to take a small punt.

"My No. 1 query right now is how to strike the CNY big draw," said my friend, a respected engineer, when I asked what his major financial questions were.

I'm sure he was speaking half in jest but decided to take him up on the challenge and investigate the lottery further.

First, a quick explanation of Toto. To play, you must pick six numbers from 1 to 45 for an entry costing 50 cents.

At each draw, six winning numbers and one additional number are announced.

You will win a prize as long as you match four numbers, including the additional number.

There are six prize categories. The top few prizes are split among all the winners so you get more money if there are fewer winners.

Winnings for the smallest categories - \$20 and \$30 - remain the same regardless of how many winners there are.

Last year's Hong Bao Draw had nine winners in the top category so each received only \$1.11 million, rather than the advertised \$10 million.

In case you think that \$1.11 million isn't so bad for a 50-cent pop, remember that the chance of being one of the lucky nine was one in 8.145 million.

A young adult is about 10 times as likely to die on the day of the draw, than to be one of the winners.

A losing bet

It's hard to calculate exactly how much you can expect to win or lose when you play Toto because the size of the prizes keeps changing for individuals - depending on how many people you need to share the cash pot with.

Perhaps we can use history as a gauge. So I analysed last year's Hong Bao Draw and found that you would be expected to lose about 36 per cent of your money if you had played.

The method used was "expected value" - also known as "expected return" - which gives the returns you will receive if you play the Toto very many times.

I calculated an "expected return" for each prize category - or how much you will earn from that category in the long run. This is taken by multiplying the category's winnings by the probability of winning.

By summing up the "expected returns" for each prize category you will get the value for the entire Toto game.

The result: For every 50 cents you bet in last year's draw, the various prizes would have allowed you to recover only about 32.23 cents.

Rounded off to 32 cents, that would have represented a loss of 36 per cent on your capital.

The figures this year will no doubt be similarly stacked against punters.

Basically gambling is a sure-lose proposition. The best way to "win", as I'll tell my engineer friend, is to avoid the Toto draw altogether.

If you insist

But of course, not everybody will be satisfied by my advice to sit it out.

After all, most people already know they are entering a losing deal the minute they enter Singapore Pools - but they place bets anyway.

They may play for other reasons. Some people like the thrill, others treat it as a fun office outing where everyone takes part together.

Basically it is an entertainment expense, like going to the movies.

It is a bonus if they win but people fully expect to kiss their money goodbye the minute they hand it to the Singapore Pools auntie.

So I did more research, in case you are dead set on playing.

One major recommendation from Western academics is to avoid picking commonly chosen numbers.

Each of the numbers on the sheet has an equal chance of being part of the winning set. So your chances are not increased or decreased by picking the figures that others overlook.

But the prize will be split with fewer people if you do win.

Singapore Pools publishes the number of times each of the 45 numbers has won.

But this is useless data. The odds of winning are the same for each number at a new draw, regardless of how it did in the past.

The really juicy data - the most commonly chosen figures by Singapore punters - are a closely kept secret by the lottery operator.

Still we can look at overseas data to try to guess the behaviour of punters here.

Remember, the aim is to pick numbers that nobody else likes.

A Scientific American article in 2012 advised United States punters to avoid the popular number one, which appears on about 15 per cent of all tickets there.

British broadcaster BBC News said back in 1998 that the UK National Lottery's most popular number was seven - a lucky number in Western cultures.

The combination 1, 2, 3, 4, 5, 6 is also chosen weekly by thousands of Britons.

The BBC said that numbers below 31 should be avoided, as these are frequently picked to match birthdays.

Both the BBC and Scientific American suggested giving preference to numbers at the edge of the ticket, which are underused. Punters tend to favour numbers in the central columns, they said.

Of course, adjustments need to be made for the local context. For instance, Britain's lottery involves choosing figures from 1 to 49, rather than 1 to 45 here.

In Singapore I would imagine that numbers such as 8 and 28 will be popular as they are considered lucky among the Chinese, although I have no figures to back me up.

So after all this research, will I take a flutter on the Hong Bao Draw personally?

Probably not, as I don't like throwing money down the drain, even if it's 50 cents.

It's not to say that I avoid Singapore Pools completely.

I place football bets against my favourite team Liverpool, to earn me some consolation cash if it loses. Of course, I prefer to lose my money and see Liverpool win.

This is the way we should approach the various betting games, Toto or football - avoid at all costs, unless you are prepared to lose.

jonkwok@sph.com.sg