Singapore Pools is back with their annual Hongbao Draw. This year, the draw’s Group 1 (jackpot) prize has shrunk slightly to $12 million from $13.9 million last year. Nonetheless, thousands of Singaporeans will be braving the long queues and possibly, torrential rain, in order to stand a miniscule chance of striking rich.

Before we get too excited about the Hongbao Draw, let’s first look at our chances of winning, and how much we can realistically expect to get if we do win.

Before we start, we like to remind readers to exercise a Responsible Play mentality and to treat Toto (or any other form of gambling) as a vice that should only be indulged in occasionally.

Toto 101: What are my odds of winning?

Anyone who bets in Toto will know that the chances of winning are extremely low. To hit the top prize of $12 million in this year’s Hongbao Draw, your chances are about one in 14,000,000.

To provide a perspective of how poor these odds are, the chances of a person in the US getting strike by lightning is about 1 in 280,000. In other words, a person is about 50 times more likely to get struck by lightning than to win the top prize in Toto.

Aside from the top prize, there are other winning categories that appear lucrative as well. Assuming that Group 1’s prize pool is $12,000,000. The total prize pool would be about $32,000,000 (12 million/38%).

Exhibit 1: Price group and winning odds

If we were to sum up all the probabilities of winning, the chances of actually winning something in any of the groups is 1.9 per cent.

Exhibit 2: Prize structure and amounts

*Source: Singapore Pools, Dollars and Sense*

Net present value of a quick pick bet

We will need to make a few assumptions for our analysis in the next part of the article. Here are our assumptions:

1. The winner buys only one $1 quick pick,

2. There is only one winner in each group,

3. We ignore the additional 54 per cent of sales that will be added to the pool,

4. The prize pool is $32,000,000,

5. Discount rate of 0 – because between now and the Hongbao draw is only a couple of weeks

If we multiply the probability of winning by the prize money and sum up the total probable winnings, we will have a present value of $77.16.

Exhibit 3: Present value of a $1 quick pick

After subtracting the $1 used to buy the quick pick, we will have the net present value (NPV) of $76.16.

Hold on, are my chances really that good?

Before you get too excited over the high NPV that a Toto ticket buys you, consider the following.

For the Prize Group 1, 2, 3 and 4, prize amount will be split in the event that there are multiple winners for each group. In other words, the NPV of $76.16 is only relevant if there is one winner for each of the top four categories.

At this point, it’s a little tricky to calculate the expected value because there is no way to know for certain how many winners there would be in each category. To help us estimate this, we took the average number of winners for each group from the past two hongbao draws

Exhibit 4: Expected value of a $1 quick pick (based on estimated number of winners)

* Based on estimated number of winners from Hongbao draw in the last two years

The expected value has significantly reduced to $0.795. If we subtract the $1 used to buy the quick pick, our expected value will now be – $0.205.

Based on a quick observation that we made from past Toto draws, it’s also worth highlighting that the actual amount won by players during the Hongbao Draw isn’t necessarily higher than the regular Toto draw.

In fact, for some of the categories, a regular Toto draw is likely to pay a higher prize amount than the Hongbao draw based on the fact that less players participate in the regular draw, and hence, the prize pool has lesser winners, compared to the Hongbao draw.

Toto gives us an illusion of increased wealth

Similar to many other lottery draws such as the Powerball in the U.S, Toto gives us the illusion of increased wealth due to what appears to be high prize money for the odds given.

Yet, like many other lottery draws around the world, the good odds (as seen in Exhibit 3) only counts if you are the only player in the lottery, or if the prize amount shown is given to each winning player, rather than to be split among all winners.

Ironically, the attractiveness of a bigger prize pool for a lottery draw is also what makes it less enticing. A bigger prize pool tends to attract more players, which in turn increases the odds of more winners, and hence, a smaller payout for each winning player.

On a lighter note, the participation in Toto betting should be one of leisure and a topic with friends and family during this festive period. However, if you are thinking of getting rich just because of this Hongbao draw, don’t put too much hope into it as you would for any other regular Toto draws.