Expected Returns of Lottery

According to this Straits Times article in March this year (non-premium so can click and read), more Singaporeans are gambling, up from 44% of all citizens and PRs (18 years old and above) in 2014 to 52% in 2017. Here are some interesting statistics:

• Most popular game - 4D (42% participation rate) followed by TOTO (36%)
• Among races - Chinese (62% participation rate, up from 53% in 2014) vs Indians (one in three) and Malays (less than one in ten)

•  Median bet per month was $30, up from $20 a month in 2014

As published on the Singapore Pools website, you are more likely to celebrate your 100th birthday (1 in 50) than win top prize at the jackpot machine (1 in 34 million). You are also more likely to be struck by lightning (1 in 240,000) than strike TOTO jackpot (1 in 14 million). If odds of winning a lottery is so low, why are so many people (more than half of the adult population) still throwing away their money?

Most people think that a 4D or TOTO ticket only costs a few bucks but provide the potential for a windfall. If you don't buy, you don't even have a chance or hope. However, more often than not, that hope quickly turns to dashed hope. Even for the serious and long-time punters who think they had devised a system for improving their odds and returns, their optimism is more likely than not misguided. When did you ever see a 4D punter keeping precised track record of all his historical trades and winnings? All will claim to have strike it big one time or another, but who can tell you his exact returns in gambling?

Let's take 4D as an example. 4D is by far the most popular game since it is the easiest game of simply choosing a 4-digit number between 0000 to 9999 and there are 3 draws every week which makes it easy to participate frequently. With a participation rate of 42% vs the total gambling rate of 52%, that means out of every five people who gamble, four will surely be involved in 4D.

The most common bet for 4D is ordinary big or small. Each number gives you exactly 1 in 10,000 probability to win something. The combined probabilities, prize amount and expected return for every $1 wagered are shown in the tables below. For every $1 bet in 4D Game (Big), your expected return is $0.38 or an expected loss of 62%. For every $1 bet in 4D Game (Small), your expected return is slightly better at $0.58 or an expected loss of 42%. The expected return for someone wagering equal amount in big and small would be a loss of 52%. Assuming a median bet per month of $30, your expected loss would be $15.60. Over 10 years, you would have bet a total amount of $3,600 and be left with just $1,728. It is not that bad in the sense that you did not lose all your capital and for the average punter who bets $30 each month, to lose $1,872 over 10 years may be totally acceptable. However, if you simply not bet and instead contribute that $30/month gambling budget at the start of each year into the CPF Special Account earning 4% each year, you would have ended up with almost $4,500 vs only $1,728 if you chose to gamble.

Casual gambling during Chinese New Year or mahjong with friends is perfectly okay as social interaction so I would not group them together with lottery buying. For lottery, the economics is extremely poor hence the only acceptable times where you should wager is either when you buy a new house or car (buying a one-time 4D for your unit number or license plate), or participating in the office pool for the annual Hong Bao TOTO (you do not want to be anti-social, anti-fun). There is no excuse for regular lottery buying with such huge negative expected returns, even with the temptation of a quick windfall.