Why Lotteries Are a Brilliant Scam!

Why Lotteries Are a Brilliant Scam!
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Lottery ScamMany people dream of winning the lottery. This dream builds on the idea that money has the power to ameliorate problems, significantly alter quality of life and bring happiness.

While it is true that having a lot of money will definitely change your life, it will not necessarily bring happiness. It is likely to invite new problems into your life.

So, winning the lottery may not be all it’s cracked up to be. The good news is that you don’t need to be a millionaire in order to quit your job and be financially independent – And playing the lottery might actually delay you reaching that goal.

Tax on the Poor

Like many games of luck, lotteries exploit people’s hopes and aspirations. They provide a false sense of hope to people that they may be able to alter the course of their life with little effort.

What is particularly unfair is that this ‘opportunity’ tends to appeal to those who are vulnerable and in need, and who cannot afford to lose money. The reason the lottery is sometimes called “a tax on the poor” is because people of low socio-economic status disproportionately play the lottery.

Indeed, many people playing the lottery are either poor or see themselves as poor. They believe that winning the lottery would allow them to pay back their debts or improve their standard of living.

The problem is that playing the lottery comes at a cost. While the price of a ticket varies between games, there is one important constancy: As ticket prices aren’t dependent on income, lower-income players will spend a larger proportion of their wealth to purchase a ticket.

Consequently, the impact of lottery spending on their total net worth is greater. This is inherently exploitative and an unfair scam.

Lotteries are particularly good at showcasing the rare jackpot winners, using them to proliferate the myth of an easy win and attract more players. However, as with many things, the only winner is the government!

It generates ongoing revenue from lottery tickets and taxing prizes. On top of that, the government will tax the companies running the lotteries. It’s a win-win for the government – If you lose, they tax you, and if you win, they also tax you!

In fact, ‘games of luck’ like lottery and gambling more broadly are huge sources of income for federal and local governments. And aren’t you paying enough tax already?

Probability of Winning

Spending money on the lottery would be fine if you had any real chance of winning the jackpot. Everyone who plays the game thinks “Well, someone’s got to win it”. And that is true – Someone will win. But sadly it is unlikely to be you. The odds are simply stacked against you.

Let’s have a look at what the chance of you actually hitting the jackpot is. As you will see, your chance of winning is close to zero. In fact, I’m putting in a few comparison examples so you get a feeling for how unlikely it really is. That will help you contextualize it and put it into perspective.

Event
Probability
Winning the Australian Powerball Jackpot1 out of 76,767,600
Developing Cancer in Your Lifetime1 out of 2
Dying from Cancer This Year1 out of 600
Losing an Appendage to a Chainsaw1 out of 4,464
Getting Injured by a Toilet Seat in Your Lifetime1 out of 6,500
Winning an Oscar1 out of 11,500
Dying tomorrow1 out of 28,000
Dating a Supermodel1 out of 88,000
Getting a Royal Flush in a Hand of Poker1 out of 649,740
Being Struck by Lightning1 out of 835,500
Becoming a Movie Star1 out of 1,505,000
Becoming a Billionaire1 out of 7,000,000
Being in a Plane Crash1 out of 10,790,000
Becoming a Saint1 out of 20,000,000
Naturally Having Quintuplets1 out of 47,458,321

Ironically, you have a better chance of becoming a billionaire – not just a millionaire – by being active (working, starting a business, investing, etc…) than by being passive and waiting for the lucky numbers to get drawn.

As the table demonstrates, there are many events that are more likely to happen to you than actually wining the jackpot. Indeed, the lottery is more likely to erode your fortune than to add to it!

When to Play

Like with any game, you should only play when you have a fair chance of winning. No one wants to be a loser, right? In probability theory, this translates into computing the expected value of the random variable, i.e. the average value one would get if allowed to repeat the random event infinitely.

Let’s take an example to better understand what an expected value is. We consider a game where you have 4 cards face down (Ace to 4). Turning up a card allows you to earn $x where x is the value on the card. Once the game is over, all cards are shuffled and put back face down for the next game.

How much would you pay to play that game? $2? $3? Less? More?

By definition, the expected value is the weighted average of all possible events. It is the sum of each outcome multiplied by the probability of it occurring. In the example of the card game, the probability of turning up any of those cards is equal to 1/4. You have 1 chance out of 4 to turn up a 3 for instance or any other card, during each game.

Here, the outcome for each event is the value of the card itself. Hence the expected value for this game is:

EV = displaystyle{frac{1}{4} * 1 + frac{1}{4} * 2 + frac{1}{4} * 3 + frac{1}{4} * 4 = 2.5}

This means that if the price to play a game is below $2.5, you will tend to make money if you play long enough. For instance, if you only have to pay $2 a game, you will expect to earn $0.5 times the number of games after a large amount of games played. The average converges towards the expected value as the number of trials increases.

Looking at the expected value of the lottery game is similar. In the case of the Australian Powerball, the probability for each division win is well-known. We can also derive the potential earnings for each of these games and come up with the expected value of the game.

Division
Required Winning Numbers
Probability
Division Prize (13 Jun 2013)
Expected Value Calculation
$0.429
1st Division6 + Powerball1 out of 76,767,600$10,000,000$0.130
2nd Division61 out of 4,040,400$144,214$0.036
3rd Division5 + Powerball1 out of 376,312$5,486$0.015
4th Division51 out of 19,806$177$0.009
5th Division4 + Powerball1 out of 9,123$65$0.007
6th Division3 + Powerball1 out of 641$37$0.058
7th Division41 out of 480$27$0.056
8th Division2 + Powerball1 out of 110$13$0.118

This means that if the ticket price exceeds $0.43 (it will vary slightly depending on the size of the jackpot), you will likely lose money over the long-term. The current price to play one game of Powerball is $0.93.

This means that you are expected to lose $0.50 every time you play the game – on average across a large number of games, considering a stable jackpot. Thus, if you want to be rational about gambling, you should only play games where the price you pay is lower than the expected value of the game.

Why? Because it means that you could make some money in the long run. But it is not certain, just remember that the expected value can only become ‘accurate’ over the very long-term; it is a probability over an infinite number of iterations.

Thus, if you have an impulsive and emotional approach, you will waste a lot of money because you only have a finite amount of cash. The best would be to avoid gambling all together. Unless you like losing and paying additional taxes!

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