Investing vs the Lottery

The Powerball jackpot is expected to be over $700,000,000 this weekend. I’m tempted to buy a ticket too. Now I only buy tickets when my office coworkers buy them as I don’t want to be all alone in the office in case they actually win, so this would be perhaps the third time I’ve played in my life. But for someone that plays regularly, what might they ‘win’ on the stock market instead of buying a $2 ticket twice a week?

How to invest $2 a week in the stock market

For investing on a really small budget, the best option I can think of is the low-cost SWPPX mutual fund from Schwab.com. It’s a passive index fund which tracks the S&P 500 index and it allows minimum purchases of $1 with no commissions. Its fees are a reasonable 0.09% and the only real catch is that the minimum initial investment to actually acquire it is $100. Most mutual funds have an entry price of $1,000 to $3,000 and only allow purchases of $100 or more so this is still cheap. It pays a small dividend yearly – somewhere around 1 to 2%.

But for the purposes of this article I’m going to assume that the would-be-investor already owns the fund and is purchasing it twice-weekly $2 at a time over an 18.5 year period from June 1997 to end of December 2015. I’m then going to compare that to the likely returns of the same amounts of lottery tickets. And I’ll throw in an online savings account at 1% just for fun too.

Disclaimer: I’m not affiliated with Schwab, nor do I receive any money from them, nor am I saying that SWPPX is the right investment for you to buy. It’s just the lowest price of entry into investing that I know of ($1) and could be bought instead of lottery tickets.

Lottery Odds

Winning the lottery is the modern day equivalent of a miracle; the likelihood is miniscule and yet several people have won multi-million jackpots several times. Randomness is a strange force of nature as I learned reading The Drunkard’s Walk. There’s also a lot of psychology behind buying lottery tickets; for some it’s the dream of escaping their situation; for others it’s an insidious form of taxation that tends to be paid by lower income families. But people do win and winning can be life changing for better or worse. And there’s a lot to be said about the “dream” or hope of winning.

My parents, who play the lottery weekly, understand that they won’t likely win if they picked the numbers 1, 2, 3, 4 and 5. “Don’t be stupid, those numbers will never come up!” was the response when I suggested that sequence to them. Yet they feel that 42, 12, 25, 38, 4 or whatever their favorite numbers are, might just win although they have the exact same odds. My take-away from this is: If you want to convince yourself not to buy a ticket; think of picking 1,2,3,4,5 & 6 as the winnings numbers.

So let’s look at the current powerball odds to see what we’re really up against.

 Combination  Odds  Winnings
 5 white balls + 1 red  1 in 292,201,338.00  Jackpot
 5 white balls 1 in 11,688,053.52 $1,000,000
 4 white balls + 1 red 1 in 913,129.18 $50,000
 4 white balls 1 in 36,525.17 $100
 3 white balls + 1 red 1 in 14,494.11 $100
 3 white balls 1 in 579.76 $7
 2 white balls + 1 red 1 in 701.33 $7
1 white ball + 1 red 1 in 91.98 $4
 1 red ball 1 in 38.32 $4

According to the website, the overall odds of winning any prize are 1 in 24.87, and the overwhelming majority of the time that prize is going to be worth $4. So if you bought a single $2 ticket once a week for a year, you can probably expect to win at least anywhere from $4 to the jackpot and you’ll have spent $52 for the chance.

Just because the odds are 1 in 24 doesn’t mean that it’s guaranteed to happen if you play 24 times. You might win every single time you try, or you might never win in that period; it’s random. The lottery doesn’t remember that you tried 23 times before so that it can make sure that your 24th ticket is a winner.

I wrote a macro in Excel to simulate the lottery drawings using the odds in the table above. We know we’ll win something, so let’s buy some virtual tickets and see how much we win!

$450 lottery winnings from buying 2 tickets a week for 2 drawings.
Typical lottery winnings when buying 2 tickets a week for 2 drawings.

$459 total winnings! Not too bad on the surface and it even included a $100 win. This is a random result – I could run the macro all day and get different results each time; if I ran it long enough I could get a result showing the $700,000,000 jackpot although I’d probably die of old age before it did that. As it is, I’m showing a result that included a $100 win; most of the simulations I ran won only $4 or $7 prizes and averaged around the $300 mark in total.

Let’s do a quick sanity check to see if the results are reasonable. We know that the odds of winning something are about 1 in 24. That something is most likely going to be $4. In the time frame that I’m modelling here starting from June 1997 through to the end of 2015, we’re buying two tickets a week since there are two lottery drawings a week. That works out to a total of 1899 tickets therefore we have 1899 chances to win a prize.

So 1899 attempts and winning a prize every 24th time = 1899 / 24 which means we’d expect around 80 “prizes” in that 18.5 year period, or at least 80 x $4 = $320. We actually won an average of $5.8 a prize because of the $100 win, so this all looks pretty reasonable. We won’t be retiring any time soon on these winnings but it’s something at least!

And keep in mind that with the odds above for the $100 being a 1 in 14,424 chance, it’s more likely that we wouldn’t win $100 in an 18.5 year period with the number of tickets we bought because we only had 1899 chances or 13.2% (1899/14424).

Lottery winnings vs ticket expenses

But, in order to “win” the $459 we had to buy 1899 tickets at $2 a throw. And that money is gone. If we subtract the expense of the tickets from the winnings we get the graph below.

Graph showing net loss of total return from lottery tickets.
Total return from buying 2 lottery tickets a week after including ticket costs.

In other words, that’s a $3,339 loss. The ticket costs were $3,798, so $459 – $798 = – $3,339. And that $100 win is looking pretty small by comparison!

What if I’d invested or saved the money instead?

To calculate the investment returns, I started with zero and bought $2 of SWPPX each time that the lottery ticket was purchased using historical share price data at Yahoo. Dividends were re-invested when they were paid. For Savings, I assumed a 1% interest rate over the time period and compounded the interest yearly.

Graph showing better investing or savings returns than lottery.
Comparison of money spent on lottery vs savings or investments

historical share price data at Yahoo

At the end of 2015 using $2 purchases twice a week, the total number of shares grew from 0 to 241.83 for a total value of $7,632. The Savings account grew to a total of $4,193. And that $100 win is looking really small now. The last year of dividends from the SWPPX stocks were $230 alone and that’s pretty much more likely to continue being paid.

What about a bigger win? Say $50,000?

The large jackpots and winnings are always going to beat the investment returns if they happen. The problem is that it’s not very likely. Let’s take $50,000 as an example. The odds to win drop to 1 in 913,129.18 attempts. We’ve just bought 1899 tickets over a 21 year period, so in that entire 20 year period we have a 0.2% chance of winning $50,000 (1899 / 913129).

We’ll have to buy a lot more tickets to have a reasonable chance of winning. So let’s buy 50 tickets twice a week instead of 1 which gives a total of 94950 tickets (50 x 1899).

Did we win?

Winning $50,000 on the lottery!
Winning $50,000 on the lottery!

Boom! There’s the $50,000 jackpot and it scales the $4, $7 and $100 wins into almost nothing! Now with these higher numbers we were still only at a 10% chance of getting the $50,000 because we bought 94,950 tickets but really needed 900,000. To get a $50,000 win for the results above, I had to run the simulation several times until it happened.

From the 1899 weeks, the weekly winnings ranged from $0 to $118 plus the jackpot week which won $50,015. There were still 244 weeks (12%) where we won absolutely nothing despite buying 100 tickets.

But $200 a week is still quite a lot of money to spend for a 10% chance of getting $50,000 over an 18 year period. Let’s see how the investments worked out by comparison.

Comparison of lottery returns from buying 50 tickets a week to investing or saving.
Comparison of lottery returns from buying 100 tickets a week to investing or saving.

Even with a $50,000 win, the lottery results are still a net loss and investing still won overall, ending up at $381,621 with a dividend payment of $11,726 in 2015.

Summary

I’ll still likely to buy a ticket before the weekend; unless of course I manage to forget about the lottery on my drive home in my usual absent-minded way. After all, I might just win $350,000 (after taxes), right?

 

Quote of the Day

Here’s something to think about: How come you never see a headline like ‘Psychic Wins Lottery’?

0 thoughts on “Investing vs the Lottery”

    1. Hi DFG,

      My parents play too – one of these days they’re even going to win apparently. Needless to say I lost my $10 investment in lottery tickets but I’ll likely try again on the next billion dollar drawing…

      Best wishes,
      -DL

  1. If I wanted to invest a few £s a week, where should I be looking at? I would want to invest for long term.
    I live in the UK if it matters.

    Thank you

    1. Hi, that’s a good question! I’m based in the US and from what I’ve searched there doesn’t seem to be as many low-cost investing options as here in the US with services like Robinhood.com and Betterment.com. I would recommend you get some more UK-specific advice especially regarding any tax savings accounts that may be better suited for your goals.

      This Guardian article gives some general info and there’s a more practical guide at monevator.com. It looks like £25-50 a month is the minimum range typically needed for investments. If you want to simplify further then look at something like the Vanguard LifeStrategy Fund 60% Equity which holds both stocks and bonds in one fund, I think the minimum is £25 for this fund.

      Best wishes,
      -DL

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