Power Odd Ball
With games of chance, I love playing craps and blackjack, in that order. I don’t care for the other casino games because the odds of losing at them are much higher than either craps or blackjack. After all, I am an engineer and software geek, love math, and always want to know my chances at such games.
One day in the mid-to-late 1990s, after reading the fine print of a Powerball ticket, I was struck by the sheer magnitude of the odds against winning the Powerball lottery (a nationwide lottery in the U.S.). I mean, when the small print above says, “The odds of winning the jackpot are 292,201,338-to-1”, just what the heck does that really mean?
So, I wrote a lottery simulator in Java to express in relatable layman terms just how insanely, unbelievably, astronomically slim your chances are at winning the Powerball lottery. As the “player”, you first choose five “white numbers” from a pool of 1 to 69 and one red “Powerball number” from 1 to 26. After you pressed GO, my Java program would generate a set of numbers randomly, and the game would tell you how many numbers you matched. I left off the money side of the game because… well, I’ll show you why.
For fun, I added a twist to my program: a “CONTINUOUS” option. Ticking this option ON would allow the game to run continuously until the player clicked STOP. For every second (in real-time) the game ran, exactly one set of numbers was generated, and the player’s score was tabulated. Because the calculation was so quick, I built in a delay to wait until a full second had elapsed (using the computer’s clock) before checking if the player wanted to continue “rolling” or playing. If the CONTINUOUS option was still ON, the program would repeat the entire process.
I turned on that option, entered my six numbers, hoped to match them all, then clicked GO with hope resplendent, and waited. And waited. And waited…
I left the room to make dinner (a fairly quick affair for I was single at the time) and then ate that dinner while watching the numbers tick by. After twenty minutes and only matching two numbers exactly once and one number a handful of times, I realized something.
I’d been too smart for my own good. Too realistic. This was taking too long.
So, I edited the code, removed the 1-second delay, added a “drawings” counter, and ran the simulation again. Much better this time! In short order, I had “drawn” 10,000 number sets, and hit perhaps one 3-ball match as well as many 2-ball and 1-ball matches (which pay nothing unless you also get the red Powerball number). But I had no big winners of the 4-ball, 5-ball, or the Grand Prize mama of matching all six balls.
So, I let the program run. And run. And run. And I waited. And waited…
Went to bed, got up, showered, ate breakfast, prepared to go to work, and checked on my program’s progress. After nearly 300 million drawings, five of my numbers finally hit three times. I had several 4-ball matches (maybe 20?), but ZERO 6-ball matches. So, no big winnings for me. Using the current-day prize chart above, I would’ve won maybe $1 MILLION (before taxes) for matching those five balls. Woohoo! However, if I’d only paid $1 per drawing (today’s costs are more like $2 and $3 per drawing), I would’ve paid out $300 MILLION. I’d be a “winner”, but I’d be in debt by $299 MILLION.
Not a good financial plan.
I let the program run some more, and (I think) I finally hit all six numbers after something like 450 million drawings. Of course, since the numbers were generated randomly and repeated results were allowed (just as in the real lottery), those 450 million drawings could have been much higher and possibly lower. But not that much lower.
The real cost, however, has been overlooked. It’s not the money you spend on the lottery. No, the real cost is TIME.
A Thought Experiment
If you could somehow magically play the lottery every second of every day (rather than once or twice per week as it is currently) and the monetary cost was no issue (i.e., you could play for FREE), how much time would you be willing to put into this? How long would it take you to “win” by matching all six numbers?
Let’s take the official Powerball odds mentioned above as an example. Let’s say it takes you 292,201,338 drawings to finally hit all six numbers (it could be higher or lower). With one drawing performed every second of every day, it would take you:
Yep, more than 9 years. And if the lottery were delayed to being held once every minute, you’d have to wait almost 556 years for that payoff, unless you were incredibly lucky.
Personally, I’d rather spend that time elsewhere, not choosing numbers and submitting & checking ticket stubs either online or in a 7–11.
Time is money, and the way you choose to spend your time can greatly affect how much wealth you build over a lifetime. Not spent well, it can cost you significantly. When we’re on holiday, that’s expected; you’re spending money and time to have fun. Those moments don’t count… unless you enjoy channeling Ebenezer Scrooge.
And sure, playing the lottery can be fun and fill you with hope for a (very) short time. I might even do it for special occasions like Christmas or someone’s birthday. But it’s no way to invest in your or your family’s future.
A Practical Experiment
What if you chose to invest that $3 not in a lottery ticket, but in an ETF that mimicked the S&P 500 index historically earning 12% per year, and do that not every second of your life, but, say, just once a day for those same 9.27 years? What would those investment returns look like in comparison?
For that, we need a more complicated formula. Apologies in advance for any googly eyes you might sustain, but here it is:
Where:
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· FV is the future value of your investment
· P is the periodic payment ($3 daily)
· r is the interest rate per period (12% per year / 365 days/year = 0.00032876712329 per day)
· n is the number of compounding periods in a year (365 days/year); and
· t is the number of years (i.e., 9.27).
· n*t is the number of periods (365 * 9.27 = 3,383.55 days)
That Future Value comes out to $18,624.98, a nice chunk of change for a family vacation. And you only had to spend perhaps 4–5 minutes a day online to transfer $3 into your brokerage account and buy partial shares of that ETF. Not a bad deal. Sure, it’s much less glamorous than buying a lottery ticket and dreaming big, but in the long run, it’s much more rewardable.
Of course, if you were to invest more each time and/or hold the fund longer, the magic of compound growth will reap even greater returns.
As I’ve shown in my article “The Best Time to Invest Is…”, a $25 weekly investment in an ETF earning only 10% per year but held for 15 years generates a Future Value = $45,178.
Online Calculators
You can determine these figures yourself using some online financial calculators.
Beware: most online Future Value calculators are only built for annual deposits and are of little real use because you’ll want to invest more than once per year to gain the advantage of compound growth. Worse, these calculators assume you’re only dealing with annual deposits, but they won’t tell you that.
One of the better online FV calculators is this one. It is excellent at illustrating the magic of compound growth with periodic investments.
When using it, make sure the numbers you enter are PER PERIOD. Whether that’s per day, per week, per month, or per year, it’s up to you to make those conversions before entering numbers into these calculators. Otherwise, your calculations will be off. Garbage In = Garbage Out.
For instance, if you expect 12% ANNUAL growth rate (i.e., interest rate) but you’re investing period is weekly, you need to divide that 12%/year by 52 weeks/year to get an interest rate of 0.230769% per week. If you’re investing daily, the interest rate per period is then 12%/year divided by 365 days/year, or 0.032876712328767123% per day. Don’t round off these numbers much either, because small changes can make a huge difference when compounded over many periods.
In my Practical Experiment example above, the period is per day. The “Number of Periods (N)” field in their calculator is equivalent to the n*t in my formula. Thus, I entered 365 days/year * 9.27 years = 3,383.55 days. In their “Interest Rate (I/Y) box, I entered the interest rate as: (12%/year) / (365 days/yr) = 0.032876712328767123% per day (i.e., per period).
Like evolution, small changes over long periods will have huge impacts because the n*t exponent in the FV formula is very powerful!
This is why I strongly recommend you buy and hold an S&P 500 index fund like SPYG, IVV, or VOO and sign up for automatic dividend reinvestments. Each quarter when dividends are paid on the shares you own in that fund, that money will be auto-invested for you, automatically buying more shares. You won’t even have to think about it. The initial amounts will be trivial, mere pittances. But in time, your number of shares AND the value of each share will grow, piling up like so many Benjamins.
In full disclosure, I own shares of SPYG and IVV, but not VOO. Over most periods, SPYG’s return has generated better returns than IVV and VOO. Plus, with its lower price (currently under $82/share as compared to $500+/share), beginning investors can establish positions in the S&P500 fund more easily.
With SPYG, I’ve done particularly well investing regularly in it, dollar-cost averaging my way to it holding between 5% and 10% of my investment portfolio.
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To Be Clear: I am not a financial advisor nor economist, just an engineer who pays attention. Do your due diligence. Any decisions you make after reading any of my posts and the repercussions you receive from those decisions are yours and yours alone. I am only describing what has helped me in the past 30+ years of investing.
Now, get some free laughs with these 50 Funny Animal Posts. I especially liked numbers 26, 32, 35, and 42.
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