Random musings: 100 million dollar giveaway

I thought that might get your attention!

A Facebook friend, Hank Yuloff, posted this photo on his wall:

Which would you choose? When Hank posted this, it was almost unanimously red. And when I re-posted it, it was unanimously red. Out of 60 comments on Hank's post, only about 5 or 6 said green. And one out of one said red on mine.

Mathematically, the correct answer is green. If you look at the expected value of the 2 choices, green is significantly higher. To find the expected value, you multiply the odds times the payout:

EV = 100% x $1,000,000 = $1,000,000 vs EV = 50% of $100,000,000 = $50,000,000 or 50 times better. And even if you factor in that the $1,000,000 is a sure thing, so in effect you're giving up $1,000,000 to press the green button, the EV is now 50% of $100,000,00 - 100% of $1,000,000, you still end up with an EV of $49,000,000. However, the EV is over the long term. For a single button press you have a 100% chance of walking away with $1,000,000 vs a 50% chance of walking away with nothing and a 50% chance of walking away with $100,000,000, so now this becomes a psychological choice instead of a mathematical choice (which for most people it probably was never a mathematical choice).

The thing is that for most people $1,000,000 is a significant amount of money, and since most people are risk averse (they don't like risk), they'll take the bird in the hand vs the 100 that may or may not be in the bush.

With $1,000,000 you could live on $50,000 a year for 20 years which is fairly comfortable and is the choice that many of the people seemed to voice...although they didn't use numbers, they said they could live comfortably.

Some people said they'd take the money, invest it and then have $100,000,000 but the odds of that are even worse...95% of investors lose money! Not everyone will lose all of it but let's say most people lose half of their money. And the stock market grows at 6 - 7 % per year over the long term. I'll use 6 - 7.2% to make it easier to work with the rule of 72...your money should double every 10 - 12 years in the stock market, if you don't lose it. If your money doubles 7 times, you'll have $128,000,000 and it will only take you 70 - 84 years. Of course, you may get lucky and make more but you may also be unlucky and lose more. Let's look at the expected value, assuming there's a 95% chance of losing half of your money vs a 5% chance of earning $128,000,000:

EV = 5% x $128,000,000 - 95% of $500,000 = $6,400,000 - $475,000 = $5,925,000 if you're willing to wait 70 or 80 years. Let's pick a much more reasonable time frame...your money could quadruple in only 20 - 24 years. Let's look at the expected value of those numbers:

EV = 5% of $4,000,000 - 95% of $500,000 = $200,000 - $475,000 = -$275,000!

So, living off the money for 20 years is a better investment than investing in the stock market.

What if the numbers were different? What if it was $1,000 vs $100,000,000? Most people would probably go for the larger amount this time but what if your car just died and it'll take $1,000 to get it fixed? Or what if your rent or mortgage is due but you don't have it? In those cases the sure thing would look appealing. But what if it was only $100? Or $10? Or $2?

A lot of people will pay $2 for a Powerball ticket, even though the expected value is terrible. Why? Because the cost is almost negligible (for most people), but the payout is enormous. The estimated payout as I write this is $148,000,000....let's look at the EV:

The odds of winning are 1 in 292,201,338 or .000000003422298!

EV = .000000003422298 x $148,000,000 - 100% x $2 = $.506500076327508 - $2 = -$1.49. Over the long run your odds don't look good...you'll lose $1.50 for every $2 invested. But for the short run, you'll either lose $2 or gain $148,000,000, assuming that you're the only winner. But even if there are multiple winners, the risk vs reward ratio is pretty good.

What if you buy multiple tickets? If you buy 10 tickets, your odds are now 10 times better. What about the EV?

EV = .00000003422298 x $148,000,000 - 100% x $20 = $5.065000763275081 - $20 = -$14.93.

100 tickets?

EV = .0000003422298 x $148,000,000 - 100% x $200 = $50.65000763275081 - $200 = -$149.35. Your expected value goes down when you buy more tickets!

When the payout is over $584,402,676 the EV is positive...at $600,000,000 the expected value is:

EV = .000000003422298 x $600,000,000 - 100% x $2 = $2.053378687814222 - $2 = $.05. Still not much in the long run...although it is positive now. But for this particular drawing there are 3 possible outcomes...you keep your $2, you lose $2 or you win $600,000,000. People say that buying lottery tickets is a waste of money since the odds of winning are so low. But 1 in 292,201,338 is better than zero in 292,201,338. I'm not saying to spend all your money on lottery tickets, but that it's OK to dream a little...if you have a positive EV!

Now back to the original choice. Would you still make the same choice? Or will you buy a Powerball ticket?

As for me...I chose green. Because it was the mathematically better choice, but also psychologically. Yes, $1,000,000 is significant but I've already earned much more than that in my lifetime and what have I got to show for it? But $100,000,000 would significantly change my life, and the lives of others, for the better in a much shorter period of time.