Do You Feel Lucky?

\"\"I don’t really like roller coasters. It’s not that I’m terrified of them – it’s just that I get absolutely no enjoyment and feel like I’m exposing myself to a bit of danger (they’re maintained by high school kids, you know) and stomach lurching for no reason at all. Plus you have to pay for it, which seems downright ridiculous.

You, on the other hand, may like roller coasters. And that’s OK.

It’s fine for us to have different views on roller coasters, because we’re totally different individuals.

You want to know something else it’s OK to have differences on? Our appetite for risk. (Wait, that could still be roller coasters…let’s clarify). Specifically, our appetite for financial risk.  

I don’t see a lot of personal finance discussions about risk. It’s alluded to – like when people suggest that asset allocation may change depending on your time horizon or when people discuss paying off their mortgage – but it’s rarely discussed outright. That’s a shame, because risk is one of the most important things to understand when discussing personal finance.

In fact, some online personas seem to be almost risk-neutral. With chiseled jaws and nerves of steel, they laugh right in the face of risk. They’re happy to be 100% invested in stocks and think folks who pay off mortgages early are fools. Granted, they’ve never actually been through a market downturn, but how can that possibly be relevant?

What’s Your Appetite for Risk?

So today, I’m going to dust off my Decision Science notes and have fun quantifying your appetite for risk. I’ve got a hypothetical wager I’d like you to consider, and you’ll need to tell me the odds you’d need to take it.

Here’s the deal:


If you win, you’re paid $1,000. If you lose, you have to pay $1,000.

What minimum probability of winning (p in the above) do you need to take this wager?

I know everyone would be willing to take the deal if you had a 99% chance of winning $1,000 and a 1% chance of losing $1,000. I need to know the minimum odds you’d need to accept it.

Sidebar for only the Decision Scientists among us: Yes, I know with one reasonable assumption I can use this single wager and the answer (as long as it’s <>50%) and plot everyone’s u-curve and project what they’d do in any deal and be done. But that’d involve a lot of boring math and explanations, and they already think we’re total nerds. So just roll with me.

Most people will require something north of 50% for p to accept this wager. Some brave souls may be OK right at 50%. And if you’re a risk-loving thrill seeker who would accept this wager with less than a 50% chance of winning, please contact me immediately as I have a deal for you.

As soon as p goes above 50%, this is, mathematically, a good deal. But that will be small solace if you happen to be on the losing end. The fear of that loss is what requires most of us to have significantly more favorable odds of winning.

Now let’s do the same offer, but increase the payouts: + $10,000 and – $10,000. If you’re troubled that you want a higher p to play for these increased stakes, don’t be. It’s a reassuring sign you’re human.


And for a final data point, let’s look at +$100,000 and – $100,000. Fear and greed are in full-fledged battle! Being handed a cool $100K would be great, but it’d be a painful check to write if you lose.


What Does p Tell Us?

If you are indeed human, you most likely needed a p greater than 50% to accept the $1,000 wager. You needed an even higher p to accept the $10,000 one and higher still for $100,000.

If you did, it means you’re risk-averse. That is not a bad thing, or a sign of weakness – it’s part of being human. All things equal, why would we favor uncertainty over a sure thing?

The nice thing about this wager is it allows you to compare your risk tolerance to that of other people. If you required a 65% chance of winning $1,000 to take that wager, and someone else only required 55%, that’s a meaningful difference. The two of you could face the same financial decision, make totally different choices, and both be perfectly rational. That’s important to understand.

What If My p Is Really High? Isn’t Being Extremely Risk-Averse Bad?

Well, I guess it’s bad in that it may make it much harder to achieve your financial goals. If you’re terrified of loss, you might avoid the stock market and other risky investments altogether, and those have historically been great ways to increase wealth.

But it’s also just a part of who you are. Telling someone he should accept lots of risk because math and history says he should is like strapping me into a roller coaster and telling me it IS fun so I’d better enjoy it.

The goal today isn’t to shift anyone’s risk tolerance. It’s just to establish that we are indeed risk-averse and then measure where our current risk tolerances lie.

And that’s where you can help. Once you have your minimum probability p to accept the $1,000 wager, please let me know what it is in the comments below. It would be helpful to show that we’re all different and there’s a range of risk tolerances among us. As fascinating as Decision Science is – oh and it is fascinating – the value of this post will be much greater if you can compare your risk tolerance with that of other readers.

I’m planning on discussing risk in future posts – especially how it influences some major investment decisions (e.g., mortgage payoff). I do want to challenge that there is ever a single “correct” choice for financial decisions involving risk. We’re all different, and our decisions should reflect that.


What odds do you need for the $1,000 wager? The $10,000 one? $100,000? Do you like roller coasters? Please me know in the comments.
If you’re a first-time commenter, it’s easy and you can be anonymous – we just want to see your p 🙂


Picture courtesy of Stefan Schweihofer


14 thoughts on “Do You Feel Lucky?”

    1. I’m not that far from you, I think. I might have some explaining to do to the missus if I lost, but I’m somewhere ~55-60% for the $1,000 punt.

      Thanks for the data!

  1. I’m supremely awful at math, but I just wanted to commiserate and say that I DESPISE rollercoasters. It almost borders on a phobia-like fear. Mr. Picky Pincher convinced me to ride Space mountain at Disney World (he said it was a “train”) and I couldn’t even get off the ride afterwards because I was crying and shaking so bad (PSA: the Disney employees do not care if you’re having a panic attack; they just want you to get off the damn rollercoaster lol)

    1. Yeah, rollercoasters are the worst. I may not have quite your level of fear, but I’m right there in terms of disliking them. They seem about as rational as sitting on the divider in the middle of a highway with cars going by at 90 mph. Sure it produces some adrenaline, but why is it I’m doing this?

      My eldest son likes them and the missus, my brother, and me all wince when he wants to go on one. Thankfully I have a brave sister-in-law who’ll step up for us 🙂

      I’m sure Disney has a decompression chamber somewhere and was about to throw you in it – they can’t have someone shaken from a ride killing the magic (tears are NOT allowed at Disney, Miss!). Tell Mr. PP to stick with the log ride next time – that’s about my max capacity.

    1. Excellent – thanks for providing! You seem to have a healthy respect for risk, so I may need your help in the future. There are some decisions that may not make sense from an NPV perspective but are still the wise choice once one weighs risk (and risk-aversion). Thanks again!

  2. Isn’t part of the equation the incremental value you place on the $1k wager? I don’t have an MBA from some fancy big time program but won’t people who make $30k generally respond differently than people who make $500k? Just asking.

    I like Eric B.’s answer.

    1. Absolutely – that is a critical part of it and further drives variance in answers. You could consider that the payoffs are +$1,000 + your current net worth and -$1,000 + your current net worth, so your own full financial situation will definitely weigh heavily.

      A billionaire would look at the $100,000 deal the same way you or I would look at a $10 bet (where I imagine, based on our times in casinos, we’re pretty risk-neutral…). You’d still expect him to be risk-averse, but you might need pretty big bets to get outside of the range where he’s almost risk-neutral.

      I think everything I learned (and definitely everything I still remember) from my fancy MBA can be picked up in about 30 minutes for free online nowadays. If you’re tempted by the allure of Decision Science, I’ll hook you up. Women will want you and men will want to be you.

      1. Can I use decision science to get my kids to do what I want them to do? That’s really where I am in life right now.

        1. I think they’re going to be a little weak embracing it right now, but you can definitely use it to deal with them. I’ve never seen a parent’s decision tree that favors leaving them behind at a store (though it was one of the options considered…), so it’s good to check some of our more base instincts!

  3. I’d say 60%, 70%, and I’d take the 100K bet at 90%, but I’d be sweating bullets and probably hate myself if I lost.

    As an aside, I absolutely love roller coasters. They’re fun. I take a far greater risk by strapping into a car and driving to work every morning, and the reward there is only a day in the office. Cars are piloted be a flawed human (me) and even more flawed humans (people on their cell phones). And safety is only one element of vehicle design, which is usually out-prioritized by cost, looks, and performance.

    Meanwhile, roller coasters are designed by some of the world’s most brilliant engineers with safety as the ever present #1 priority, and are piloted by an automated process with multiple levels of redundancy. And those high school kids you see are just the operators. They’ll be stopped by said multiple levels of redundancy before they can make anything bad happen. Tradesmen are the ones doing the maintenance every morning, and the rides are such engineering marvels that even their job is far less important than it looks.

    All that said, I absolutely refuse to go on any sort of carnival ride. Any ride that can pack up into a semi-truck trailer and quickly put together by a carnie is an engineering marvel, but not the sort of marvel I’d like to trust with my safety.

    1. Excellent! Thanks for the odds. Though a true decision scientist would tell you that you should never hate yourself if you lose – it’s just a bad outcome from a good decision.

      Somehow I’ve got the incorrect image that all roller coasters are designed by carnies and built by carnies and based on engineering concepts developed by carnies. So I’m pretty irrational, but since they don’t float my boat I’ll just stay away anyway. I’m glad you like them because the people who seem to like them seem to really be having fun. Plus they support our economy.

      Thanks again for the note!

    1. Thanks for the data! Those are some pretty risk-averse odds – they would seem to imply that the stock market is a bit too much a roller coaster for your tastes, but I know you’ve got plans to retire in the short term and imagine equity returns are part of the formula. Since the odds here are in your favor, perhaps if you recast it as “investing” rather than gambling it’d be an easier deal to accept! But you provide a great example that all of our risk tolerances are different – thanks again for stopping by.

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