Super Coin Flip Risk Assessment

In the Coin Flip Risk Assessment, I presented a hypothetical coin flip as an introspective view of your feelings on risk. Well, one of my readers, (OK fine, it was my wife) put the screws to me and gave me a hypothetical Super Coin Flip Risk Assessment with the same premise as my initial question.

Risk Assessment

As a reminder,

Initial Coin Flip Risk Assessment

Pretend you walk into a casino and are given an opportunity as a new customer. You can bet $1,000 on a (fair) coin flip. You need to risk $1,000 of your own money from your taxable or retirement investment account. Any winnings would go right back to the same account. You have a 50% chance to win. If you call the flip correctly, you win 2x your bet plus your initial wager back, a profit of $2,000. If you call it wrong, you lose your $1,000 wager. You can only play once. Your expected value (EV) is the average result of the bet based on the odds. In our risk assessment, your EV would be a profit of $500. [EV=(2,000*50%)+(-1,000*50%)] Would you take this bet?

Result Profit/(Loss) (a) Probability (b) EV=a*b
Win 2,000 50% 1,000
Loss (1,000) 50% (500)
Expected Value (EV) 100% 500

Super Coin Flip Risk Assessment

Mrs. WPF asked me what I would do if it were a $200K coin flip instead of $1K. It’s the same situation as above but substituting $200K for $1K.

Result Profit/(Loss) (a) Probability (b) EV=a*b
Win 400K 50% 200K
Loss (200K) 50% (100K)
Expected Value (EV) 100% 100K

My Knee Jerk Reply

My initial reaction was “it depends” – and I could already see her frustration with me. She is naturally more risk averse than I am and would probably never risk $200K on a coin flip no matter the payoff. After thinking about it a little…

Here is my official response:

For all scenarios, I’ll assume I can make the $200K bet within my 401(K).

Scenario 1 – If I Had This Opportunity Today

With our current financial position, I’d call Mrs. WPF right away. I’d explain the rules of the bet. I’d ask her very nicely not to hang up on me. Then I’d explain that on average, we’d be financially independent earlier by taking the bet.  Financial Independence (FI) is having the financial resources necessary for us to stop working. Since Mrs. WPF is currently not working and our financial plan is for her to go back to work at some point, it would mean both of us could stop working earlier. If we won the bet, we would be on track for FI 4 years earlier than currently planned. If we lost, we would have to work an additional 2 years from our current plan before reaching FI. On the call, I’d beg for her agreement to take the bet. Personally, I’m very willing to risk two years of working to save four with 50/50 odds. If she was still not okay with it, I’d pass on the bet. Her trust is way more important to me than the expected profit. I may not be happy with her decision to pass on the bet at the moment but I would not hold it against her.


Scenario 2 – What If I had to Decide Solo?

If I had to make the bet before talking to Mrs. WPF I’d pass. I could not look her in the eye and say I lost $200K even if the bet had a huge expected EV. She may never trust me again and that’s not a healthy life. Her trust is worth much more than $100K in EV. I know that she would be more upset at me for risking $200K than turning down an EV of $100K.

Scenario 3 – What if we just retired?

If we were already retired without any extra cushion in our savings, I’d pass. It’s not worth having to go back to work for a chance to win extra money we don’t need. This is the perfect example of the marginal utility of money. Having an extra $400K at that point would not really impact our lives but losing $200K would force us to go back to work. No thanks. This is why you focus on protecting your assets once you have all the money you need (but not much more) and it makes sense to take less risk.

Scenario 4 – What if we were retired and had extra?

My last scenario is if we were already retired and our investments increased significantly after retirement, giving us much more than we need for our planned lifestyle.  In this scenario, I’d probably take the bet. This decision would hopefully allow us to increase our lifestyle or accomplish some other goal like donating more to a cause important to us. This situation is summarized as: when you already have more than enough, why not take a risk to earn extra in a profitable situation?

How Your Life Situation Impacts Your Risk Tolerance

Based on these answers, I think you can see my natural willingness to accept risk.  At the same time, you can see the ways I’m able to control my natural tendency to take a profitable bet by considering the life situation, impact of a win/loss and the feelings of my partner. I also think my answers are in line with my financial advice for newlyweds.

What do you think about my answers? Would you take the $200K flip? Let us know in the comments.

5 thoughts on “Super Coin Flip Risk Assessment”

  1. That’s very interesting and reminds me of the situation that sometimes occurs when lotteries go unclaimed several times and the prize grows to where the actual prize amount when divided into the number of lottery tickets sold is greater than the price of a ticket. In other words a $500 million dollar prize is available and only one hundred million tickets are sold making prize money of $5 per ticket available for a ticket that only costs $2. On paper you should buy as many tickets as you can afford because each one is worth $5 on average. In fact there were investment funds set up just to buy these under priced lottery tickets and they actually worked! The problem with those and your example are that you cannot “play” a large enough number of times for the outcome to reliably resemble the theoretical odds. Statistics mean nothing in a one try event. Which of course is why only crazy people play Russian Roulette even though the odds of survival are pretty good. And if you really have more money than you need of course you don’t make the flip. What good is more money when you have plenty? Your wife by the way is a genius!

    1. I could not agree more that my wife is a genius…well except for the fact that she committed to spending the rest of her life with me ;). I always figured that those lottery overages would be offset by the reduced lump sum payout and the taxes due. It’s interesting to hear that some funds were successful investing in it. I agree that the “problem” in the example is that you can’t play a large enough number of times. In a way, that’s the point I’m trying to make. If it was a $1 bet 200K times everybody would do it because there is no real risk. Betting $200K on one flip is a crazy amount of risk but may be worth doing depending on your life situation. In life, sometimes positive EV situations arise but come with risk. If you want to get ahead, you may need to take a chance. This could be as simple as putting money in a stock index fund. Yes, there is risk and you can lose, but historically it’s been one of the best investments available. In the situation when I had extra money, I’d make the flip because there is always something else you can do with the money. Let’s say that my estate is going to a charity, I’d take the chance to give the charity a positive expectation of more.

  2. Interesting concept. I agree that for many things it depends. My risk tolerance at times is lower depending on what’s happening with my kids. Having been homeless and rebuilt, I know I can do it again if I did lose everything so I think often my risk tolerance is higher than many.

    However, I know at this stage in my life, I’d be unwilling to do a $200k coin flip 🙂

    Interesting post!

    1. Thanks for stopping by Kylie. Glad you liked the post. Based on my informal poll, I have not yet heard of one taker for the $200K. Maybe my risk tolerance is even higher than I thought. I wonder if part of it is that I live in a higher cost of living area than most and I’m downplaying the value of that significant sum. Sorry to hear about your past struggles. If you have a post with your story coming back from homelessness, feel free to drop a link to it in the comments. I’d love to hear your success story.

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