Left Penniless

Isaac Cathey

AS A PARENT, it’s my responsibility to teach my children good financial habits. Core among these are deferring gratification, saving diligently, giving generously and making sensible spending choices. I feel it’s also important to make my children aware of financial pitfalls. Succeeding financially—and in life generally—seems to be as much about avoiding self-destructive habits as it is about cultivating good ones.

My wife and I have been homeschooling our children for the last couple of years. Our attempt at home education has been a smashing success, thanks almost entirely to my wife. While she handles the bulk of the teaching, I do occasionally step in to teach certain concepts. Recently, I was tasked with helping my five-year-old daughter understand probability.

Seeing an opportunity to turn a dry academic exercise into a valuable life lesson, I designed a game for the two of us to play. In the game, I offered my daughter the opportunity to take money from her piggybank and quickly turn it into more money. To play the game, we needed 50 cents in pennies and a die (or dice for those who aren’t sticklers for proper English usage). The rules were simple:

  • To throw the die, you must pay one cent to the dealer (me).
  • Before throwing the die, you must guess how it will land (one through six).
  • If you’re wrong, there are no consequences beyond losing the initial penny paid.
  • If you’re right, you get five cents.

At first, my daughter was doubtful that this game would be any fun. I started her with 30 cents from her piggybank. After her first couple of throws, she’d lost a couple of cents. But before long, she guessed correctly and was rewarded accordingly. My reaction to her losses was muted—basically a subdued shrug. I struck a sympathetic tone and reassured her that the losses were but a temporary and inconsequential setback. Meanwhile, when she won, my reaction was boisterous and jubilant.

This commotion attracted the attention of her younger siblings, who gathered around her to observe the spectacle and take part in the celebration. When her balance temporarily hit 50 cents, I pointed out that today must be her lucky day. When I asked if she wanted to stop playing, claim her winnings and go do something else, she enthusiastically responded that she wanted to keep having fun making money.

Within a few minutes, her luck predictably turned and (to borrow a phrase from John Bogle) the relentless rules of humble arithmetic took over. As her balance fell below her original 30 cents, she set the goal of breaking even so she could walk away. Ultimately, this attempt failed within minutes and she was left penniless (pun intended). Interestingly, she asked me if she could take more money from her piggybank to try to make back her losses, but I decided it would be best to end the game and move on to the teachable moment. Here’s a summary of the lessons learned:

1. Probability. As requested by my wife, we discussed the probability of a correct guess on any one throw. After realizing that the odds were one-in-six, but her payout was only five cents, she concluded the game was rigged unfairly and that a fair payout would have been six cents. That lead to my next lesson.

2. Costs matter. The breakeven payout was six cents because she paid one cent for each throw. In effect, her winnings were reduced by the cost of each transaction. Therefore, to more than break even, the payout would need to have been seven cents.

3. Psychological biases. We discussed the emotions she experienced during the game and how they guided her decisions. As a proud dad, it was humbling to recognize that my own child is susceptible to common human biases.

Recency bias. After each winning throw, and especially after consecutive winning throws, she felt confident that a trend was developing. Similarly, after a long streak of losing throws, she began to feel despair that her luck had run out.

Sunk cost bias. Once her balance dropped below the amount she started at, and her losses continued to mount, she doubled down on the possibility of returning to her original balance. This also demonstrates loss aversion.

Confirmation bias. Her siblings and I were very supportive of her successes and I praised her “skill” in accurately guessing how the die would land. When she correctly guessed three times in a row, she saw this as confirmation that she was indeed very skilled at guessing.

4. Skill vs. luck. I felt it was important to emphasize that, despite my praise for her die-rolling abilities, her instances of success were the result of dumb, random luck. Skills can be taught, learned and refined through practice. But if a strategy is solely dependent on chance, the player has surrendered any control over the outcome. I’ll need to revisit this theme when she’s old enough to invest.

5. Street smarts. The object lesson here is that, when a person or advertisement invites you to be part of an easy, fun, get-rich-quick scheme, you should be suspicious. In fairness to her, she obviously trusted me more than she would trust a stranger. Rest assured, I made it very clear that I needed to assume the role of a trickster to teach the lesson and, once our debrief was complete, I returned all of her money to the piggybank.

Clearly, some parental discretion is necessary for this to be a productive exercise. Before playing the game, I think a parent should consider whether the child is mature enough to understand the lessons it’s intended to teach. Also, if there’s any possibility that the child will mistake your feigned deception for a real breach of trust, it may be best to modify or avoid the game. In the case of my daughter, I believe that the principles she learned far outweighed her unpleasant experience of losing it all at the kitchen table “casino.”

Isaac Cathey is a public sector employee and professional pilot. The bulk of his financial knowledge comes from books by the likes of John Bogle and JL Collins. He spends his free time running, swimming, hiking, camping, biking with his children and doing DIY projects. His previous articles were Ode to a CivicDebtors’ Prison and Crash Test.

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Break Even
Break Even
1 year ago

While a statistically breakeven payout would have been six cents, she paid one cent for each throw, so her winnings were reduced by the cost of each transaction. Therefore, to break even, the payout would need to have been seven cents.

This reasoning is not correct. The correct “break even” payout is in fact six cents. If you’re willing to pay her seven cents for a winning throw, she should continue to play until she wins all your money.

Langston Holland
Langston Holland
1 year ago

Nothing to add other than my way of thinking. Usually the hardest thing for me is to understand the question. 🙂

1¢ Outflow for wrong guess, 5¢ inflow for correct guess:
5/6 x -1¢ = -0.83⅓¢ probable value per roll.
1/6 x 5¢ = 0.83⅓¢ probable value per roll.
Expected result: break even.

1¢ Outflow per roll regardless of guess, 5¢ inflow for correct guess:
6/6 x -1¢ = -1¢ probable value per roll.
1/6 x 5¢ = 0.83⅓¢ probable value per roll.
Expected result: About -0.17¢ probable value per roll. Example: after 30 rolls, the gambler is down 5¢.

1¢ Outflow per roll regardless of guess, 6¢ inflow for correct guess:
6/6 x -1¢ = -1¢ probable value per roll.
1/6 x 6¢ = 1¢ probable value per roll.
Expected result: break even.

Notes: Obviously we’re all assuming random rolls and enough of them to keep the math honest. Apparently it’s not that easy to find truly balanced dice. In school they told me that you needed at least 30 random trials (Central Limit Theorem) before probability distributions started to behave.

The Wikipedia article on lottery mathematics says that in a “typical 6/49 game”, there is about 1 in 14 million chances of winning. Like a die with 14 million sides… How can that be enjoyable?

Edit: I just looked at FL’s regressive state tax (the lottery) and it costs $2 per play and you have to guess (6) numbers out of (53), not (49). Excel’s combination function =COMBIN(53,6) says that’s 22,957,480. Like a die with about 23 million sides, although each losing roll improves your odds by 1.

$2 Outflow per play regardless of guess, $6.5 million inflow for correct guess:
22,957,480/22,957,480 x -$2 = -$2 probable value per play.
1/22,957,480 x $6,500,000 = 28¢ probable value per play.
Expected result: no retirement savings.

1 year ago

wise father

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