With the stock market as it is just now, I have decided to add a lottery ticket to my portfolio.
I am following the thinking of Daniel Bernoulli, the 18th century Swiss polymath. In his thinking on probability he decided that we make decisions under uncertainty based on the likelihood of a desirable outcome. Desirability in this context has to do with the “utility” of the outcome.
Some details. Canada’s Lottery 6/49 tickets cost $3.00. The current jackpot tomorrow is $24,000,000 if I win and many subprizes if I don’t get all the numbers. There is about 1 chance in 6 of winning something so 60 cents of the $3.00 is my expected cost of winning at least a free ticket. Other prizes range up to a $million, so I am guessing that is worth another 30 cents. That leaves $2.10 to invest in the big prize. The odds of winning it are around 13 million to one so that’s worth paying $1.86 for. That leaves me 24 cents short, but I am still willing to make the purchase.
Based on expectations, it is a losing proposition and as everyone knows lottery tickets are a “tax on the stupid.’ The question is Bernoulli’s idea of utility. The utility of $24,000,000 is quite large. The utility of the $0.24 expected loss is quite small. So on balance I am ahead accepting the near certain loss.
Bernoulli is not the only one who might make this purchase.
Paulo Coelho de Souza the Brazilian novelist offers this thought:
“It’s the possibility of having a dream come true that makes life interesting.”
I think dreams are valuable and since this one costs an expected loss of just 24 cents, I choose ot buy it just to make life a little more interesting.
If you use this reasoning to buy a ticket when you ordinarily would not and you win, I expect a small commission.
Watch for the idea of utility when making decisions with incomplete information
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