# Page 227 of The Undoing Project

Sorry but I am back with another question from Michael Lewis' The Undoing Project. The "Paul Samuelson bet" is cited as an example of of irrational thinking (because the expected value is the same in the two choices). The issue is that most people decline a single bet with a 50:50 chance of success and \$150 payout when you win and loss of \$100 if you lose but most of these same people agree to 100 bets. This seems rational to me. People are risk averse and in the first instance you have a 50% chance of losing money. In the second instance you have a very small chance of losing money (2.5%?). The book acknowledges that the more times you play the less likely you are to lose but implies that this should be weighed against the fact that the more times you play the greater the total sum of money you stood to lose. But the chance of losing any at all is only 2.5% and the chance of losing a lot is even lower. No?

• The original Samuelson paper: Risk and Uncertainty: A Fallacy of Large Numbers, available at casact.org/pubs/forum/94sforum/94sf049.pdf Feb 23, 2017 at 16:42
• Also mentioned at faculty.chicagobooth.edu/richard.thaler/research/pdf/… Feb 23, 2017 at 16:42
• Read this quote carefully: "The theorem states that if an individual is unwilling to take a single play of a bet at any wealth level that could obtain over a series of such bets (here current wealth minus $10,000 to plus$20,000) then she should not accept multiple plays of the same bet." Feb 23, 2017 at 16:44
• Thanks. The Thayer article makes the helpful distinction between risk aversion and loss aversion. It still seems rational to me (no matter your wealth and how it might fluctuate each day) that if you have reasons to be loss averse that you would rationally take the 100 bets but not the single bet. Say one who has a high utility for "winning" and aversion to the feeling of losing a bet or you needed the \$100 that day for a reason. In venture capital we always prefer among choices with the same expected value one based on a myriad of future outcomes versus one binary outcome. Feb 23, 2017 at 18:20