"But if you take Samuelson’s argument seriously, then Vanguard’s advice is… wrong?"
No, the key difference is that the results of the coin flips are independent of each other, while the performance of stocks show high degrees of temporal correlation. If there is a recession right before your retirement, it doesn't matter if you hold 100 different stocks (or an index fund) - it's going to severely derail your retirement plans.
That being said, I agree with the rest of the essay - you should take the bet for one coin flip if you would take it for 100 coin flips given the positive expected value, unless if $100 represents a huge fraction of your overall wealth such that the diminishing marginal returns to wealth result in negative expected utility for the bet.
"But if you take Samuelson’s argument seriously, then Vanguard’s advice is… wrong?"
No, the key difference is that the results of the coin flips are independent of each other, while the performance of stocks show high degrees of temporal correlation. If there is a recession right before your retirement, it doesn't matter if you hold 100 different stocks (or an index fund) - it's going to severely derail your retirement plans.
That being said, I agree with the rest of the essay - you should take the bet for one coin flip if you would take it for 100 coin flips given the positive expected value, unless if $100 represents a huge fraction of your overall wealth such that the diminishing marginal returns to wealth result in negative expected utility for the bet.