This is assuming additive growth, not multiplicative growth. The expectation is relevant when you have additive growth, but multiplicative growth is the relevan

This is assuming additive growth, not multiplicative growth. The expectation is relevant when you have additive growth, but multiplicative growth is the relevant model here because you are increasing by 50% of your wealth vs. decreasing by 40% of your wealth (not adding fixed amounts, e.g., +$0.50 vs. -$0.40). Multiplicative growth also returns 0.95 per unit time, whereas the (irrelevant) expectation value is 1.05 (hence the violation of most people's intuition). Here is some R code demonstrating it: set.seed(123) # simulating multiplicative growth n <- 1e4 init_wealth <- 1 x <- sample(c(0.6, 1.5), n, replace=TRUE) init_wealth * prod(x) # analytic model n1 <- length(x[x==0.6])/n n2 <- length(x[x==1.5])/n rate <- (0.6^n1) * (1.5^n2) init_wealth * (rate^n) (Edit: formatting, and wording for clarity)