Earlier quoted context omitted.
Yeah, that's after 1 round. Both the individuals and the collective expect to gain if they only play 1 round. The interesting part is that they expect to lose money over time even though they expect to gain money if they only play once. But that holds for both the individuals and the collective. A less confusing game with the same mechanism is "flip a coin, if it's heads I give you 1000x your initial investment, if i…
The collective also gains in round 2, and each subsequent round. From the intuition that you have about the first round, treat each group with the same amount of money separately, and you will see that money grows in every round. Example: Round 1: 100x$100 (total $10000) -> 50x$60 + 50x$150 (total $10500) Gain of $500 total Round 2: 50x$60 ($3000) -> 25x$90 + 25x$36 ($3150) 50x$150 ($7500) -> 25x$225 + 25x$90 ($7875)…
Think of it this way: If everyone's individual wealth approaches zero, why would the total go up?
Just run the following simulation in a python REPL:
import random
POPULATION = 100
INITIAL_MONEY = 1000
ROUNDS = 10000
wallets = [INITIAL_MONEY for _ in range(POPULATION)]
for iteration in range(ROUNDS):
for person in range(POPULATION):
if random.random() > 0.5:
wallets[person] = wallets[person] * 1.5
else:
wallets[person] = wallets[person] * 0.6
print(f"{sum(wallets)=}")