Comment by pclmulqdq

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)

Gain of $150+$375=$575.

Round 3: 25x$36 ($900) -> half $54 and half $21.60 ($945 total) And so on.

Each round, the collective wealth goes up 5%, no matter how many rounds you run.