The geometric expected value for the +100% or −60% gamble in the post is straightforward.
If you gain 100% and then lose 60% (or lose 60% and then gain 100%), overall you’ll end up down 20% from where you started since (1 + 100%) * (1 − 60%) = 2 * 0.4 = 80% = 1 − 20%. This loss is what’s expected over two iterations, so the loss over one iteration is sqrt(80%) = 89.44% = 1 − 10.56%, so the expected loss is that 10.56% of your starting capital per flip.
The geometric expected value for the +100% or −60% gamble in the post is straightforward.
If you gain 100% and then lose 60% (or lose 60% and then gain 100%), overall you’ll end up down 20% from where you started since (1 + 100%) * (1 − 60%) = 2 * 0.4 = 80% = 1 − 20%. This loss is what’s expected over two iterations, so the loss over one iteration is sqrt(80%) = 89.44% = 1 − 10.56%, so the expected loss is that 10.56% of your starting capital per flip.