Arithmetic Mean vs. Geometric Mean

Arithmetic Mean = the sum of 'X' values divided by 'X' = Average.
Geometric Mean = the 'X' root of the product of 'X' values.

Geometric Mean < Arithmetic Mean, except when equal average values.
if Geometric Mean < Arithmetic Mean, then any risk is unfavorable

if an investor trades then zero sum game loses payments in trade
if a gambler makes a fair wager then risk makes wager unfavorable

if you wager or invest then you chose the highest Geometric Mean
if a Gemetric Mean = 0 then you can go to zero and will in time