In conclusion, this paper evaluates the rationality of the lottery schemes and designs a better lottery scheme
with higher ‘‘charming index’’. On the basis of utility in mathematical economics, we adopt logarithm linear
function to describe the ‘‘charming index’’ of the present lottery schemes, which determines whether the rule
and award of a certain lottery is reasonable or not. The results show that the scheme of ‘‘choose 5 in the integers
from 01 to 60’’ (5/60) has the highest ‘‘charming index’’, and 7/37 is in the next place. Furthermore, we
design an optimum lottery scheme 10/31 with the highest ‘‘charming index’’ based on Genetic Arithmetic combining
Monte Carlo simulation.