  We review the simplex method and two interior-point methods (the affine
scaling and the primal-dual) for solving linear programming problems for
checking avoiding sure loss, and propose novel improvements. We exploit the
structure of these problems to reduce their size. We also present an extra
stopping criterion, and direct ways to calculate feasible starting points in
almost all cases. For benchmarking, we present algorithms for generating random
sets of desirable gambles that either avoid or do not avoid sure loss. We test
our improvements on these linear programming methods by measuring the
computational time on these generated sets. We assess the relative performance
of the three methods as a function of the number of desirable gambles and the
number of outcomes. Overall, the affine scaling and primal-dual methods benefit
from the improvements, and they both outperform the simplex method in most
scenarios. We conclude that the simplex method is not a good choice for
checking avoiding sure loss. If problems are small, then there is no tangible
difference in performance between all methods. For large problems, our improved
primal-dual method performs at least three times faster than any of the other
methods.
