  In the spirit of "multi-culturalism", we use four kinds of computations:
simulation, numeric, symbolic, and "conceptual" to explore some "games of pure
chance" inspired by children board games like "Snakes and Ladders" (aka as
"Chutes and Ladders") and "gambler's ruin with unlimited credit". Even more
interesting than the many computer-generated actual results described in this
paper and its web-site extension, is our broad-minded, ecunemical approach, not
favoring, a priori, any one of the above four kinds of computation, but showing
that, a posteriori, symbolic computation is the most important one, since
(except for simulation, that is very inaccurate) numerics can be made more
efficient with the help of symbolics (in the "downward" direction), and, (in
the "upward" direction) the mere existence of certain symbolic-computational
algorithms imply interesting "qualitative" results, that certain numbers are
always rational, or always algebraic, and certain sequences are always
polynomial, or C-recursive, or algebraic, or holonomic. This article is
accompanied by four Maple packages, and numerous input and output files, that
readers can use as templates for their own investigations.
