Since the conference is in Las Vegas, I’ve been thinking a lot about games of chance: blackjack, craps, roulette, and the like. You can analyze these games by computing the odds of certain events in a probability model. Or you can be lazy, like me, and let the computer do the work by running a simulation to compute the odds of certain outcomes.

Random samples are the basis of every simulation. If you do not sample efficiently, then your simulation is doomed to take a long time. In SAS/IML software, you can generate random samples by using the RANDGEN subroutine. Novice programmers often use RANDGEN inefficiently and generate one random observation at a time within a loop. Don’t do it!

To generate, say, 1000 random samples from a uniform distribution on [0, 1], simply allocate a vector of length 1000 and call RANDGEN:

proc iml;
u = j(1000, 1);             /** allocate 1000 x 1 vector **/
call randgen(u, "Uniform"); /** random sample from uniform distribution **/

If you want to simulate 1000 dice rolls, transform the uniform variates into the range {1, 2, 3, 4, 5, 6}:

rolls = ceil(6*u);          /** 1 through 6 **/

If you are interested in simulating outcomes from a single-zero roulette wheel, transform the uniform variates into the range {0, 1, 2, …, 36}:

roulette = floor(37*u);     /** 0 through 36 **/

Incidentally, Caesars Palace has one single-zero roulette wheel on the main casino floor. The single-zero wheels lessen the house advantage as compared with the more ubiquitous double-zero wheels, but you won’t see me playing either version of roulette. I agree with Einstein who supposedly said, “You cannot beat a roulette table unless you steal money from it.” However, by using the RANDGEN subroutine, I can quickly simulate my losses for any betting scheme that I might be tempted to employ.