Generic simulation template

The purpose of simulation is to investigate the unknown values of parameters of interest. In the initial exercises you may want to simulate the events that you know how to compute probabilities of. The purpose of such exercises is to develop intuition about reliability of simulations.

In more advanced exercises you may want to estimate probabilities that aren't known. In such cases it is always a good idea to run simulations of various lengths and compare the results. In this section we briefly discuss how such a simulation can be organized in a way that promotes multiple uses of the same program.

The key is organizing the programs carefully into manageable blocks of small size. Modern BASIc is a structural programming language. The generic program to study the effects of the length of simulation on its output can be written as follows

' PROGRAM Generic.bas
'Generic Simulator
'Size is simulation size varied from Min=100 to Max=10000
For Size 100 to 10000 Step 100
Simulate(Size, Result)
Print "Simulation size="; Size ; "Output="; Result
Next Size
End

The actual simulation is performed by

SUB Simulate (SizeRequested, Result)
'Runs requested number of simulations and returns average
'Trial numbers consecutive simulations from 1 to SizeRequested
For Trial=1 to SizeRequested
SimulateOne(Score)
Result=Result+Score
Next Size
'Most simulations return averages of single trials
Result=Score/Size
End SUB

The actual modeling is performed in another SUB, which in the generic program we named SimulateOne. This SUB may be as simple as simulating a toss of a single coin

SUB SimulateONe(Outcome)
'simulate One occurrence, return numerical outcome
OutCome=0
if RND(1)<1/2 THEN Outcome=1
END SUB

Or it can be as complicated as we wish. The example below simulates a toss of five dice, and uses previously introduced function CountEq(a,b,c,d,e). four-of-a-kind.

SUB SimulateONe(Outcome)
'simulate One occurrence, return numerical outcome
d1=int(RND(1)*6+1)
d2=int(RND(1)*6+1)
d3=int(RND(1)*6+1)
d4=int(RND(1)*6+1)
d5=int(RND(1)*6+1)
IF CountEq(d1,d2,d3,d4,d5)=4 THEN Outcome=1
END SUB