Start with a program that implements an easier task. Estimate the 
probability of throwing a six with a single dice. Make one million 
throws by putting a loop (1-1,000,000) in the program.

The first problem is how to simulate a random dice throw. Use the 
function rand() for this purpose. Remember that rand() generates
a number between 0 and 1. Multiply the result with 6 to get a number
between 0 and 6. Compute the integer value of that number (int()) to
get one of the numbers (0,1,2,3,4,5). rand() will never generate 1.0
so you can never get a 6 this way. Add 1 to the result to get one of
the numbers (1,2,3,4,5,6).

Test the result of this function. If it is equal to six then you
should increase a second variable (for example with the name 
$successes). After the loop has completed, you should divide this 
variable by a million. Print the result. It should be about 0.167.

When this version works properly then try to estimate the probability
that someone throws a six with one of a maximum of three throws.
Create a loop (1-3) which performs the dice throw three times. As 
soon as a six is thrown, the program should jump out of the loop. If
no six is thrown in three attempts, the program should also leave
the loop.

Like before, you add 1 to the $successes variable when a six is
thrown. After the main loop (1-1,000,000) is finished, divide 
$successes by a million and print the result. It should be about 
0.421.

Now you have a program which simulates playing Yathzee with one 
dice. The actual game is played with five dice. To simulate this, 
you need to put a loop (1-5) around the (1-3) loop. This loop 
should stop immediately when the (1-3) loop fails to produce a
six. Only when the loop (1-5) finishes without a throw different
from six, then the $successes variable should be increased.

After the main loop (1-1,000,000) is finished, divide $successes 
by a million and print the result. It should be about 0.0133.

This completes the exercise. You have written a program that
simulates the actions of a Yathzee player trying to achieve 
five sixes. The only difference in style between the program 
and a common Yathzee player is that the program throws only
one dice at a time rather than many of them. For the estimation
of the probability, this does not make a difference.