Question

I did a search but didn’t really get any proper hits. Maybe I used incorrect terms?

What I want to ask about is an algorithm for simulating a biased role rather than a standard supposedly-random roll.

It wouldn’t be a problem if you can’t give me exact answers (maybe the explanation is lengthy?) but I would appreciate &pointers to material I can read about it.

What I have in mind is to for example, shift the bias towards the 5, 6 area so that the numbers rolls would have a higher chances of getting a 5 or a 6; that’s the sort of problem I’m trying to solve.

[Update]

Upon further thought and by inspecting some of the answers, I’ve realized that what I want to achieve is really the Roulette Wheel Selection operator that’s used in genetic algorithms since having a larger sector means increasing the odds the ball will land there. Am I correct with this line of thought?

Answer 1

In general, if your probabilities are {p1,p2, …,p6}, construct the following helper list:

{a1, a2, ... a5} = { p1, p1+p2, p1+p2+p3, p1+p2+p3+p4, p1+p2+p3+p4+p5}  

Now get a random number X in [0,1]

If

        X <= a1  choose 1 as outcome  
   a1 < X <= a2  choose 2 as outcome 
   a2 < X <= a3  choose 3 as outcome  
   a3 < X <= a4  choose 4 as outcome  
   a4 < X <= a5  choose 5 as outcome  
   a5 < X        choose 6 as outcome 

Or, more efficient pseudocode

   if     X > a5 then N=6
   elseif X > a4 then N=5
   elseif X > a3 then N=4
   elseif X > a2 then N=3
   elseif X > a1 then N=2
   else               N=1

Edit

This is equivalent to the roulette wheel selection you mention in your question update as shown in this picture: