How to simulate a loaded dice in Igor Pro?

how about

Function return_prob(Probability)
    Variable Probability
    Return (enoise(0.5)+0.5)<Probability
End

A roll of the die is floor(enoise(3) + 4), so for p(6) > 1/6, try this:

function RollTheDie(p6)
	variable p6
	return floor(min(6, enoise(3) + 3 + 6*p6))
end

for p(6) = 1/4, as per your example:

In your example, IVP, the probabilities of the loaded dice do not add up to 100%. Is that intentional? If the probability of rolling a 6 is 3/2*1/6 I would expect the probability of rolling a 1 to be 1/2*1/6. This is assuming that the only effect of the loaded dice is to convert a given fraction of 1s into 6s.

To make that clear, I would write the code like this:

Function RollLoadedDice(LoadEfficiency)
//	Rolls a loaded six-sided dice, where a roll of 1 is converted to a roll of 6 with a probability of LoadEfficiency
Variable LoadEfficiency

	//	Generates a random value between 0 and 6
	Variable Roll=enoise(3)+3

	//	Converts a roll of 1 to a 6 with a probability of LoadEfficiency
	if (Roll<LoadEfficiency)
		Roll=6
		
	//	Rounds up the generated random number to the closest integer, producing rolls of 1, 2, 3, 4, 5 and 6
	else
		Roll=Ceil(Roll)
	endif

	//	Returns the rolled value
	Return Roll
end
​

or do you need something more general where you have a list of events, each with different probabilities?

event 1      0.10
event 2      0.20
event 3      0.20
event 4      0.40
event 5      0.90
etc...

This is how I would handle the more generalized case. I haven't tested the histogram. You'll want to make sure to do that before you use the code.

Function RandomEventTest()

	//	Creates a not-normalised probability wave with 7 events, each with a given probability
	Make/O root:MyProbabilityWave={0.01, 0.05, 0.05, 0.20, 0.30, 0.90, 0.90}
	Wave MyProbabilityWave=root:MyProbabilityWave

	//	Creates a list of random events based on the probabilities in MyProbabilityWave
	Make/O/N=100 root:ListOfRandomEvents=RandomEventGenerator(MyProbabilityWave)
	Wave ListOfRandomEvents=root:ListOfRandomEvents
	
	//	Displays the probability wave and the list of random events
	Edit MyProbabilityWave, ListOfRandomEvents
end




Function RandomEventGenerator(ProbabilityWave)
//	Selects a random event, based on a list of probabilities for each event
Wave ProbabilityWave

	//	Calculates the sum off all probabilities in the wave. For a normalised wave this should be 1. This step is included just in case it is not
	Variable SumOfAllProbabilities=sum(ProbabilityWave)
	
	//	Generates the random number used to select an event
	Variable RandomNumber=enoise(SumOfAllProbabilities/2)+SumOfAllProbabilities/2
	
	//	Integrates the values in the probability wave. This is needed to select an event with the random number
	Duplicate/O/FREE ProbabilityWave IntegratedProbabilityWave
	Integrate ProbabilityWave /D=IntegratedProbabilityWave

	//	Counts through the events one at a time and selects the event where the combined probability have passed the random number
	Variable NumberOfEvents=NumPnts(IntegratedProbabilityWave)
	Variable Event=0
	for (Event=0; (RandomNumber>IntegratedProbabilityWave[Event]) && (Event<NumberOfEvents); Event+=1)
	endfor
	
	//	Returns the selected event
	Return Event
end

Hi Olelytken,

It was unintentional... I picked that example from the internet... Probabilities should add up to 1.

Thanks