Roll a die until n consecutive rolls have the same value

Let n be a positive integer. We plan to roll a fair 6-sided die until n consecutive rolls have the same value. My task is to write a MATLAB function that approximates the expected value EV. The routine will preform NTrials trials where a trial consists of rolling the 6-sided die until n consecutive rolls have the same value, and will then calculate EV by averaging the number of rolls over all of the trials. The program I have written so far works, however I do not know how to implement the 'n consecutive rolls' into my program.

Here is what I have so far.

function EV = ex1(n,NTrials)
%
%
rng('shuffle')
TotalNRolls = 0;

for trial = 1:NTrials
    die = randi(6);
    lastroll = randi(6);
    TotalNRolls = TotalNRolls + 2;
    while die ~= lastroll
        die = lastroll;
        lastroll = randi(6);
        TotalNRolls = TotalNRolls + 1;
        end
end
EV = TotalNRolls/NTrials;

[Adam Danz]

" I do not know how to implement the 'n consecutive rolls' into my program. "

I would use a while loop that ends when roll n-1 matches roll n. That could be set up in many ways. Here's one way.

isMatch = false;
previousRoll = nan;
counter = 0; 
while ~isMatch
    counter = counter+1; 
    roll = randi(6); 
    if roll==previousRoll
        isMatch = true;
        continue
    else
        previousRoll = roll;
    end
end

or maybe you want to store each round within a vector which would be simple to implement.

Answer 1

[James Tursa]

You made a good start, but it might help to change your inner while loop exit condition to be exactly what you are looking for ... the number of consecutive values being some number n. I.e.,

for trial = 1:NTrials
    lastroll = randi(6);  % just roll one die to begin
    TotalNRolls = TotalNRolls + 1;
    number_of_consecutive_values = 1; % just one die roll in the current streak
    while( number_of_consecutive_values < n ) % keep rolling until you get n consecutive values
        die = randi(6); % roll the new value
        TotalNRolls = TotalNRolls + 1;
        if( die == lastroll ) % we matched the value in the current streak
            % do something <-- see if you can figure out what goes here
        else % we did not match the value in the current streak
            % do something else <-- see if you can figure out what goes here
        end
    end
end
EV = TotalNRolls/NTrials;

See if you can write code for the two places indicated. If die == lastroll you got a successful roll, so what would you want to happen with your number_of_consecutive_values counter? And if die ~= lastroll (the "else" part) you did not get a successful roll, so what would you want to happen with your number_of_consecutive_values counter and lastroll value in that case? Give this a try and come back if you still have problems.

[Sophie Culhane]

In the if statement I added:

if die == lastroll

ConsecutiveValues = n;

else

ConsecutiveValues = 0;

end

Would this work for my program? The expected value, EV, seems too large to be correct.

[James Tursa]

No, this is not correct. Let's talk about the first part:

if die == lastroll
    ConsecutiveValues = n;

If die == lastroll, that means that the current roll matched the last roll. If ConsecutiveValues happened to be 5 at the moment, that means that the current streak is 5 and gets extended by one more roll, right? So you just need to add 1 to ConsecutiveValues and then do another roll. I.e.,

if die == lastroll
    ConsecutiveValues = ConsecutiveValues + 1;

Then for the "else" part when die ~= lastroll, you need to ask yourself what needs to happen. In this case you broke the current streak before it reached n and had to start a new streak, right? So you need to restart the streak from scratch. That means setting the values of ConsecutiveValues and lastroll to initial values. See if you can figure out what those should be. You are starting the new streak with just one die roll in this case.

[Sophie Culhane]

Thank you for the help, I figured it out.