Rolling a Fair 6-Sided Die Until Two Consecutive Rolls Have the Same Value

Question

Sophie Culhane 2020-10-2

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https://ww2.mathworks.cn/matlabcentral/answers/603835-rolling-a-fair-6-sided-die-until-two-consecutive-rolls-have-the-same-value

评论： Sophie Culhane 2020-10-5

My task is to simulate rolling a fair 6-sided die until two consecutive rolls have the same value and write a function that approximates the expected value EV. I believe I have most of the program figured out until I reach 'same number' in which I get lost. Please help me find out what to put in place of 'same number' to get my program to work. Here is my block of code:

function EV = hw20(NTrials)
%
%
rng('shuffle)
TotalNRolls = 0;
for Trial = 1:NTrials
    die = randi(6);
    TotalNRolls = TotalNRolls + 1;
     
    while die == 'same number'
            TotalNRolls = TotalNRolls + 1;
    end
end
EV = TotalNRolls/NTrials;

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Answer 1

Ameer Hamza 2020-10-2

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编辑：Ameer Hamza 2020-10-2

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Try this code

function EV = hw20(NTrials)
%
%
rng('shuffle')
TotalNRolls = 1;
last_die = inf; % any number other then 1 to 6
while true
    die = randi(6);
    
    if die == last_die || TotalNRolls==NTrials
        break;
    else
        last_die = die;
    end
    TotalNRolls = TotalNRolls + 1;
end
EV = TotalNRolls/NTrials;
end

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Ameer Hamza 2020-10-2

Thanks, Steven. Your approach also makes sense for this problem. It is just my guess that NTrials is the maximum number of trials.

Sophie Culhane 2020-10-5

We have not yet learned 'break' therefore I cannot use that in my program. Thank you for the responses so far.

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Answer 2

Alan Stevens 2020-10-2

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I think the above will produce a probability, rather than an expected value. Try

NTrials = 1000;
N = zeros(NTrials,1);
for Trial = 1:NTrials
    
    TotalNRolls = 1;
    die = randi(6);
    keepgoing = true;
    while keepgoing == true
        oldie = die;
        die = randi(6);
        if die == oldie
            keepgoing = false;
        end
        TotalNRolls = TotalNRolls + 1;
    end
    N(Trial) = TotalNRolls;
      
       
end
EV = sum(N)/NTrials;