clear; clf;

nbmax = 5;
resultat = zeros(6^nbmax, nbmax); // initialisation
 
for i = 1:nbmax // colonne
    serie = 6^(nbmax - i);
    nbseries = 6^(i - 1);
    for j = 1:nbseries
        init = 6*serie*(j - 1) + 1;
        for k = 1:6
            i0 = init + (k - 1)*serie;
            resultat(i0:i0 + serie - 1, i) = k;
        end
    end
end
 
// sélection du meilleur dé
meilleur = zeros(resultat);
for i = 1:nbmax
    meilleur(:, i) = max(resultat(:, 1:i), "c");
end

// frequences

freq1d = tabul(meilleur(:, 1), "i");
freq2d = tabul(meilleur(:, 2), "i");
freq3d = tabul(meilleur(:, 3), "i");
freq4d = tabul(meilleur(:, 4), "i");
freq5d = tabul(meilleur(:, 5), "i");

// normalisation
freq1d(:, 2) = 100*freq1d(:, 2)/sum(freq1d(:, 2));
freq2d(:, 2) = 100*freq2d(:, 2)/sum(freq2d(:, 2));
freq3d(:, 2) = 100*freq3d(:, 2)/sum(freq3d(:, 2));
freq4d(:, 2) = 100*freq4d(:, 2)/sum(freq4d(:, 2));
freq5d(:, 2) = 100*freq5d(:, 2)/sum(freq5d(:, 2));

cumul1d = freq1d();
cumul1d(:, 2) = cumsum(freq1d(:, 2));

cumul2d = freq2d();
cumul2d(:, 2) = cumsum(freq2d(:, 2));

cumul3d = freq3d();
cumul3d(:, 2) = cumsum(freq3d(:, 2));

cumul4d = freq4d();
cumul4d(:, 2) = cumsum(freq4d(:, 2));

cumul5d = freq5d();
cumul5d(:, 2) = cumsum(freq5d(:, 2));


// Tracé

subplot(2, 1, 1)
plot2d(freq1d(:, 1), freq1d(:, 2), style = 1)
plot2d(freq2d(:, 1), freq2d(:, 2), style = 2)
plot2d(freq3d(:, 1), freq3d(:, 2), style = 3)
plot2d(freq4d(:, 1), freq4d(:, 2), style = 4)
plot2d(freq5d(:, 1), freq5d(:, 2), style = 5)
legend(["1d6" ; "2d6" ; "3d6" ; "4d6" ; "5d6"], "in_upper_left");
xtitle("Fréquence (probabilité d''obtenir une valeur)", "résultat",...
    "probabilité (%)")

subplot(2, 1, 2)
plot2d(cumul1d(:, 1), cumul1d(:, 2), style = 1)
plot2d(cumul2d(:, 1), cumul2d(:, 2), style = 2)
plot2d(cumul3d(:, 1), cumul3d(:, 2), style = 3)
plot2d(cumul4d(:, 1), cumul4d(:, 2), style = 4)
plot2d(cumul5d(:, 1), cumul5d(:, 2), style = 5)
 legend(["1d6" ; "2d6" ; "3d6" ; "4d6" ; "5d6"], "in_upper_left");
xtitle("Fréquence cumulées (probabilité de faire moins qu''une valeur)",...
    "résultat", "probabilité (%)")