File:2d6 choisis parmi n.png

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Summary

[edit]

Probabilité en sommant deux dés à six faces choisis parmi n :

  • somme des deux plus mauvais dés parmi trois ou quatre dés ;
  • somme des deux meilleurs dés parmi trois ou quatre dés ;
  • somme de deux dés simplement.

Image du haut : probabilité d'obtenir un score. Image du bas : probabilité d'atteindre ou de dépasser un seuil.

Probability summing two six-sided dice chosen amongst n:

  • sum of the two worst dice amongst three or four dice;
  • sum of the two best dice amongst three or four dice;
  • sum of two dice, simply.

Top picture: probability to have a value. Bottom picture: probability to reach or make better than a threshold.

Statistiques des jets
Dice probability
Jet
Type of throwing		 Valeur la plus probable
most probable value		 Moyenne
Mean
2 pires parmi 4
2 worst amongst 4		 4 4,65
2 pires parmi 3
2 worst amongst 3		 5 5,54
2d6 7 7
2 meilleurs parmi 3
2 best amongst 3		 9 8,46
2 meilleurs parmi 4
2 best amongst 4		 10 9,34

Mécanisme du jeu de rôle/mechanism of the roleplaying game P'tites sorcières archive copy at the Wayback Machine

Auteur/author : Christophe Dang Ngoc Chan (cdang)

Scilab source

Scilab source
Scilab source
 This media was created with Scilab, a free open-source software.

Here is a listing of the Scilab source used to create this file. 

clear;
clf;

// Initialisations
meilleurs4d = zeros(12,1);
meilleurs3d = zeros(12,1);
pires4d = zeros(12,1);
pires3d = zeros(12,1);
deuxd = zeros(12,1);
d = zeros(4);

// Calculs de dénombrement
for i=1:6
   d(1)=i;
   for j=1:6
      d(2)=j;
// deux dés
      somme = sum(d(1:2));
      deuxd(somme) = deuxd(somme) + 1;
      for k=1:6
         d(3)=k;
// trois dés
         d_trie3 = gsort(d(1:3)) ;
         somme_meilleurs = sum(d_trie3(1:2));
         somme_pires = sum(d_trie3(2:3));
         meilleurs3d(somme_meilleurs) = meilleurs3d(somme_meilleurs) + 1;
         pires3d(somme_pires) = pires3d(somme_pires) + 1;
         for l=1:6
            d(4)=l;
// quatre dés
            d_trie4 = gsort(d) ;
            somme_meilleurs = sum(d_trie4(1:2));
            somme_pires = sum(d_trie4(3:4));
            meilleurs4d(somme_meilleurs) = meilleurs4d(somme_meilleurs) + 1;
            pires4d(somme_pires) = pires4d(somme_pires) + 1;
         end
      end
   end
end

// pourcentage

meilleurs4d = 1/sum(meilleurs4d)*meilleurs4d*100;
meilleurs3d = 1/sum(meilleurs3d)*meilleurs3d*100;
deuxd = 1/sum(deuxd)*deuxd*100;
pires3d = 1/sum(pires3d)*pires3d*100;
pires4d = 1/sum(pires4d)*pires4d*100;

// cumul (dépasser un seuil)

cumul_meilleurs4d = 100-cumsum(meilleurs4d);
cumul_meilleurs3d = 100-cumsum(meilleurs3d);
cumul_deuxd = 100-cumsum(deuxd);
cumul_pires3d = 100-cumsum(pires3d);
cumul_pires4d = 100-cumsum(pires4d);

// tracé
 
subplot(2,1,1)
plot2d([1:12],[pires4d, pires3d, deuxd, meilleurs3d, meilleurs4d],...
   rect=[2,0,12,21], leg='2 pires parmi 4@2 pires parmi 3@2 dés@2 meillleurs parmi 3@2 meilleurs parmi 4')
xtitle(['Probabilité dobtenir un score' ; 'en sommant deux dés choisis parmi n'],'score','probabilité (%)')
xset('font size', 0.5)
 
subplot(2,1,2)
plot2d([2:12],[cumul_pires4d(1:$-1), cumul_pires3d(1:$-1), cumul_deuxd(1:$-1), cumul_meilleurs3d(1:$-1), cumul_meilleurs4d(1:$-1)],...
   rect=[2,0,12,100],leg='2 pires parmi 4@2 pires parmi 3@2 dés@2 meillleurs parmi 3@2 meilleurs parmi 4')
xtitle({'Probabilité datteindre un score' ; 'en sommant deux dés choisis parmi n'],'score','probabilité (%)')
xset('font size', 0.5)

Licensing

[edit]
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution share alike 		This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
This licensing tag was added to this file as part of the GFDL licensing update.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current08:33, 30 January 2006Thumbnail for version as of 08:33, 30 January 2006581 × 673 (9 KB)Cdang (talk | contribs)cumulated probability : reach or make better than a threshold
15:23, 27 January 2006Thumbnail for version as of 15:23, 27 January 2006610 × 461 (6 KB)Cdang (talk | contribs)Probabilité d'obtenir un score en sommant deux dés à six faces choisis parmi ''n'' : * somme des deux plus mauvais dés parmi trois ou quatre dés ; * somme des deux meilleurs dés parmi trois ou quatre dés ; * somme de deux dés simplement. ---- Pro

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