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Linenn - Jeux et Mathematiques - <br /> <b>Deprecated</b>: Non-static method plxUtils::strCheck() should not be called statically in <b>/homepages/3/d170528928/htdocs/jm/bn/core/lib/class.plx.show.php</b> on line <b>127</b><br /> Un jeu de Pile ou Face - linenn


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Un jeu de Pile ou Face

Par
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jp, le
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mardi 22 décembre 2009 à
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21:43 |
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Probabilités | Page principale Jeux et Mathématiques

Variations du capital d'un joueur durant d'un jeu de Pile ou Face

Vous commencez avec un certain capital C (de C pièces d'or) et tous les jours vous le jouez en totalité, pièce après pièce, à pile ou face.
Chaque jour j+1, votre capital C(j+1) est donc compris entre 0 (vous avez perdu toutes les pièces) et 2× C(j) (toutes les pièces ont gagné).
0 ≤ C(j+1) ≤ C(j)
De plus on se fixe une limite de durée pour chaque partie. Évidemment on s'arrête aussi lorsqu'on est ruiné.

On peut se poser plusieurs questions. Quels sont par exemple, suivant le capital de départ et suivant le nombre de jours maximal que dure la partie :
  1. Quel a été le capital maximal en ma possession ?
  2. Suis-je ruiné en fin de partie ?
  3. Après combien de jours suis-je ruiné ?
  4. Quand ai-je intérêt à quitter la partie avec tout mon capital, (si on autorise cette possibilité) ?
  5. etc.
(Juste des simulations. Aucune solution mathématique ne sera donnée).

Capital initial C =
Durée du jeu d =
Que voulez-vous connaître ?
  • Une seule simulation
  • Les maximum atteints et les derniers gains après N = simulations






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