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17/12/2012 8:50 pm
En quelle langue faut il que je te parle ?
Si tu prenais le temps de comprendre, on n'aurait pas tous ces quiproquo ou ces contresens !.
Je viens de relire
Ce que tu écris est incompréhensible..
Je dis qu'il faut une base de comparaison !
Si tu donnes un résultat seul, cela ne veut strictement rien dire.
Une base de comparaison ?
Tu veux comparer la roulette française avec la pièce?
Je l'ai déjà fait et cela ne pose absolument aucun problème.
Pour une française :
Il y a 43.81% de cycles gagnants pendant lesquels on gagne en moyenne 1.62686211 mise
Il y a 45.97% de cycles perdants pendant lesquels on perd en moyenne -1.89713238 mise
Bilan: l'espérance de gain est bien -1/74 par lancer.
Pour un jeu de pile ou face :
Il y a 41.19% de cycles gagnants pendant lesquels on gagne en moyenne 1.76197052 mise
Il y a 41.19% de cycles perdants pendant lesquels on perd en moyenne -1.76197052mise
Bilan: l'espérance de gain est bien 0
Où est le problème ? Il n'y a aucun problème !
18/12/2012 8:16 pm
Je dis qu'il faut une base de comparaison !
Si tu donnes un résultat seul, cela ne veut strictement rien dire.Une base de comparaison ?
Tu veux comparer la roulette française avec la pièce?
Tu le fais exprès ou quoi ? Qui te parle de la comparaison avec une pièce ?
Comparer la roulette française avec la roulette européenne via la loi multinomiale sur les trois probabilités suivantes ;
--> Prob[Zéro] = 1 / 37.
--> Prob[Rouge] = 18 / 37.
--> Prob[Noir] = 18 / 37.
c'est de cela dont je parle. J'ai l'impression que tu ne comprends pas le française, mon cher Glups.
La différence dans les deux calculs, seul le "bilan" des jetons change.
Dans les deux cas, tu vas trouver une probabilité des gains et tu es alors en mesure de dire laquelle des deux roulettes est la plus performante.
Mais donner une probabilité des gains sur la loi binomiale et ensuite donner une probabilité des gains sur la loi multinomiale et indiquer que la seconde est meilleure que la première n'a pas de sens. Il faut la même base de calcul.
C'est comme si tu disais que 3 kilomètres, c'est plus petit que 5 kilogrammes ! Ça y est, as-tu enfin compris ?
Encore une fois, je ne critique pas tes calculs, mais le sens que tu leur attributs ! C'est ce manque de rigueur qui m'énerve.
@+
18/12/2012 8:35 pm
Tu le fais exprès ou quoi ? Qui te parle de la comparaison avec une pièce ?
C'est toi qui a parlé de pièce.
On se trouve alors en présence de 3 jeux.
Tu parles de comparaison sans préciser ce que tu compares (voir plus bas).
Comparer la roulette française avec la roulette européenne via la loi multinomiale sur les trois probabilités suivantes ;
Je pouvais considérer que tu avais un problème entre la française et la pièce car tu disais qu'il était aberrant de trouver plus de cycles gagnants avec la française qu' avec la pièce. Reconnais que ce n'est pas clair !
Mais entre l' européenne et la française, il y a encore moins de problème de comparaison.
Mais donner une probabilité des gains sur la loi binomiale et ensuite donner une probabilité des gains sur la loi multinomiale et indiquer que la seconde est meilleure que la première n'a pas de sens. Il faut la même base de calcul.
Ok, ce qui te gêne cette fois, c'est qu'on n'utilise pas la même loi pour calculer les probabilités ? C'est ça ?
Mais donner une probabilité des gains sur la loi binomiale et ensuite donner une probabilité des gains sur la loi multinomiale et indiquer que la seconde est meilleure que la première n'a pas de sens. Il faut la même base de calcul.
On ne calcule pas la probabilité sur une loi.
C'est une loi qui permet de calculer la probabilité. Mais pour calculer la probabilité, il faut prendre la loi appropriée.
La roulette européenne a 2 retours, on utilise la loi binomiale.
La roulette française a 3 retours, on utilise la loi multinomiale.
Il faut prendre l'outil adapté sinon le résultat ne sera pas bon.
Et pour la roulette française, il n'y a pas 2 résultats.
19/12/2012 2:53 am
On ne calcule pas la probabilité sur une loi.
C'est une loi qui permet de calculer la probabilité. Mais pour calculer la probabilité, il faut prendre la loi appropriée.
Qu'est-ce que c'est que ce charabia que tu nous racontes ?
La roulette européenne a 2 retours, on utilise la loi binomiale.
La roulette française a 3 retours, on utilise la loi multinomiale.
Il faut prendre l'outil adapté sinon tes résultats ne seront pas bons.
Le problème, ce n'est pas le nombre de retours comme tu sembles l'indiquer.
Le problème, ce sont les probabilités.
Pour la roulette française et la roulette européenne, il y a trois probabilité :
--> Prob[Zéro] = 1 / 37.
--> Prob[Rouge] = 18 / 37.
--> Prob[Noir] = 18 / 37.
Donc on peut utiliser la loi multinomiale. As-tu compris ?
Et ainsi on peut comparer la roulette européenne avec la roulette française !
On peut aussi simplifier la roulette européenne, en ne prenant que deux probabilités :
--> Prob[Rouge] = 18 / 37.
--> Prob[Noir] = 19 / 37.
à la condition de miser sur Rouge, bien sûr.
Et tu peux comparer avec le jeu de Pile ou Face (je suppose que c'est ce que tu appelle Pièce) :
--> Prob[Rouge] = 1 / 2.
--> Prob[Noir] = 1 / 2.
Et ici, tu utilises la loi binomiale. As-tu compris ?
Mais tu ne peux pas comparer la loi binomiale sur le jeu de Pile ou Face avec la loi multinomiale avec la roulette française.
Pourquoi ? Car ce n'est pas la même loi, et ce ne sont pas les mêmes probabilités.
Donc si tu veux comparer le jeu de Pile ou face avec la roulette française, tu dois prendre les mêmes probabilités :
--> Prob[Zéro] = 1 / 37.
--> Prob[Rouge] = 18 / 37.
--> Prob[Noir] = 18 / 37.
et faire en sorte, que le bilan soit adapter à ces deux jeux.
Par exemple, au jeu de pile ou face, si le zéro sort, le bilan est zéro !
C'est bon maintenant !
Et voici le calcul, avec la loi multinomiale, selon le jeu de Pile ou face.
Triplets | Combinaisons | Probabilités | Bilan | Espérances Mathématiques | ============== | ============ | ================================================== | ===== | =================================================== | ( 0 ; 0 ; 20) | 1 | 0.000000551335072831166730000000000000000000000000 | -20.0 | -0.000000551335072831166730000000000000000000000000 | ( 0 ; 1 ; 19) | 20 | 0.000011026701456623334000000000000000000000000000 | -18.0 | -0.000009924031310961000900000000000000000000000000 | ( 0 ; 2 ; 18) | 190 | 0.000104753663837921680000000000000000000000000000 | -16.0 | -0.000083802931070337347000000000000000000000000000 | ( 0 ; 3 ; 17) | 1140 | 0.000628521983027530090000000000000000000000000000 | -14.0 | -0.000439965388119271050000000000000000000000000000 | ( 0 ; 4 ; 16) | 4845 | 0.002671218427867002600000000000000000000000000000 | -12.0 | -0.001602731056720201500000000000000000000000000000 | ( 0 ; 5 ; 15) | 15504 | 0.008547898969174409100000000000000000000000000000 | -10.0 | -0.004273949484587204500000000000000000000000000000 | ( 0 ; 6 ; 14) | 38760 | 0.021369747422936021000000000000000000000000000000 | -8.0 | -0.008547898969174409100000000000000000000000000000 | ( 0 ; 7 ; 13) | 77520 | 0.042739494845872042000000000000000000000000000000 | -6.0 | -0.012821848453761612000000000000000000000000000000 | ( 0 ; 8 ; 12) | 125970 | 0.069451679124542073000000000000000000000000000000 | -4.0 | -0.013890335824908414000000000000000000000000000000 | ( 0 ; 9 ; 11) | 167960 | 0.092602238832722755000000000000000000000000000000 | -2.0 | -0.009260223883272276200000000000000000000000000000 | ( 0 ; 10 ; 10) | 184756 | 0.101862462715995030000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 0 ; 11 ; 9) | 167960 | 0.092602238832722755000000000000000000000000000000 | +2.0 | +0.009260223883272276200000000000000000000000000000 | ( 0 ; 12 ; 8) | 125970 | 0.069451679124542073000000000000000000000000000000 | +4.0 | +0.013890335824908414000000000000000000000000000000 | ( 0 ; 13 ; 7) | 77520 | 0.042739494845872042000000000000000000000000000000 | +6.0 | +0.012821848453761612000000000000000000000000000000 | ( 0 ; 14 ; 6) | 38760 | 0.021369747422936021000000000000000000000000000000 | +8.0 | +0.008547898969174409100000000000000000000000000000 | ( 0 ; 15 ; 5) | 15504 | 0.008547898969174409100000000000000000000000000000 | +10.0 | +0.004273949484587204500000000000000000000000000000 | ( 0 ; 16 ; 4) | 4845 | 0.002671218427867002600000000000000000000000000000 | +12.0 | +0.001602731056720201500000000000000000000000000000 | ( 0 ; 17 ; 3) | 1140 | 0.000628521983027530090000000000000000000000000000 | +14.0 | +0.000439965388119271050000000000000000000000000000 | ( 0 ; 18 ; 2) | 190 | 0.000104753663837921680000000000000000000000000000 | +16.0 | +0.000083802931070337347000000000000000000000000000 | ( 0 ; 19 ; 1) | 20 | 0.000011026701456623334000000000000000000000000000 | +18.0 | +0.000009924031310961000900000000000000000000000000 | ( 0 ; 20 ; 0) | 1 | 0.000000551335072831166730000000000000000000000000 | +20.0 | +0.000000551335072831166730000000000000000000000000 | ( 1 ; 0 ; 19) | 20 | 0.000000612594525367962980000000000000000000000000 | -19.0 | -0.000000581964799099564800000000000000000000000000 | ( 1 ; 1 ; 18) | 380 | 0.000011639295981991295000000000000000000000000000 | -17.0 | -0.000009893401584692600000000000000000000000000000 | ( 1 ; 2 ; 17) | 3420 | 0.000104753663837921660000000000000000000000000000 | -15.0 | -0.000078565247878441247000000000000000000000000000 | ( 1 ; 3 ; 16) | 19380 | 0.000593604095081556200000000000000000000000000000 | -13.0 | -0.000385842661803011550000000000000000000000000000 | ( 1 ; 4 ; 15) | 77520 | 0.002374416380326224800000000000000000000000000000 | -11.0 | -0.001305929009179423700000000000000000000000000000 | ( 1 ; 5 ; 14) | 232560 | 0.007123249140978673900000000000000000000000000000 | -9.0 | -0.003205462113440403400000000000000000000000000000 | ( 1 ; 6 ; 13) | 542640 | 0.016620914662283572000000000000000000000000000000 | -7.0 | -0.005817320131799250300000000000000000000000000000 | ( 1 ; 7 ; 12) | 1007760 | 0.030867412944240915000000000000000000000000000000 | -5.0 | -0.007716853236060228700000000000000000000000000000 | ( 1 ; 8 ; 11) | 1511640 | 0.046301119416361385000000000000000000000000000000 | -3.0 | -0.006945167912454208000000000000000000000000000000 | ( 1 ; 9 ; 10) | 1847560 | 0.056590257064441686000000000000000000000000000000 | -1.0 | -0.002829512853222084300000000000000000000000000000 | ( 1 ; 10 ; 9) | 1847560 | 0.056590257064441686000000000000000000000000000000 | +1.0 | +0.002829512853222084300000000000000000000000000000 | ( 1 ; 11 ; 8) | 1511640 | 0.046301119416361385000000000000000000000000000000 | +3.0 | +0.006945167912454208000000000000000000000000000000 | ( 1 ; 12 ; 7) | 1007760 | 0.030867412944240918000000000000000000000000000000 | +5.0 | +0.007716853236060229600000000000000000000000000000 | ( 1 ; 13 ; 6) | 542640 | 0.016620914662283572000000000000000000000000000000 | +7.0 | +0.005817320131799250300000000000000000000000000000 | ( 1 ; 14 ; 5) | 232560 | 0.007123249140978673900000000000000000000000000000 | +9.0 | +0.003205462113440403400000000000000000000000000000 | ( 1 ; 15 ; 4) | 77520 | 0.002374416380326224800000000000000000000000000000 | +11.0 | +0.001305929009179423700000000000000000000000000000 | ( 1 ; 16 ; 3) | 19380 | 0.000593604095081556200000000000000000000000000000 | +13.0 | +0.000385842661803011550000000000000000000000000000 | ( 1 ; 17 ; 2) | 3420 | 0.000104753663837921660000000000000000000000000000 | +15.0 | +0.000078565247878441247000000000000000000000000000 | ( 1 ; 18 ; 1) | 380 | 0.000011639295981991296000000000000000000000000000 | +17.0 | +0.000009893401584692601700000000000000000000000000 | ( 1 ; 19 ; 0) | 20 | 0.000000612594525367962980000000000000000000000000 | +19.0 | +0.000000581964799099564800000000000000000000000000 | ( 2 ; 0 ; 18) | 190 | 0.000000323313777277536050000000000000000000000000 | -18.0 | -0.000000290982399549782450000000000000000000000000 | ( 2 ; 1 ; 17) | 3420 | 0.000005819647990995648200000000000000000000000000 | -16.0 | -0.000004655718392796518400000000000000000000000000 | ( 2 ; 2 ; 16) | 29070 | 0.000049467007923463012000000000000000000000000000 | -14.0 | -0.000034626905546424111000000000000000000000000000 | ( 2 ; 3 ; 15) | 155040 | 0.000263824042258469420000000000000000000000000000 | -12.0 | -0.000158294425355081650000000000000000000000000000 | ( 2 ; 4 ; 14) | 581400 | 0.000989340158469260290000000000000000000000000000 | -10.0 | -0.000494670079234630150000000000000000000000000000 | ( 2 ; 5 ; 13) | 1627920 | 0.002770152443713928600000000000000000000000000000 | -8.0 | -0.001108060977485571300000000000000000000000000000 | ( 2 ; 6 ; 12) | 3527160 | 0.006001996961380179400000000000000000000000000000 | -6.0 | -0.001800599088414053800000000000000000000000000000 | ( 2 ; 7 ; 11) | 6046560 | 0.010289137648080307000000000000000000000000000000 | -4.0 | -0.002057827529616061400000000000000000000000000000 | ( 2 ; 8 ; 10) | 8314020 | 0.014147564266110422000000000000000000000000000000 | -2.0 | -0.001414756426611042200000000000000000000000000000 | ( 2 ; 9 ; 9) | 9237800 | 0.015719515851233802000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 2 ; 10 ; 8) | 8314020 | 0.014147564266110422000000000000000000000000000000 | +2.0 | +0.001414756426611042200000000000000000000000000000 | ( 2 ; 11 ; 7) | 6046560 | 0.010289137648080307000000000000000000000000000000 | +4.0 | +0.002057827529616061400000000000000000000000000000 | ( 2 ; 12 ; 6) | 3527160 | 0.006001996961380179400000000000000000000000000000 | +6.0 | +0.001800599088414053800000000000000000000000000000 | ( 2 ; 13 ; 5) | 1627920 | 0.002770152443713928600000000000000000000000000000 | +8.0 | +0.001108060977485571300000000000000000000000000000 | ( 2 ; 14 ; 4) | 581400 | 0.000989340158469260290000000000000000000000000000 | +10.0 | +0.000494670079234630150000000000000000000000000000 | ( 2 ; 15 ; 3) | 155040 | 0.000263824042258469420000000000000000000000000000 | +12.0 | +0.000158294425355081650000000000000000000000000000 | ( 2 ; 16 ; 2) | 29070 | 0.000049467007923463019000000000000000000000000000 | +14.0 | +0.000034626905546424111000000000000000000000000000 | ( 2 ; 17 ; 1) | 3420 | 0.000005819647990995648200000000000000000000000000 | +16.0 | +0.000004655718392796518400000000000000000000000000 | ( 2 ; 18 ; 0) | 190 | 0.000000323313777277536050000000000000000000000000 | +18.0 | +0.000000290982399549782450000000000000000000000000 | ( 3 ; 0 ; 17) | 1140 | 0.000000107771259092512000000000000000000000000000 | -17.0 | -0.000000091605570228635205000000000000000000000000 | ( 3 ; 1 ; 16) | 19380 | 0.000001832111404572704000000000000000000000000000 | -15.0 | -0.000001374083553429527900000000000000000000000000 | ( 3 ; 2 ; 15) | 155040 | 0.000014656891236581632000000000000000000000000000 | -13.0 | -0.000009526979303778061200000000000000000000000000 | ( 3 ; 3 ; 14) | 775200 | 0.000073284456182908165000000000000000000000000000 | -11.0 | -0.000040306450900599488000000000000000000000000000 | ( 3 ; 4 ; 13) | 2713200 | 0.000256495596640178590000000000000000000000000000 | -9.0 | -0.000115423018488080370000000000000000000000000000 | ( 3 ; 5 ; 12) | 7054320 | 0.000666888551264464230000000000000000000000000000 | -7.0 | -0.000233410992942562490000000000000000000000000000 | ( 3 ; 6 ; 11) | 14108640 | 0.001333777102528928500000000000000000000000000000 | -5.0 | -0.000333444275632232110000000000000000000000000000 | ( 3 ; 7 ; 10) | 22170720 | 0.002095935446831173300000000000000000000000000000 | -3.0 | -0.000314390317024675990000000000000000000000000000 | ( 3 ; 8 ; 9) | 27713400 | 0.002619919308538966600000000000000000000000000000 | -1.0 | -0.000130995965426948330000000000000000000000000000 | ( 3 ; 9 ; 8) | 27713400 | 0.002619919308538966600000000000000000000000000000 | +1.0 | +0.000130995965426948330000000000000000000000000000 | ( 3 ; 10 ; 7) | 22170720 | 0.002095935446831173300000000000000000000000000000 | +3.0 | +0.000314390317024675990000000000000000000000000000 | ( 3 ; 11 ; 6) | 14108640 | 0.001333777102528928500000000000000000000000000000 | +5.0 | +0.000333444275632232110000000000000000000000000000 | ( 3 ; 12 ; 5) | 7054320 | 0.000666888551264464230000000000000000000000000000 | +7.0 | +0.000233410992942562490000000000000000000000000000 | ( 3 ; 13 ; 4) | 2713200 | 0.000256495596640178590000000000000000000000000000 | +9.0 | +0.000115423018488080370000000000000000000000000000 | ( 3 ; 14 ; 3) | 775200 | 0.000073284456182908165000000000000000000000000000 | +11.0 | +0.000040306450900599488000000000000000000000000000 | ( 3 ; 15 ; 2) | 155040 | 0.000014656891236581631000000000000000000000000000 | +13.0 | +0.000009526979303778059500000000000000000000000000 | ( 3 ; 16 ; 1) | 19380 | 0.000001832111404572704000000000000000000000000000 | +15.0 | +0.000001374083553429527900000000000000000000000000 | ( 3 ; 17 ; 0) | 1140 | 0.000000107771259092512000000000000000000000000000 | +17.0 | +0.000000091605570228635205000000000000000000000000 | ( 4 ; 0 ; 16) | 4845 | 0.000000025445991730176449000000000000000000000000 | -16.0 | -0.000000020356793384141160000000000000000000000000 | ( 4 ; 1 ; 15) | 77520 | 0.000000407135867682823190000000000000000000000000 | -14.0 | -0.000000284995107377976230000000000000000000000000 | ( 4 ; 2 ; 14) | 581400 | 0.000003053519007621173400000000000000000000000000 | -12.0 | -0.000001832111404572704000000000000000000000000000 | ( 4 ; 3 ; 13) | 2713200 | 0.000014249755368898811000000000000000000000000000 | -10.0 | -0.000007124877684449405300000000000000000000000000 | ( 4 ; 4 ; 12) | 8817900 | 0.000046311704948921134000000000000000000000000000 | -8.0 | -0.000018524681979568454000000000000000000000000000 | ( 4 ; 5 ; 11) | 21162960 | 0.000111148091877410710000000000000000000000000000 | -6.0 | -0.000033344427563223214000000000000000000000000000 | ( 4 ; 6 ; 10) | 38798760 | 0.000203771501775252960000000000000000000000000000 | -4.0 | -0.000040754300355050594000000000000000000000000000 | ( 4 ; 7 ; 9) | 55426800 | 0.000291102145393218570000000000000000000000000000 | -2.0 | -0.000029110214539321859000000000000000000000000000 | ( 4 ; 8 ; 8) | 62355150 | 0.000327489913567370880000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 4 ; 9 ; 7) | 55426800 | 0.000291102145393218520000000000000000000000000000 | +2.0 | +0.000029110214539321852000000000000000000000000000 | ( 4 ; 10 ; 6) | 38798760 | 0.000203771501775252960000000000000000000000000000 | +4.0 | +0.000040754300355050594000000000000000000000000000 | ( 4 ; 11 ; 5) | 21162960 | 0.000111148091877410720000000000000000000000000000 | +6.0 | +0.000033344427563223214000000000000000000000000000 | ( 4 ; 12 ; 4) | 8817900 | 0.000046311704948921134000000000000000000000000000 | +8.0 | +0.000018524681979568454000000000000000000000000000 | ( 4 ; 13 ; 3) | 2713200 | 0.000014249755368898811000000000000000000000000000 | +10.0 | +0.000007124877684449405300000000000000000000000000 | ( 4 ; 14 ; 2) | 581400 | 0.000003053519007621173400000000000000000000000000 | +12.0 | +0.000001832111404572704000000000000000000000000000 | ( 4 ; 15 ; 1) | 77520 | 0.000000407135867682823140000000000000000000000000 | +14.0 | +0.000000284995107377976180000000000000000000000000 | ( 4 ; 16 ; 0) | 4845 | 0.000000025445991730176449000000000000000000000000 | +16.0 | +0.000000020356793384141160000000000000000000000000 | ( 5 ; 0 ; 15) | 15504 | 0.000000004523731863142479100000000000000000000000 | -15.0 | -0.000000003392798897356859100000000000000000000000 | ( 5 ; 1 ; 14) | 232560 | 0.000000067855977947137198000000000000000000000000 | -13.0 | -0.000000044106385665639179000000000000000000000000 | ( 5 ; 2 ; 13) | 1627920 | 0.000000474991845629960390000000000000000000000000 | -11.0 | -0.000000261245515096478190000000000000000000000000 | ( 5 ; 3 ; 12) | 7054320 | 0.000002058297997729827800000000000000000000000000 | -9.0 | -0.000000926234098978422520000000000000000000000000 | ( 5 ; 4 ; 11) | 21162960 | 0.000006174893993189484300000000000000000000000000 | -7.0 | -0.000002161212897616319600000000000000000000000000 | ( 5 ; 5 ; 10) | 46558512 | 0.000013584766785016867000000000000000000000000000 | -5.0 | -0.000003396191696254216800000000000000000000000000 | ( 5 ; 6 ; 9) | 77597520 | 0.000022641277975028109000000000000000000000000000 | -3.0 | -0.000003396191696254216300000000000000000000000000 | ( 5 ; 7 ; 8) | 99768240 | 0.000029110214539321855000000000000000000000000000 | -1.0 | -0.000001455510726966092800000000000000000000000000 | ( 5 ; 8 ; 7) | 99768240 | 0.000029110214539321852000000000000000000000000000 | +1.0 | +0.000001455510726966092600000000000000000000000000 | ( 5 ; 9 ; 6) | 77597520 | 0.000022641277975028109000000000000000000000000000 | +3.0 | +0.000003396191696254216300000000000000000000000000 | ( 5 ; 10 ; 5) | 46558512 | 0.000013584766785016867000000000000000000000000000 | +5.0 | +0.000003396191696254216800000000000000000000000000 | ( 5 ; 11 ; 4) | 21162960 | 0.000006174893993189484300000000000000000000000000 | +7.0 | +0.000002161212897616319600000000000000000000000000 | ( 5 ; 12 ; 3) | 7054320 | 0.000002058297997729827800000000000000000000000000 | +9.0 | +0.000000926234098978422520000000000000000000000000 | ( 5 ; 13 ; 2) | 1627920 | 0.000000474991845629960340000000000000000000000000 | +11.0 | +0.000000261245515096478190000000000000000000000000 | ( 5 ; 14 ; 1) | 232560 | 0.000000067855977947137198000000000000000000000000 | +13.0 | +0.000000044106385665639179000000000000000000000000 | ( 5 ; 15 ; 0) | 15504 | 0.000000004523731863142479100000000000000000000000 | +15.0 | +0.000000003392798897356859100000000000000000000000 | ( 6 ; 0 ; 14) | 38760 | 0.000000000628296092103122160000000000000000000000 | -14.0 | -0.000000000439807264472185530000000000000000000000 | ( 6 ; 1 ; 13) | 542640 | 0.000000008796145289443711100000000000000000000000 | -12.0 | -0.000000005277687173666226800000000000000000000000 | ( 6 ; 2 ; 12) | 3527160 | 0.000000057174944381384111000000000000000000000000 | -10.0 | -0.000000028587472190692056000000000000000000000000 | ( 6 ; 3 ; 11) | 14108640 | 0.000000228699777525536420000000000000000000000000 | -8.0 | -0.000000091479911010214573000000000000000000000000 | ( 6 ; 4 ; 10) | 38798760 | 0.000000628924388195225300000000000000000000000000 | -6.0 | -0.000000188677316458567590000000000000000000000000 | ( 6 ; 5 ; 9) | 77597520 | 0.000001257848776390450600000000000000000000000000 | -4.0 | -0.000000251569755278090110000000000000000000000000 | ( 6 ; 6 ; 8) | 116396280 | 0.000001886773164585675600000000000000000000000000 | -2.0 | -0.000000188677316458567570000000000000000000000000 | ( 6 ; 7 ; 7) | 133024320 | 0.000002156312188097915100000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 6 ; 8 ; 6) | 116396280 | 0.000001886773164585675600000000000000000000000000 | +2.0 | +0.000000188677316458567570000000000000000000000000 | ( 6 ; 9 ; 5) | 77597520 | 0.000001257848776390450600000000000000000000000000 | +4.0 | +0.000000251569755278090110000000000000000000000000 | ( 6 ; 10 ; 4) | 38798760 | 0.000000628924388195225300000000000000000000000000 | +6.0 | +0.000000188677316458567590000000000000000000000000 | ( 6 ; 11 ; 3) | 14108640 | 0.000000228699777525536450000000000000000000000000 | +8.0 | +0.000000091479911010214573000000000000000000000000 | ( 6 ; 12 ; 2) | 3527160 | 0.000000057174944381384105000000000000000000000000 | +10.0 | +0.000000028587472190692052000000000000000000000000 | ( 6 ; 13 ; 1) | 542640 | 0.000000008796145289443709400000000000000000000000 | +12.0 | +0.000000005277687173666226000000000000000000000000 | ( 6 ; 14 ; 0) | 38760 | 0.000000000628296092103122160000000000000000000000 | +14.0 | +0.000000000439807264472185530000000000000000000000 | ( 7 ; 0 ; 13) | 77520 | 0.000000000069810676900346914000000000000000000000 | -13.0 | -0.000000000045376939985225495000000000000000000000 | ( 7 ; 1 ; 12) | 1007760 | 0.000000000907538799704509870000000000000000000000 | -11.0 | -0.000000000499146339837480420000000000000000000000 | ( 7 ; 2 ; 11) | 6046560 | 0.000000005445232798227058200000000000000000000000 | -9.0 | -0.000000002450354759202176100000000000000000000000 | ( 7 ; 3 ; 10) | 22170720 | 0.000000019965853593499215000000000000000000000000 | -7.0 | -0.000000006988048757724725500000000000000000000000 | ( 7 ; 4 ; 9) | 55426800 | 0.000000049914633983748041000000000000000000000000 | -5.0 | -0.000000012478658495937010000000000000000000000000 | ( 7 ; 5 ; 8) | 99768240 | 0.000000089846341170746465000000000000000000000000 | -3.0 | -0.000000013476951175611969000000000000000000000000 | ( 7 ; 6 ; 7) | 133024320 | 0.000000119795121560995300000000000000000000000000 | -1.0 | -0.000000005989756078049765100000000000000000000000 | ( 7 ; 7 ; 6) | 133024320 | 0.000000119795121560995280000000000000000000000000 | +1.0 | +0.000000005989756078049764200000000000000000000000 | ( 7 ; 8 ; 5) | 99768240 | 0.000000089846341170746465000000000000000000000000 | +3.0 | +0.000000013476951175611969000000000000000000000000 | ( 7 ; 9 ; 4) | 55426800 | 0.000000049914633983748041000000000000000000000000 | +5.0 | +0.000000012478658495937010000000000000000000000000 | ( 7 ; 10 ; 3) | 22170720 | 0.000000019965853593499215000000000000000000000000 | +7.0 | +0.000000006988048757724725500000000000000000000000 | ( 7 ; 11 ; 2) | 6046560 | 0.000000005445232798227058200000000000000000000000 | +9.0 | +0.000000002450354759202176100000000000000000000000 | ( 7 ; 12 ; 1) | 1007760 | 0.000000000907538799704509870000000000000000000000 | +11.0 | +0.000000000499146339837480420000000000000000000000 | ( 7 ; 13 ; 0) | 77520 | 0.000000000069810676900346914000000000000000000000 | +13.0 | +0.000000000045376939985225495000000000000000000000 | ( 8 ; 0 ; 12) | 125970 | 0.000000000006302352775725761800000000000000000000 | -12.0 | -0.000000000003781411665435457100000000000000000000 | ( 8 ; 1 ; 11) | 1511640 | 0.000000000075628233308709139000000000000000000000 | -10.0 | -0.000000000037814116654354569000000000000000000000 | ( 8 ; 2 ; 10) | 8314020 | 0.000000000415955283197900350000000000000000000000 | -8.0 | -0.000000000166382113279160140000000000000000000000 | ( 8 ; 3 ; 9) | 27713400 | 0.000000001386517610659667600000000000000000000000 | -6.0 | -0.000000000415955283197900300000000000000000000000 | ( 8 ; 4 ; 8) | 62355150 | 0.000000003119664623984252200000000000000000000000 | -4.0 | -0.000000000623932924796850480000000000000000000000 | ( 8 ; 5 ; 7) | 99768240 | 0.000000004991463398374803000000000000000000000000 | -2.0 | -0.000000000499146339837480320000000000000000000000 | ( 8 ; 6 ; 6) | 116396280 | 0.000000005823373964770603900000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 8 ; 7 ; 5) | 99768240 | 0.000000004991463398374803000000000000000000000000 | +2.0 | +0.000000000499146339837480320000000000000000000000 | ( 8 ; 8 ; 4) | 62355150 | 0.000000003119664623984252200000000000000000000000 | +4.0 | +0.000000000623932924796850480000000000000000000000 | ( 8 ; 9 ; 3) | 27713400 | 0.000000001386517610659667800000000000000000000000 | +6.0 | +0.000000000415955283197900350000000000000000000000 | ( 8 ; 10 ; 2) | 8314020 | 0.000000000415955283197900300000000000000000000000 | +8.0 | +0.000000000166382113279160120000000000000000000000 | ( 8 ; 11 ; 1) | 1511640 | 0.000000000075628233308709151000000000000000000000 | +10.0 | +0.000000000037814116654354576000000000000000000000 | ( 8 ; 12 ; 0) | 125970 | 0.000000000006302352775725761800000000000000000000 | +12.0 | +0.000000000003781411665435457100000000000000000000 | ( 9 ; 0 ; 11) | 167960 | 0.000000000000466840946350056460000000000000000000 | -11.0 | -0.000000000000256762520492531030000000000000000000 | ( 9 ; 1 ; 10) | 1847560 | 0.000000000005135250409850621100000000000000000000 | -9.0 | -0.000000000002310862684432779600000000000000000000 | ( 9 ; 2 ; 9) | 9237800 | 0.000000000025676252049253103000000000000000000000 | -7.0 | -0.000000000008986688217238586700000000000000000000 | ( 9 ; 3 ; 8) | 27713400 | 0.000000000077028756147759322000000000000000000000 | -5.0 | -0.000000000019257189036939830000000000000000000000 | ( 9 ; 4 ; 7) | 55426800 | 0.000000000154057512295518620000000000000000000000 | -3.0 | -0.000000000023108626844327792000000000000000000000 | ( 9 ; 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1 ; 9) | 1847560 | 0.000000000000285291689436145630000000000000000000 | -8.0 | -0.000000000000114116675774458250000000000000000000 | (10 ; 2 ; 8) | 8314020 | 0.000000000001283812602462655300000000000000000000 | -6.0 | -0.000000000000385143780738796600000000000000000000 | (10 ; 3 ; 7) | 22170720 | 0.000000000003423500273233747900000000000000000000 | -4.0 | -0.000000000000684700054646749620000000000000000000 | (10 ; 4 ; 6) | 38798760 | 0.000000000005991125478159058000000000000000000000 | -2.0 | -0.000000000000599112547815905840000000000000000000 | (10 ; 5 ; 5) | 46558512 | 0.000000000007189350573790870100000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | (10 ; 6 ; 4) | 38798760 | 0.000000000005991125478159058900000000000000000000 | +2.0 | +0.000000000000599112547815905840000000000000000000 | (10 ; 7 ; 3) | 22170720 | 0.000000000003423500273233747500000000000000000000 | +4.0 | +0.000000000000684700054646749520000000000000000000 | (10 ; 8 ; 2) | 8314020 | 0.000000000001283812602462655300000000000000000000 | +6.0 | +0.000000000000385143780738796600000000000000000000 | (10 ; 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4 ; 4) | 8817900 | 0.000000000000004202529095229418300000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | (12 ; 5 ; 3) | 7054320 | 0.000000000000003362023276183533900000000000000000 | +2.0 | +0.000000000000000336202327618353390000000000000000 | (12 ; 6 ; 2) | 3527160 | 0.000000000000001681011638091767100000000000000000 | +4.0 | +0.000000000000000336202327618353440000000000000000 | (12 ; 7 ; 1) | 1007760 | 0.000000000000000480289039454790560000000000000000 | +6.0 | +0.000000000000000144086711836437170000000000000000 | (12 ; 8 ; 0) | 125970 | 0.000000000000000060036129931848819000000000000000 | +8.0 | +0.000000000000000024014451972739528000000000000000 | (13 ; 0 ; 7) | 77520 | 0.000000000000000002052517262627310100000000000000 | -7.0 | -0.000000000000000000718381041919558520000000000000 | (13 ; 1 ; 6) | 542640 | 0.000000000000000014367620838391170000000000000000 | -5.0 | -0.000000000000000003591905209597792600000000000000 | (13 ; 2 ; 5) | 1627920 | 0.000000000000000043102862515173520000000000000000 | -3.0 | -0.000000000000000006465429377276028200000000000000 | (13 ; 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3 ; 3) | 775200 | 0.000000000000000001140287368126283400000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | (14 ; 4 ; 2) | 581400 | 0.000000000000000000855215526094712380000000000000 | +2.0 | +0.000000000000000000085521552609471238000000000000 | (14 ; 5 ; 1) | 232560 | 0.000000000000000000342086210437885000000000000000 | +4.0 | +0.000000000000000000068417242087577005000000000000 | (14 ; 6 ; 0) | 38760 | 0.000000000000000000057014368406314167000000000000 | +6.0 | +0.000000000000000000017104310521894251000000000000 | (15 ; 0 ; 5) | 15504 | 0.000000000000000000001266985964584759500000000000 | -5.0 | -0.000000000000000000000316746491146189870000000000 | (15 ; 1 ; 4) | 77520 | 0.000000000000000000006334929822923797200000000000 | -3.0 | -0.000000000000000000000950239473438569660000000000 | (15 ; 2 ; 3) | 155040 | 0.000000000000000000012669859645847596000000000000 | -1.0 | -0.000000000000000000000633492982292379840000000000 | (15 ; 3 ; 2) | 155040 | 0.000000000000000000012669859645847594000000000000 | +1.0 | +0.000000000000000000000633492982292379740000000000 | (15 ; 4 ; 1) | 77520 | 0.000000000000000000006334929822923798000000000000 | +3.0 | +0.000000000000000000000950239473438569660000000000 | (15 ; 5 ; 0) | 15504 | 0.000000000000000000001266985964584759500000000000 | +5.0 | +0.000000000000000000000316746491146189870000000000 | (16 ; 0 ; 4) | 4845 | 0.000000000000000000000021996284107374294000000000 | -4.0 | -0.000000000000000000000004399256821474859200000000 | (16 ; 1 ; 3) | 19380 | 0.000000000000000000000087985136429497177000000000 | -2.0 | -0.000000000000000000000008798513642949718300000000 | (16 ; 2 ; 2) | 29070 | 0.000000000000000000000131977704644245780000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | (16 ; 3 ; 1) | 19380 | 0.000000000000000000000087985136429497177000000000 | +2.0 | +0.000000000000000000000008798513642949718300000000 | (16 ; 4 ; 0) | 4845 | 0.000000000000000000000021996284107374294000000000 | +4.0 | +0.000000000000000000000004399256821474859200000000 | (17 ; 0 ; 3) | 1140 | 0.000000000000000000000000287533125586592110000000 | -3.0 | -0.000000000000000000000000043129968837988816000000 | (17 ; 1 ; 2) | 3420 | 0.000000000000000000000000862599376759776370000000 | -1.0 | -0.000000000000000000000000043129968837988816000000 | (17 ; 2 ; 1) | 3420 | 0.000000000000000000000000862599376759776370000000 | +1.0 | +0.000000000000000000000000043129968837988816000000 | (17 ; 3 ; 0) | 1140 | 0.000000000000000000000000287533125586592110000000 | +3.0 | +0.000000000000000000000000043129968837988816000000 | (18 ; 0 ; 2) | 190 | 0.000000000000000000000000002662343755431408000000 | -2.0 | -0.000000000000000000000000000266234375543140800000 | (18 ; 1 ; 1) | 380 | 0.000000000000000000000000005324687510862816000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | (18 ; 2 ; 0) | 190 | 0.000000000000000000000000002662343755431408000000 | +2.0 | +0.000000000000000000000000000266234375543140800000 | (19 ; 0 ; 1) | 20 | 0.000000000000000000000000000015569261727669054000 | -1.0 | -0.000000000000000000000000000000778463086383452730 | (19 ; 1 ; 0) | 20 | 0.000000000000000000000000000015569261727669054000 | +1.0 | +0.000000000000000000000000000000778463086383452730 | (20 ; 0 ; 0) | 1 | 0.000000000000000000000000000000043247949243525151 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ============== | ============ | ================================================== | ===== | =================================================== | Probabilité du gain : +0.441044184688224540 Probabilité du nul : +0.117911630623551810 Probabilité de la perte : +0.441044184688224590 Cumul des Probabilités : +1.000000000000001100 Espérance mathématique : +0.000000000000000004
19/12/2012 3:10 am
(désolé, mais je n'ai pas pu tout mettre dans le même message)
Et voici la roulette européenne, toujours avec la loi multinomiale :
Triplets | Combinaisons | Probabilités | Bilan | Espérances Mathématiques | ============== | ============ | ================================================== | ===== | =================================================== | ( 0 ; 0 ; 20) | 1 | 0.000000551335072831166730000000000000000000000000 | -20.0 | -0.000000551335072831166730000000000000000000000000 | ( 0 ; 1 ; 19) | 20 | 0.000011026701456623334000000000000000000000000000 | -18.0 | -0.000009924031310961000900000000000000000000000000 | ( 0 ; 2 ; 18) | 190 | 0.000104753663837921680000000000000000000000000000 | -16.0 | -0.000083802931070337347000000000000000000000000000 | ( 0 ; 3 ; 17) | 1140 | 0.000628521983027530090000000000000000000000000000 | -14.0 | -0.000439965388119271050000000000000000000000000000 | ( 0 ; 4 ; 16) | 4845 | 0.002671218427867002600000000000000000000000000000 | -12.0 | -0.001602731056720201500000000000000000000000000000 | ( 0 ; 5 ; 15) | 15504 | 0.008547898969174409100000000000000000000000000000 | -10.0 | -0.004273949484587204500000000000000000000000000000 | ( 0 ; 6 ; 14) | 38760 | 0.021369747422936021000000000000000000000000000000 | -8.0 | -0.008547898969174409100000000000000000000000000000 | ( 0 ; 7 ; 13) | 77520 | 0.042739494845872042000000000000000000000000000000 | -6.0 | -0.012821848453761612000000000000000000000000000000 | ( 0 ; 8 ; 12) | 125970 | 0.069451679124542073000000000000000000000000000000 | -4.0 | -0.013890335824908414000000000000000000000000000000 | ( 0 ; 9 ; 11) | 167960 | 0.092602238832722755000000000000000000000000000000 | -2.0 | -0.009260223883272276200000000000000000000000000000 | ( 0 ; 10 ; 10) | 184756 | 0.101862462715995030000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 0 ; 11 ; 9) | 167960 | 0.092602238832722755000000000000000000000000000000 | +2.0 | +0.009260223883272276200000000000000000000000000000 | ( 0 ; 12 ; 8) | 125970 | 0.069451679124542073000000000000000000000000000000 | +4.0 | +0.013890335824908414000000000000000000000000000000 | ( 0 ; 13 ; 7) | 77520 | 0.042739494845872042000000000000000000000000000000 | +6.0 | +0.012821848453761612000000000000000000000000000000 | ( 0 ; 14 ; 6) | 38760 | 0.021369747422936021000000000000000000000000000000 | +8.0 | +0.008547898969174409100000000000000000000000000000 | ( 0 ; 15 ; 5) | 15504 | 0.008547898969174409100000000000000000000000000000 | +10.0 | +0.004273949484587204500000000000000000000000000000 | ( 0 ; 16 ; 4) | 4845 | 0.002671218427867002600000000000000000000000000000 | +12.0 | +0.001602731056720201500000000000000000000000000000 | ( 0 ; 17 ; 3) | 1140 | 0.000628521983027530090000000000000000000000000000 | +14.0 | +0.000439965388119271050000000000000000000000000000 | ( 0 ; 18 ; 2) | 190 | 0.000104753663837921680000000000000000000000000000 | +16.0 | +0.000083802931070337347000000000000000000000000000 | ( 0 ; 19 ; 1) | 20 | 0.000011026701456623334000000000000000000000000000 | +18.0 | +0.000009924031310961000900000000000000000000000000 | ( 0 ; 20 ; 0) | 1 | 0.000000551335072831166730000000000000000000000000 | +20.0 | +0.000000551335072831166730000000000000000000000000 | ( 1 ; 0 ; 19) | 20 | 0.000000612594525367962980000000000000000000000000 | -20.0 | -0.000000612594525367962980000000000000000000000000 | ( 1 ; 1 ; 18) | 380 | 0.000011639295981991295000000000000000000000000000 | -18.0 | -0.000010475366383792165000000000000000000000000000 | ( 1 ; 2 ; 17) | 3420 | 0.000104753663837921660000000000000000000000000000 | -16.0 | -0.000083802931070337333000000000000000000000000000 | ( 1 ; 3 ; 16) | 19380 | 0.000593604095081556200000000000000000000000000000 | -14.0 | -0.000415522866557089360000000000000000000000000000 | ( 1 ; 4 ; 15) | 77520 | 0.002374416380326224800000000000000000000000000000 | -12.0 | -0.001424649828195734900000000000000000000000000000 | ( 1 ; 5 ; 14) | 232560 | 0.007123249140978673900000000000000000000000000000 | -10.0 | -0.003561624570489337000000000000000000000000000000 | ( 1 ; 6 ; 13) | 542640 | 0.016620914662283572000000000000000000000000000000 | -8.0 | -0.006648365864913428900000000000000000000000000000 | ( 1 ; 7 ; 12) | 1007760 | 0.030867412944240915000000000000000000000000000000 | -6.0 | -0.009260223883272274500000000000000000000000000000 | ( 1 ; 8 ; 11) | 1511640 | 0.046301119416361385000000000000000000000000000000 | -4.0 | -0.009260223883272276200000000000000000000000000000 | ( 1 ; 9 ; 10) | 1847560 | 0.056590257064441686000000000000000000000000000000 | -2.0 | -0.005659025706444168600000000000000000000000000000 | ( 1 ; 10 ; 9) | 1847560 | 0.056590257064441686000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 1 ; 11 ; 8) | 1511640 | 0.046301119416361385000000000000000000000000000000 | +2.0 | +0.004630111941636138100000000000000000000000000000 | ( 1 ; 12 ; 7) | 1007760 | 0.030867412944240918000000000000000000000000000000 | +4.0 | +0.006173482588848183900000000000000000000000000000 | ( 1 ; 13 ; 6) | 542640 | 0.016620914662283572000000000000000000000000000000 | +6.0 | +0.004986274398685071700000000000000000000000000000 | ( 1 ; 14 ; 5) | 232560 | 0.007123249140978673900000000000000000000000000000 | +8.0 | +0.002849299656391469400000000000000000000000000000 | ( 1 ; 15 ; 4) | 77520 | 0.002374416380326224800000000000000000000000000000 | +10.0 | +0.001187208190163112400000000000000000000000000000 | ( 1 ; 16 ; 3) | 19380 | 0.000593604095081556200000000000000000000000000000 | +12.0 | +0.000356162457048933730000000000000000000000000000 | ( 1 ; 17 ; 2) | 3420 | 0.000104753663837921660000000000000000000000000000 | +14.0 | +0.000073327564686545161000000000000000000000000000 | ( 1 ; 18 ; 1) | 380 | 0.000011639295981991296000000000000000000000000000 | +16.0 | +0.000009311436785593036800000000000000000000000000 | ( 1 ; 19 ; 0) | 20 | 0.000000612594525367962980000000000000000000000000 | +18.0 | +0.000000551335072831166730000000000000000000000000 | ( 2 ; 0 ; 18) | 190 | 0.000000323313777277536050000000000000000000000000 | -20.0 | -0.000000323313777277536050000000000000000000000000 | ( 2 ; 1 ; 17) | 3420 | 0.000005819647990995648200000000000000000000000000 | -18.0 | -0.000005237683191896083300000000000000000000000000 | ( 2 ; 2 ; 16) | 29070 | 0.000049467007923463012000000000000000000000000000 | -16.0 | -0.000039573606338770407000000000000000000000000000 | ( 2 ; 3 ; 15) | 155040 | 0.000263824042258469420000000000000000000000000000 | -14.0 | -0.000184676829580928600000000000000000000000000000 | ( 2 ; 4 ; 14) | 581400 | 0.000989340158469260290000000000000000000000000000 | -12.0 | -0.000593604095081556200000000000000000000000000000 | ( 2 ; 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1 ; 2) | 3420 | 0.000000000000000000000000862599376759776370000000 | -18.0 | -0.000000000000000000000000776339439083798720000000 | (17 ; 2 ; 1) | 3420 | 0.000000000000000000000000862599376759776370000000 | -16.0 | -0.000000000000000000000000690079501407821060000000 | (17 ; 3 ; 0) | 1140 | 0.000000000000000000000000287533125586592110000000 | -14.0 | -0.000000000000000000000000201273187910614480000000 | (18 ; 0 ; 2) | 190 | 0.000000000000000000000000002662343755431408000000 | -20.0 | -0.000000000000000000000000002662343755431408000000 | (18 ; 1 ; 1) | 380 | 0.000000000000000000000000005324687510862816000000 | -18.0 | -0.000000000000000000000000004792218759776534400000 | (18 ; 2 ; 0) | 190 | 0.000000000000000000000000002662343755431408000000 | -16.0 | -0.000000000000000000000000002129875004345126400000 | (19 ; 0 ; 1) | 20 | 0.000000000000000000000000000015569261727669054000 | -20.0 | -0.000000000000000000000000000015569261727669054000 | (19 ; 1 ; 0) | 20 | 0.000000000000000000000000000015569261727669054000 | -18.0 | -0.000000000000000000000000000014012335554902147000 | (20 ; 0 ; 0) | 1 | 0.000000000000000000000000000000043247949243525151 | -20.0 | -0.000000000000000000000000000000043247949243525151 | ============== | ============ | ================================================== | ===== | =================================================== | Probabilité du gain : +0.365026235224989000 Probabilité du nul : +0.174914225073299400 Probabilité de la perte : +0.460059539701712590 Cumul des Probabilités : +1.000000000000001100 Espérance mathématique : -0.027027027027027070
D'ailleurs, c'est facile à les distinguer. Jeu de Pile ou Face : l'espérance est nulle.
La roulette européenne : l'espérance est de -0,027027.
Donc maintenant, tu peux comparer le résultat de :
--> la roulette européenne :+0.36502623.
--> la roulette française : +0.43810194.
--> le jeu de pile ou face : +0,44104418.
Et tu constates que la roulette française est moins intéressant que le jeu de pile ou face, mais bien meilleur que la roulette européenne.
Pourquoi ? Car on a les mêmes bases de comparaison !
En fait, tous ces calculs ne servaient strictement à rien, car l'espérance mathématique nous donnait déjà la réponse.
Sur vingt coups, l'espérance mathématique ramené à un coup, nous donne un jeu défavorable à la roulette, tandis que le jeu est équitable à Pile ou face. Et il n'existe pas de stratégies pouvant modifier ce résultat sur le long terme !
@+
19/12/2012 4:00 am
Par exemple, au jeu de pile ou face, si le zéro sort, le bilan est zéro !
Au jeu de Pile ou face le zéro sort ??
le jeu de pile ou face : +0,44104418
Quand on fait un cycle de 20 lancers avec une pièce, la probabilité d'avoir un cycle gagnant n'est pas 0.4414418.
Nous l'avons calculé auparavant, c'est 0.411901474
19/12/2012 5:28 am
Tu utilises les probabilités de la roulette, et il y en a trois. Faut-il que je te les redonne ou pas ?
Ensuite, qu'est-ce que tu ne comprends pas dans cette phrase :
Par exemple, au jeu de pile ou face, si le zéro sort, le bilan est zéro !
Tu attribues un zéro à la sortie du zéro au lieu d'un -1 comme sur la roulette européenne ou un -0,5 comme à la roulette française.
Le mot "bilan", c'est bien toi qui l'utilise dans ton classeur Excel, non ?
Et donc, avec ce nouveau bilan, tu simules un jeu de Pile ou Face.
Et comme par miracle, l'espérance mathématique est nulle !
Il te le faut ou pas ce nouveau tableau sur le jeu de pile ou face ? Car j'ai l'impression que tu ne comprends pas ce que je dis !
Et à ce jeu, tu obtiens bien +0.441044184688224540 de probabilité pour le gain.
Et je te le rappelle, ce calcul se fait avec la loi multinomiale et non la loi binomiale !
Ça y est tu es en phase maintenant ?
Si tu fait de même avec la roulette européenne, tu trouves (toujours pour la probabilité des gains) : +0.365026235224989000
Donc si compares ces trois résultats, tu trouves :
--> jeu de Pile ou Face : +0.441044184688224540
--> Roulette française : +0.438101948114484940
--> Roulette européenne : +0.365026235224989000
Donc la comparaison est possible, car tu as la même base de calcul !
@+
19/12/2012 5:45 am
La question est simple:
On joue à Pile ou Face et on parie systématiquement sur Pile
Quand on fait un cycle de 20 lancers, quelle est d'après toi la probabilité d'avoir un cycle gagnant ?
19/12/2012 8:22 am
Je viens de te répondre. Tu pourrais faire l'effort de me lire.
Avec la loi multinomiale, la réponse est : +0.441044184688224540.
C'est comme si tu avais une roulette sans zéro !
Maintenant, si tu considères la loi binomiale, la réponse est : +0.411901473999023438.
C'est comme le lancer d'une pièce au jeu de Pile ou Face.
Dans les deux cas, l'espérance mathématique est nulle !
@+
19/12/2012 12:52 pm
Je viens de te répondre. Tu pourrais faire l'effort de me lire.
Avec la loi multinomiale, la réponse est : +0.441044184688224540.
C'est comme si tu avais une roulette sans zéro !
Mais le jeu de Pile ou Face n'est pas une roulette.
Tu peux obtenir Pile ou Face mais pas zéro.
Maintenant, si tu considères la loi binomiale, la réponse est : +0.411901473999023438.
C'est la bonne probabilité.
Il n'y a pas 2 probabilités !
Quand tu auras fait 10000 cycles de 20 lancers, la moyenne des cycles gagnants ne peut pas être à la fois 4119 et 4410 !
C'est soit l'un soit l'autre. C'est l'un.
1 ; 11 ; 8 | 1511640 | 0.046301119416361385000000000000000000000000000000
Voici un détail de tes calculs.
Selon toi, on a une probabilité de 4.63% de faire 11 Piles, 8 Faces et 1 zéro en lançant 20 fois une pièce ???
Tu te sens bien ?
20/12/2012 3:52 am
Je vois que c'est le terme de "jeu à pile ou face" qui te dérange. Je ne sais pas pourquoi tu te focalises la dessus.
Ce qui caractérise le jeu de Pile ou Face, c'est d'être un jeu équitable.
Donc j'ai construit un jeu équitable, avec la roulette à un seul zéro où l'espérance mathématique est nulle.
Quand le zéro sort, le joueur est remboursé intégralement de sa mise.
Et de cela, j'ai les mêmes bases pour pourvoir comparer :
--> un jeu équitable (espérance mathématique nulle).
--> Roulette française (espérance mathématique de -1/74).
--> Roulette européenne (espérance mathématique de -1/37).
Et ces bases sont les trois probabilités, celle du Zéro, du Rouge et du Noir.
Après quelques réflexions, Glups, tu soulèves une question fort intéressante. Pourquoi entre le jeu de Pile ou Face avec la loi binomiale et la roulette équitable avec la loi multinomiale, nous ne trouvons pas la même probabilité du gain ?
Cela ne peut pas venir des probabilités unitaires (1/37; 18/37: 18/37) de la loi multinomiale. ni de la loi multinomiale (1/2: 1/2).
Pourquoi ?
J'ai refait le même genre de calcul avec la roulette européenne, et je retrouve le même résultat !
Est-ce que cela vient du bilan ? A première vue, cela me semble correcte !
Reste alors le calcul de la probabilité. Mais la aussi, cela me semble correcte car la somme de toutes les probabilité donne 1.
Le calcul de l'espérance mathématique est correcte aussi !
Dois-je conclure que rembourser la totalité de la mise sur une roulette européenne lors de la sortie du zéro, n'est pas équivalent au jeu de Pile ou Face ?
Il y a sûrement une erreur, mais je ne la voie pas ! As-tu une opinion à ce sujet ?
@+
20/12/2012 7:56 am
Je vois que c'est le terme de "jeu à pile ou face" qui te dérange.
Oui et comment !
Je ne sais pas pourquoi tu te focalises la dessus.
Pourquoi je me focalise sur le jeu de pile ou face ?
Parce que tu lui attribues une probabilité pour les cycles gagnants (44.10%) qui n'est pas la sienne (41.19%)
Donc j'ai construit un jeu équitable, avec la roulette à un seul zéro où l'espérance mathématique est nulle.
Quand le zéro sort, le joueur est remboursé intégralement de sa mise.
Ah, je préfère ça!
Oui, tu peux bien sûr imaginer cette roulette (mais ce n'est pas un pile ou face)
Après quelques réflexions, Glups, tu soulèves une question fort intéressante. Pourquoi entre le jeu de Pile ou Face avec la loi binomiale et la roulette équitable avec la loi multinomiale, nous ne trouvons pas la même probabilité du gain ?
Parce que ce ne sont pas les mêmes jeux et ils ont leurs caractéristiques propres.
Dois-je conclure que rembourser la totalité de la mise sur une roulette européenne lors de la sortie du zéro, n'est pas équivalent au jeu de Pile ou Face ?
C'est exactement ce que je te dis depuis le début.
Tu y trouves des ressemblances mais ce ne sont pas des jeux équivalents.
J'espère que tu valides donc que pour une pièce (pile ou face), il y a 41.19% de cycles gagnants de 20 lancers
Or tu as validé que pour une française, il y a 43.81% de cycles gagnants de 20 lancers
Tu ne trouves plus ça aberrant ?
Je te rappelle que tu disais:
Or tu trouves 0,4381. Ce résultat est meilleur que le jeu de Pile ou face et de ce fait, il est aberrant car le jeu de la roulette française à une espérance mathématique négative alors que Pile ou face a une espérance mathématique nulle.
20/12/2012 8:23 am
J'essaye de comprendre, voila là !
J'ai fait le calcul avec une roulette européenne comme hypothèse de départ.
Et je trouve exactement la même chose avec la loi binomiale et la loi multinomiale.
Je te redonne les résultats pour la loi binomiale :
Couples | Combinaisons | Probabilités | Bilan | Espérances Mathématiques | ========= | ============ | ============================== | ===== | =============================== | ( 0 ; 20) | 1 | 0.0000016256892641574018000000 | -20.0 | -0.0000016256892641574018000000 | ( 1 ; 19) | 20 | 0.0000308025334261402420000000 | -18.0 | -0.0000277222800835262160000000 | ( 2 ; 18) | 190 | 0.0002772228008352622400000000 | -16.0 | -0.0002217782406682097800000000 | ( 3 ; 17) | 1140 | 0.0015757927626425436000000000 | -14.0 | -0.0011030549338497805000000000 | ( 4 ; 16) | 4845 | 0.0063446392811660306000000000 | -12.0 | -0.0038067835686996184000000000 | ( 5 ; 15) | 15504 | 0.0192342748734296540000000000 | -10.0 | -0.0096171374367148271000000000 | ( 6 ; 14) | 38760 | 0.0455548615423333960000000000 | -8.0 | -0.0182219446169333590000000000 | ( 7 ; 13) | 77520 | 0.0863144745012632830000000000 | -6.0 | -0.0258943423503789840000000000 | ( 8 ; 12) | 125970 | 0.1328788620611553500000000000 | -4.0 | -0.0265757724122310700000000000 | ( 9 ; 11) | 167960 | 0.1678469836561962100000000000 | -2.0 | -0.0167846983656196220000000000 | (10 ; 10) | 184756 | 0.1749142250732992300000000000 | +0.0 | +0.0000000000000000000000000000 | (11 ; 9) | 167960 | 0.1506438302066692200000000000 | +2.0 | +0.0150643830206669220000000000 | (12 ; 8) | 125970 | 0.1070364056731597200000000000 | +4.0 | +0.0214072811346319450000000000 | (13 ; 7) | 77520 | 0.0624017911616801740000000000 | +6.0 | +0.0187205373485040510000000000 | (14 ; 6) | 38760 | 0.0295587431818485030000000000 | +8.0 | +0.0118234972727394010000000000 | (15 ; 5) | 15504 | 0.0112012079425952250000000000 | +10.0 | +0.0056006039712976127000000000 | (16 ; 4) | 4845 | 0.0033161470882683234000000000 | +12.0 | +0.0019896882529609940000000000 | (17 ; 3) | 1140 | 0.0007392030661155396000000000 | +14.0 | +0.0005174421462808777200000000 | (18 ; 2) | 190 | 0.0001167162735971904900000000 | +16.0 | +0.0000933730188777523910000000 | (19 ; 1) | 20 | 0.0000116392959819912960000000 | +18.0 | +0.0000104753663837921670000000 | (20 ; 0) | 1 | 0.0000005513350728311667300000 | +20.0 | +0.0000005513350728311667300000 | ========= | ============ | ============================== | ===== | =============================== | Probabilité du gain : +0.365026235224988620 Probabilité du nul : +0.174914225073299230 Probabilité de la perte : +0.460059539701712040 Cumul des Probabilités : +1.000000000000000200 Espérance mathématique : -0.027027027027026959
et pour la loi multinomiale :
Triplets | Combinaisons | Probabilités | Bilan | Espérances Mathématiques | ============== | ============ | ================================================== | ===== | =================================================== | ( 0 ; 0 ; 20) | 1 | 0.000000551335072831166730000000000000000000000000 | -20.0 | -0.000000551335072831166730000000000000000000000000 | ( 0 ; 1 ; 19) | 20 | 0.000011026701456623334000000000000000000000000000 | -18.0 | -0.000009924031310961000900000000000000000000000000 | ( 0 ; 2 ; 18) | 190 | 0.000104753663837921680000000000000000000000000000 | -16.0 | -0.000083802931070337347000000000000000000000000000 | ( 0 ; 3 ; 17) | 1140 | 0.000628521983027530090000000000000000000000000000 | -14.0 | -0.000439965388119271050000000000000000000000000000 | ( 0 ; 4 ; 16) | 4845 | 0.002671218427867002600000000000000000000000000000 | -12.0 | -0.001602731056720201500000000000000000000000000000 | ( 0 ; 5 ; 15) | 15504 | 0.008547898969174409100000000000000000000000000000 | -10.0 | -0.004273949484587204500000000000000000000000000000 | ( 0 ; 6 ; 14) | 38760 | 0.021369747422936021000000000000000000000000000000 | -8.0 | -0.008547898969174409100000000000000000000000000000 | ( 0 ; 7 ; 13) | 77520 | 0.042739494845872042000000000000000000000000000000 | -6.0 | -0.012821848453761612000000000000000000000000000000 | ( 0 ; 8 ; 12) | 125970 | 0.069451679124542073000000000000000000000000000000 | -4.0 | -0.013890335824908414000000000000000000000000000000 | ( 0 ; 9 ; 11) | 167960 | 0.092602238832722755000000000000000000000000000000 | -2.0 | -0.009260223883272276200000000000000000000000000000 | ( 0 ; 10 ; 10) | 184756 | 0.101862462715995030000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 0 ; 11 ; 9) | 167960 | 0.092602238832722755000000000000000000000000000000 | +2.0 | +0.009260223883272276200000000000000000000000000000 | ( 0 ; 12 ; 8) | 125970 | 0.069451679124542073000000000000000000000000000000 | +4.0 | +0.013890335824908414000000000000000000000000000000 | ( 0 ; 13 ; 7) | 77520 | 0.042739494845872042000000000000000000000000000000 | +6.0 | +0.012821848453761612000000000000000000000000000000 | ( 0 ; 14 ; 6) | 38760 | 0.021369747422936021000000000000000000000000000000 | +8.0 | +0.008547898969174409100000000000000000000000000000 | ( 0 ; 15 ; 5) | 15504 | 0.008547898969174409100000000000000000000000000000 | +10.0 | +0.004273949484587204500000000000000000000000000000 | ( 0 ; 16 ; 4) | 4845 | 0.002671218427867002600000000000000000000000000000 | +12.0 | +0.001602731056720201500000000000000000000000000000 | ( 0 ; 17 ; 3) | 1140 | 0.000628521983027530090000000000000000000000000000 | +14.0 | +0.000439965388119271050000000000000000000000000000 | ( 0 ; 18 ; 2) | 190 | 0.000104753663837921680000000000000000000000000000 | +16.0 | +0.000083802931070337347000000000000000000000000000 | ( 0 ; 19 ; 1) | 20 | 0.000011026701456623334000000000000000000000000000 | +18.0 | +0.000009924031310961000900000000000000000000000000 | ( 0 ; 20 ; 0) | 1 | 0.000000551335072831166730000000000000000000000000 | +20.0 | +0.000000551335072831166730000000000000000000000000 | ( 1 ; 0 ; 19) | 20 | 0.000000612594525367962980000000000000000000000000 | -20.0 | -0.000000612594525367962980000000000000000000000000 | ( 1 ; 1 ; 18) | 380 | 0.000011639295981991295000000000000000000000000000 | -18.0 | -0.000010475366383792165000000000000000000000000000 | ( 1 ; 2 ; 17) | 3420 | 0.000104753663837921660000000000000000000000000000 | -16.0 | -0.000083802931070337333000000000000000000000000000 | ( 1 ; 3 ; 16) | 19380 | 0.000593604095081556200000000000000000000000000000 | -14.0 | -0.000415522866557089360000000000000000000000000000 | ( 1 ; 4 ; 15) | 77520 | 0.002374416380326224800000000000000000000000000000 | -12.0 | -0.001424649828195734900000000000000000000000000000 | ( 1 ; 5 ; 14) | 232560 | 0.007123249140978673900000000000000000000000000000 | -10.0 | -0.003561624570489337000000000000000000000000000000 | ( 1 ; 6 ; 13) | 542640 | 0.016620914662283572000000000000000000000000000000 | -8.0 | -0.006648365864913428900000000000000000000000000000 | ( 1 ; 7 ; 12) | 1007760 | 0.030867412944240915000000000000000000000000000000 | -6.0 | -0.009260223883272274500000000000000000000000000000 | ( 1 ; 8 ; 11) | 1511640 | 0.046301119416361385000000000000000000000000000000 | -4.0 | -0.009260223883272276200000000000000000000000000000 | ( 1 ; 9 ; 10) | 1847560 | 0.056590257064441686000000000000000000000000000000 | -2.0 | -0.005659025706444168600000000000000000000000000000 | ( 1 ; 10 ; 9) | 1847560 | 0.056590257064441686000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 1 ; 11 ; 8) | 1511640 | 0.046301119416361385000000000000000000000000000000 | +2.0 | +0.004630111941636138100000000000000000000000000000 | ( 1 ; 12 ; 7) | 1007760 | 0.030867412944240918000000000000000000000000000000 | +4.0 | +0.006173482588848183900000000000000000000000000000 | ( 1 ; 13 ; 6) | 542640 | 0.016620914662283572000000000000000000000000000000 | +6.0 | +0.004986274398685071700000000000000000000000000000 | ( 1 ; 14 ; 5) | 232560 | 0.007123249140978673900000000000000000000000000000 | +8.0 | +0.002849299656391469400000000000000000000000000000 | ( 1 ; 15 ; 4) | 77520 | 0.002374416380326224800000000000000000000000000000 | +10.0 | +0.001187208190163112400000000000000000000000000000 | ( 1 ; 16 ; 3) | 19380 | 0.000593604095081556200000000000000000000000000000 | +12.0 | +0.000356162457048933730000000000000000000000000000 | ( 1 ; 17 ; 2) | 3420 | 0.000104753663837921660000000000000000000000000000 | +14.0 | +0.000073327564686545161000000000000000000000000000 | ( 1 ; 18 ; 1) | 380 | 0.000011639295981991296000000000000000000000000000 | +16.0 | +0.000009311436785593036800000000000000000000000000 | ( 1 ; 19 ; 0) | 20 | 0.000000612594525367962980000000000000000000000000 | +18.0 | +0.000000551335072831166730000000000000000000000000 | ( 2 ; 0 ; 18) | 190 | 0.000000323313777277536050000000000000000000000000 | -20.0 | -0.000000323313777277536050000000000000000000000000 | ( 2 ; 1 ; 17) | 3420 | 0.000005819647990995648200000000000000000000000000 | -18.0 | -0.000005237683191896083300000000000000000000000000 | ( 2 ; 2 ; 16) | 29070 | 0.000049467007923463012000000000000000000000000000 | -16.0 | -0.000039573606338770407000000000000000000000000000 | ( 2 ; 3 ; 15) | 155040 | 0.000263824042258469420000000000000000000000000000 | -14.0 | -0.000184676829580928600000000000000000000000000000 | ( 2 ; 4 ; 14) | 581400 | 0.000989340158469260290000000000000000000000000000 | -12.0 | -0.000593604095081556200000000000000000000000000000 | ( 2 ; 5 ; 13) | 1627920 | 0.002770152443713928600000000000000000000000000000 | -10.0 | -0.001385076221856964300000000000000000000000000000 | ( 2 ; 6 ; 12) | 3527160 | 0.006001996961380179400000000000000000000000000000 | -8.0 | -0.002400798784552071700000000000000000000000000000 | ( 2 ; 7 ; 11) | 6046560 | 0.010289137648080307000000000000000000000000000000 | -6.0 | -0.003086741294424091900000000000000000000000000000 | ( 2 ; 8 ; 10) | 8314020 | 0.014147564266110422000000000000000000000000000000 | -4.0 | -0.002829512853222084300000000000000000000000000000 | ( 2 ; 9 ; 9) | 9237800 | 0.015719515851233802000000000000000000000000000000 | -2.0 | -0.001571951585123380100000000000000000000000000000 | ( 2 ; 10 ; 8) | 8314020 | 0.014147564266110422000000000000000000000000000000 | +0.0 | +0.000000000000000000000000000000000000000000000000 | ( 2 ; 11 ; 7) | 6046560 | 0.010289137648080307000000000000000000000000000000 | +2.0 | +0.001028913764808030700000000000000000000000000000 | ( 2 ; 12 ; 6) | 3527160 | 0.006001996961380179400000000000000000000000000000 | +4.0 | +0.001200399392276035900000000000000000000000000000 | ( 2 ; 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4 ; 1) | 77520 | 0.000000000000000000006334929822923798000000000000 | -12.0 | -0.000000000000000000003800957893754278600000000000 | (15 ; 5 ; 0) | 15504 | 0.000000000000000000001266985964584759500000000000 | -10.0 | -0.000000000000000000000633492982292379740000000000 | (16 ; 0 ; 4) | 4845 | 0.000000000000000000000021996284107374294000000000 | -20.0 | -0.000000000000000000000021996284107374294000000000 | (16 ; 1 ; 3) | 19380 | 0.000000000000000000000087985136429497177000000000 | -18.0 | -0.000000000000000000000079186622786547456000000000 | (16 ; 2 ; 2) | 29070 | 0.000000000000000000000131977704644245780000000000 | -16.0 | -0.000000000000000000000105582163715396630000000000 | (16 ; 3 ; 1) | 19380 | 0.000000000000000000000087985136429497177000000000 | -14.0 | -0.000000000000000000000061589595500648025000000000 | (16 ; 4 ; 0) | 4845 | 0.000000000000000000000021996284107374294000000000 | -12.0 | -0.000000000000000000000013197770464424576000000000 | (17 ; 0 ; 3) | 1140 | 0.000000000000000000000000287533125586592110000000 | -20.0 | -0.000000000000000000000000287533125586592110000000 | (17 ; 1 ; 2) | 3420 | 0.000000000000000000000000862599376759776370000000 | -18.0 | -0.000000000000000000000000776339439083798720000000 | (17 ; 2 ; 1) | 3420 | 0.000000000000000000000000862599376759776370000000 | -16.0 | -0.000000000000000000000000690079501407821060000000 | (17 ; 3 ; 0) | 1140 | 0.000000000000000000000000287533125586592110000000 | -14.0 | -0.000000000000000000000000201273187910614480000000 | (18 ; 0 ; 2) | 190 | 0.000000000000000000000000002662343755431408000000 | -20.0 | -0.000000000000000000000000002662343755431408000000 | (18 ; 1 ; 1) | 380 | 0.000000000000000000000000005324687510862816000000 | -18.0 | -0.000000000000000000000000004792218759776534400000 | (18 ; 2 ; 0) | 190 | 0.000000000000000000000000002662343755431408000000 | -16.0 | -0.000000000000000000000000002129875004345126400000 | (19 ; 0 ; 1) | 20 | 0.000000000000000000000000000015569261727669054000 | -20.0 | -0.000000000000000000000000000015569261727669054000 | (19 ; 1 ; 0) | 20 | 0.000000000000000000000000000015569261727669054000 | -18.0 | -0.000000000000000000000000000014012335554902147000 | (20 ; 0 ; 0) | 1 | 0.000000000000000000000000000000043247949243525151 | -20.0 | -0.000000000000000000000000000000043247949243525151 | ============== | ============ | ================================================== | ===== | =================================================== | Probabilité du gain : +0.365026235224989000 Probabilité du nul : +0.174914225073299400 Probabilité de la perte : +0.460059539701712590 Cumul des Probabilités : +1.000000000000001100 Espérance mathématique : -0.027027027027027070
Et pourtant, ce ne sont pas les mêmes probabilités.
Donc pourquoi je trouve les mêmes résultats pour la roulette européenne, et pas du tout la même chose pour la roulette française et la roulette équitable vis-à-vis du jeu pile ou face, lorsque je compare la loi binomiale avec la loi multinomiale ?
Je ne comprends pas !
Il semble que le problème vient des coups nuls ! Ils sont plus nombreux pour la loi binomiale que pour la loi multinomiale.
Tant que je n'aurai pas compris ce qui cloche dans ces comparaisons, oui, je continuerai d'affirmer que cela est aberrant !
Les probabilités ne sont pas en cause.
L'espérance mathématique non plus car je retrouve le même résultats.
Le bilan non plus.
La seule chose qui me dérange, ce sont les vingt coups !
Cela représente en principe des coups gagnants et perdants.
Or quand tu as des coups nuls, le nombre de coups gagnants et perdants diminues.
Et cela déséquilibre les trois probabilités : du gain, du nul et de la perte, sans modifier ni le cumul des probabilités ni l'espérance mathématique.
Donc pourquoi les calculs sur la roulette européenne sont correctes mais pas pour les deux autres roulettes (équitables et française ) ?
@+
20/12/2012 9:20 am
Tant que je n'aurai pas compris ce qui cloche dans ces comparaisons, oui, je continuerai d'affirmer que cela est aberrant !
J'ai cru comprendre que tu pensais la chose suivante:
Si on dans un jeu1, la probabilité de gagner est supérieure à celle d'un jeu 2 alors l'espérance de gain au jeu 1 est forcément supérieure à celle du jeu 2
Est-ce le cas ?
Si c'est le cas, il est facile de te montrer que c'est faux par un exemple simple.
Si ce n'est pas le cas, les résultats que nous avons obtenus ne sont pas aberrants et je vais donc en terminer avec ce sujet.
Ces résultats, je les ai donnés dès le 5 décembre !
Ils étaient corrects.
Je pense qu'il serait bon que tu réédites ou corriges les propos suivants que tu as tenu depuis plus de 2 semaines:
Glups, tu t'amuses bien avec Excel ?
Il te faudrait un peu plus de rigueur.Je fais un reproche à Glups qui ne sait pas développer correctement.
De plus, il veut se faire passer pour un expert alors qu'il ne maitrise pas du tout les probabilités !Tu me fais penser à un barbouilleur qui prend un saut de peinture et le lance contre un mur.
Ensuite, il dit que c'est de l'art et que le simple mortel ne comprend rien à ce qui le dépasse.Donc déjà ton résultat de 36,5% est faux car le bon résultat est 41,190%.
Ne pas confondre l'espérance qui est une moyenne et la probabilité, ce que tu fais régulièrement !Mais qu'est-ce que tu viens de nous inventer ?
Maintenant il y a trois retours au jeu de la rouletteTon calcul de l'espérance mathématique est faux
20/12/2012 9:36 am
Qu'est-ce que tu essayes de me faire dire ?
D'abord, j'ai cru que tu ne parlais que de la loi binomiale, d'où ma réponse (celle de l'encadré) !
Ensuite je n'ai jamais dit ce que tu crois avoir compris.
Je dis que si le jeu de Pile ou Face donne un résultat pour la probabilité du gain, tu ne peux pas avoir une probabilité de gain supérieure pour un jeu ayant une espérance mathématique négative. Attention, cela est vrai que si tu as les mêmes bases de comparaisons, ce qui n'est pas le cas ici, si tu compares ton résultat issu de la loi multinomiale, avec l'autre résultat du jeu de Pile ou Face issu de la loi binomiale.
@+
20/12/2012 10:38 am
Ensuite je n'ai jamais dit ce que tu crois avoir compris.
Ah bon, tu me rassures !
Je dis que si le jeu de Pile ou Face donne un résultat pour la probabilité du gain, tu ne peux pas avoir une probabilité de gain supérieure pour un jeu ayant une espérance mathématique négative.
Ok, tu parles du jeu de pile ou face où il y a 2 retours et où on utilise la loi binomiale.
Il y a 41.19% de cycles gagnants de 20 lancers et l'espérance de gain est 0
Nous sommes d'accord?
Tu penses qu'il n'existe pas de jeu à 2 retours où l'espérance est négative et la probabilité de cycles gagnants supérieure à 41.19% ?
Il en existe des tonnes, je t'en fabrique à la pelle, quand tu veux !
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