[{"data":1,"prerenderedAt":1838},["ShallowReactive",2],{"article-alternates":3,"article-\u002Ffr\u002Fgaming\u002Foptimisation-prix-bayesienne-f2p-mobile":13},{"i18nKey":4,"paths":5},"gaming-002-2026-06",{"de":6,"en":7,"es":8,"fr":9,"it":10,"ru":11,"tr":12},"\u002Fde\u002Fgaming\u002Fbayesian-price-optimization-mobile-f2p","\u002Fen\u002Fgaming\u002Fbayesian-price-optimization-mobile-f2p","\u002Fes\u002Fgaming\u002Foptimizacion-de-precios-bayesiana-f2p-movil","\u002Ffr\u002Fgaming\u002Foptimisation-prix-bayesienne-f2p-mobile","\u002Fit\u002Fgaming\u002Fottimizzazione-del-prezzo-bayesiana-f2p-mobile","\u002Fru\u002Fgaming\u002Fbayesovskaya-optimizaciya-ceny-v-mobilnom-f2p","\u002Ftr\u002Fgaming\u002Fmobile-f2pde-bayesian-price-optimization",{"_path":9,"_dir":14,"_draft":15,"_partial":15,"_locale":16,"title":17,"description":18,"publishedAt":19,"modifiedAt":19,"category":14,"i18nKey":4,"tags":20,"readingTime":26,"author":27,"body":28,"_type":1832,"_id":1833,"_source":1834,"_file":1835,"_stem":1836,"_extension":1837},"gaming",false,"","Optimisation Bayésienne des Prix en F2P Mobile","Optimisez vos tests IAP avec l'estimation posterior. Segmentation, durée de test, trade-offs de conversion — framework éprouvé pour augmenter le revenue F2P.","2026-06-24",[21,22,23,24,25],"monetisation-f2p","optimisation-bayesienne","test-iap","jeux-mobiles","strategie-tarifaire",8,"Roibase",{"type":29,"children":30,"toc":1825},"root",[31,54,61,79,97,115,121,132,143,167,189,194,681,686,692,703,749,791,808,813,1395,1418,1424,1435,1451,1676,1681,1696,1712,1718,1729,1774,1809,1819],{"type":32,"tag":33,"props":34,"children":35},"element","p",{},[36,39,45,47,52],{"type":37,"value":38},"text","Dans les jeux F2P mobiles, l'optimisation tarifaire fonctionne encore selon la logique des tests A\u002FB classiques : deux price points, 7-14 jours, on choisit le gagnant. Mais quand le taux de conversion passe de 2,8 % à 3,1 %, s'agit-il vraiment d'un gain, ou avez-vous sacrifié le segment des ",{"type":32,"tag":40,"props":41,"children":42},"em",{},[43],{"type":37,"value":44},"whales",{"type":37,"value":46}," en réduisant le LTV global ? Le test A\u002FB fréquentiste répond « quel variant a gagné », mais pas « quel prix, pour quel segment, à quel moment ? ». L'optimisation Bayésienne des prix comble cette lacune : en mettant à jour votre échelle IAP sur la distribution ",{"type":32,"tag":40,"props":48,"children":49},{},[50],{"type":37,"value":51},"posterior",{"type":37,"value":53},", vous optimisez simultanément la conversion et le revenue segment-spécifique.",{"type":32,"tag":55,"props":56,"children":58},"h2",{"id":57},"pourquoi-le-test-ab-fréquentiste-est-insuffisant-en-f2p",[59],{"type":37,"value":60},"Pourquoi le Test A\u002FB Fréquentiste Est Insuffisant en F2P",{"type":32,"tag":33,"props":62,"children":63},{},[64,66,71,73,77],{"type":37,"value":65},"Le test A\u002FB classique repose sur deux hypothèses : (1) le comportement utilisateur est stable pendant la durée du test, (2) le variant gagnant est optimal pour tous les segments. En F2P, les deux sont faux. Le comportement change drastiquement à J1, J7, et J30 — le même prix performera différemment selon les cohortes de rétention. Prenez cet exemple : le starter pack à 4,99 $ affiche une conversion de 3,5 %, le variant à 9,99 $ de 2,8 % — logique A\u002FB, le 4,99 $ gagne. Pourtant, l'analyse LTV sur 30 jours révèle que le variant à 9,99 $ génère 42 % de ",{"type":32,"tag":40,"props":67,"children":68},{},[69],{"type":37,"value":70},"lifetime spend",{"type":37,"value":72}," supplémentaire chez les ",{"type":32,"tag":40,"props":74,"children":75},{},[76],{"type":37,"value":44},{"type":37,"value":78}," (top 5 % des dépensiers). Le test fréquentiste ne voit pas cette dynamique car il n'estime pas les posteriors par segment.",{"type":32,"tag":33,"props":80,"children":81},{},[82,84,88,90,95],{"type":37,"value":83},"Le second problème : la durée fixe du test. Un A\u002FB dure 14 jours, décision prise — mais vous n'avez peut-être pas atteint la puissance statistique requise. Avec Bayes, la distribution ",{"type":32,"tag":40,"props":85,"children":86},{},[87],{"type":37,"value":51},{"type":37,"value":89}," se met à jour en continu ; vous pouvez arrêter tôt si la confiance est suffisante, ou prolonger si le résultat est ambigu. C'est critique en F2P car le calendrier ",{"type":32,"tag":40,"props":91,"children":92},{},[93],{"type":37,"value":94},"live ops",{"type":37,"value":96}," n'attend pas deux semaines — un nouvel événement arrive, le contexte change, votre test devient obsolète.",{"type":32,"tag":33,"props":98,"children":99},{},[100,102,106,108,113],{"type":37,"value":101},"Troisième problème : la logique binaire. Le test fréquentiste dit « A gagne », mais en F2P, il n'y a pas de gagnant absolu — le bon prix est le bon prix pour le bon segment au bon moment. L'optimisation Bayésienne, via l'estimation ",{"type":32,"tag":40,"props":103,"children":104},{},[105],{"type":37,"value":51},{"type":37,"value":107},", fournit pour chaque segment la fourchette de prix optimale, ce qui alimente un moteur de ",{"type":32,"tag":40,"props":109,"children":110},{},[111],{"type":37,"value":112},"dynamic pricing",{"type":37,"value":114},".",{"type":32,"tag":55,"props":116,"children":118},{"id":117},"test-bayésien-de-léchelle-iap-optimisation-itérative-par-estimation-posterior",[119],{"type":37,"value":120},"Test Bayésien de l'Échelle IAP : Optimisation Itérative par Estimation Posterior",{"type":32,"tag":33,"props":122,"children":123},{},[124,126,130],{"type":37,"value":125},"L'optimisation Bayésienne des prix fonctionne sur trois couches : prior (données antérieures + connaissance métier), fonction de vraisemblance (conversion data actuelle), distribution ",{"type":32,"tag":40,"props":127,"children":128},{},[129],{"type":37,"value":51},{"type":37,"value":131}," (leur produit — croyance mise à jour). Voici comment l'appliquer aux tests IAP :",{"type":32,"tag":33,"props":133,"children":134},{},[135,141],{"type":32,"tag":136,"props":137,"children":138},"strong",{},[139],{"type":37,"value":140},"Établir le prior :",{"type":37,"value":142}," Vous disposez de données de tests prix antérieurs. Par exemple, pour un IAP à 4,99 $, votre prior de taux de conversion est Beta(120, 3800) — 120 conversions, 3800 impressions. C'est la baseline de votre jeu. Pour un nouveau test avec un prix à 6,99 $, calibrez le prior selon la connaissance métier : une hausse de 40 % du prix entraîne généralement une baisse de 25-35 % de la conversion (élasticité entre -0,6 et -0,9). Votre prior pourrait être Beta(80, 3840).",{"type":32,"tag":33,"props":144,"children":145},{},[146,151,153,157,159,165],{"type":32,"tag":136,"props":147,"children":148},{},[149],{"type":37,"value":150},"Mise à jour par vraisemblance :",{"type":37,"value":152}," Le test démarre, chaque jour apporte de nouvelles données de conversion. Le framework Bayésien met à jour le ",{"type":32,"tag":40,"props":154,"children":155},{},[156],{"type":37,"value":51},{"type":37,"value":158}," quotidiennement. Au jour 3, le variant à 6,99 $ affiche 45 conversions sur 1200 impressions — vraisemblance Beta(45, 1155). Posterior = prior × vraisemblance = Beta(125, 4995). Vous obtenez une estimation du taux de conversion actuel : 125\u002F(125+4995) ≈ 2,44 %. L'important : ce n'est pas qu'une estimée ponctuelle, c'est une distribution — intervalle de crédibilité à 95 % : ",{"type":32,"tag":160,"props":161,"children":162},"span",{},[163],{"type":37,"value":164},"2,1 %, 2,8 %",{"type":37,"value":166},". Autrement dit, la conversion se situe entre 2,1 % et 2,8 % avec 95 % de probabilité.",{"type":32,"tag":33,"props":168,"children":169},{},[170,175,177,181,183,187],{"type":32,"tag":136,"props":171,"children":172},{},[173],{"type":37,"value":174},"Allocation dynamique par Thompson Sampling :",{"type":37,"value":176}," En A\u002FB classique, le trafic est réparti 50-50. Avec l'optimisation Bayésienne, vous utilisez Thompson Sampling : à chaque impression, tirez un échantillon de la distribution ",{"type":32,"tag":40,"props":178,"children":179},{},[180],{"type":37,"value":51},{"type":37,"value":182},", présentez le variant avec le revenue attendu le plus élevé. Ainsi, au fur et à mesure du test, le trafic bascule vers le meilleur variant, sans jamais arrêter l'exploration. C'est crucial en F2P car les ",{"type":32,"tag":40,"props":184,"children":185},{},[186],{"type":37,"value":44},{"type":37,"value":188}," sont peu nombreux mais très précieux — les écarter trop tôt signifie les perdre.",{"type":32,"tag":33,"props":190,"children":191},{},[192],{"type":37,"value":193},"Exemple de code (Python + PyMC) :",{"type":32,"tag":195,"props":196,"children":200},"pre",{"className":197,"code":198,"language":199,"meta":16,"style":16},"language-python shiki shiki-themes github-dark","import pymc as pm\nimport numpy as np\n\n# Prior : conversion IAP à 4,99 $\nprior_alpha_499 = 120\nprior_beta_499 = 3800\n\n# Variant à 6,99 $ — nouveau test\nconversions_699 = 45\nimpressions_699 = 1200\n\nwith pm.Model() as price_test:\n    # Mise à jour du posterior\n    conv_rate_699 = pm.Beta('conv_rate_699', \n                             alpha=prior_alpha_499*0.7 + conversions_699,\n                             beta=prior_beta_499*1.0 + (impressions_699 - conversions_699))\n    \n    # Attente de revenue (prix IAP × conversion)\n    expected_revenue = conv_rate_699 * 6.99\n    \n    # Sampling\n    trace = pm.sample(2000, return_inferencedata=True)\n\n# Intervalle de crédibilité 95 %\nprint(pm.summary(trace, var_names=['conv_rate_699']))\n","python",[201],{"type":32,"tag":202,"props":203,"children":204},"code",{"__ignoreMap":16},[205,232,254,264,274,294,312,320,328,346,364,372,395,404,433,472,518,527,536,563,571,580,627,635,644],{"type":32,"tag":160,"props":206,"children":209},{"class":207,"line":208},"line",1,[210,216,222,227],{"type":32,"tag":160,"props":211,"children":213},{"style":212},"--shiki-default:#F97583",[214],{"type":37,"value":215},"import",{"type":32,"tag":160,"props":217,"children":219},{"style":218},"--shiki-default:#E1E4E8",[220],{"type":37,"value":221}," pymc ",{"type":32,"tag":160,"props":223,"children":224},{"style":212},[225],{"type":37,"value":226},"as",{"type":32,"tag":160,"props":228,"children":229},{"style":218},[230],{"type":37,"value":231}," pm\n",{"type":32,"tag":160,"props":233,"children":235},{"class":207,"line":234},2,[236,240,245,249],{"type":32,"tag":160,"props":237,"children":238},{"style":212},[239],{"type":37,"value":215},{"type":32,"tag":160,"props":241,"children":242},{"style":218},[243],{"type":37,"value":244}," numpy ",{"type":32,"tag":160,"props":246,"children":247},{"style":212},[248],{"type":37,"value":226},{"type":32,"tag":160,"props":250,"children":251},{"style":218},[252],{"type":37,"value":253}," np\n",{"type":32,"tag":160,"props":255,"children":257},{"class":207,"line":256},3,[258],{"type":32,"tag":160,"props":259,"children":261},{"emptyLinePlaceholder":260},true,[262],{"type":37,"value":263},"\n",{"type":32,"tag":160,"props":265,"children":267},{"class":207,"line":266},4,[268],{"type":32,"tag":160,"props":269,"children":271},{"style":270},"--shiki-default:#6A737D",[272],{"type":37,"value":273},"# Prior : conversion IAP à 4,99 $\n",{"type":32,"tag":160,"props":275,"children":277},{"class":207,"line":276},5,[278,283,288],{"type":32,"tag":160,"props":279,"children":280},{"style":218},[281],{"type":37,"value":282},"prior_alpha_499 ",{"type":32,"tag":160,"props":284,"children":285},{"style":212},[286],{"type":37,"value":287},"=",{"type":32,"tag":160,"props":289,"children":291},{"style":290},"--shiki-default:#79B8FF",[292],{"type":37,"value":293}," 120\n",{"type":32,"tag":160,"props":295,"children":297},{"class":207,"line":296},6,[298,303,307],{"type":32,"tag":160,"props":299,"children":300},{"style":218},[301],{"type":37,"value":302},"prior_beta_499 ",{"type":32,"tag":160,"props":304,"children":305},{"style":212},[306],{"type":37,"value":287},{"type":32,"tag":160,"props":308,"children":309},{"style":290},[310],{"type":37,"value":311}," 3800\n",{"type":32,"tag":160,"props":313,"children":315},{"class":207,"line":314},7,[316],{"type":32,"tag":160,"props":317,"children":318},{"emptyLinePlaceholder":260},[319],{"type":37,"value":263},{"type":32,"tag":160,"props":321,"children":322},{"class":207,"line":26},[323],{"type":32,"tag":160,"props":324,"children":325},{"style":270},[326],{"type":37,"value":327},"# Variant à 6,99 $ — nouveau test\n",{"type":32,"tag":160,"props":329,"children":331},{"class":207,"line":330},9,[332,337,341],{"type":32,"tag":160,"props":333,"children":334},{"style":218},[335],{"type":37,"value":336},"conversions_699 ",{"type":32,"tag":160,"props":338,"children":339},{"style":212},[340],{"type":37,"value":287},{"type":32,"tag":160,"props":342,"children":343},{"style":290},[344],{"type":37,"value":345}," 45\n",{"type":32,"tag":160,"props":347,"children":349},{"class":207,"line":348},10,[350,355,359],{"type":32,"tag":160,"props":351,"children":352},{"style":218},[353],{"type":37,"value":354},"impressions_699 ",{"type":32,"tag":160,"props":356,"children":357},{"style":212},[358],{"type":37,"value":287},{"type":32,"tag":160,"props":360,"children":361},{"style":290},[362],{"type":37,"value":363}," 1200\n",{"type":32,"tag":160,"props":365,"children":367},{"class":207,"line":366},11,[368],{"type":32,"tag":160,"props":369,"children":370},{"emptyLinePlaceholder":260},[371],{"type":37,"value":263},{"type":32,"tag":160,"props":373,"children":375},{"class":207,"line":374},12,[376,381,386,390],{"type":32,"tag":160,"props":377,"children":378},{"style":212},[379],{"type":37,"value":380},"with",{"type":32,"tag":160,"props":382,"children":383},{"style":218},[384],{"type":37,"value":385}," pm.Model() ",{"type":32,"tag":160,"props":387,"children":388},{"style":212},[389],{"type":37,"value":226},{"type":32,"tag":160,"props":391,"children":392},{"style":218},[393],{"type":37,"value":394}," price_test:\n",{"type":32,"tag":160,"props":396,"children":398},{"class":207,"line":397},13,[399],{"type":32,"tag":160,"props":400,"children":401},{"style":270},[402],{"type":37,"value":403},"    # Mise à jour du posterior\n",{"type":32,"tag":160,"props":405,"children":407},{"class":207,"line":406},14,[408,413,417,422,428],{"type":32,"tag":160,"props":409,"children":410},{"style":218},[411],{"type":37,"value":412},"    conv_rate_699 ",{"type":32,"tag":160,"props":414,"children":415},{"style":212},[416],{"type":37,"value":287},{"type":32,"tag":160,"props":418,"children":419},{"style":218},[420],{"type":37,"value":421}," pm.Beta(",{"type":32,"tag":160,"props":423,"children":425},{"style":424},"--shiki-default:#9ECBFF",[426],{"type":37,"value":427},"'conv_rate_699'",{"type":32,"tag":160,"props":429,"children":430},{"style":218},[431],{"type":37,"value":432},", \n",{"type":32,"tag":160,"props":434,"children":436},{"class":207,"line":435},15,[437,443,447,452,457,462,467],{"type":32,"tag":160,"props":438,"children":440},{"style":439},"--shiki-default:#FFAB70",[441],{"type":37,"value":442},"                             alpha",{"type":32,"tag":160,"props":444,"children":445},{"style":212},[446],{"type":37,"value":287},{"type":32,"tag":160,"props":448,"children":449},{"style":218},[450],{"type":37,"value":451},"prior_alpha_499",{"type":32,"tag":160,"props":453,"children":454},{"style":212},[455],{"type":37,"value":456},"*",{"type":32,"tag":160,"props":458,"children":459},{"style":290},[460],{"type":37,"value":461},"0.7",{"type":32,"tag":160,"props":463,"children":464},{"style":212},[465],{"type":37,"value":466}," +",{"type":32,"tag":160,"props":468,"children":469},{"style":218},[470],{"type":37,"value":471}," conversions_699,\n",{"type":32,"tag":160,"props":473,"children":475},{"class":207,"line":474},16,[476,481,485,490,494,499,503,508,513],{"type":32,"tag":160,"props":477,"children":478},{"style":439},[479],{"type":37,"value":480},"                             beta",{"type":32,"tag":160,"props":482,"children":483},{"style":212},[484],{"type":37,"value":287},{"type":32,"tag":160,"props":486,"children":487},{"style":218},[488],{"type":37,"value":489},"prior_beta_499",{"type":32,"tag":160,"props":491,"children":492},{"style":212},[493],{"type":37,"value":456},{"type":32,"tag":160,"props":495,"children":496},{"style":290},[497],{"type":37,"value":498},"1.0",{"type":32,"tag":160,"props":500,"children":501},{"style":212},[502],{"type":37,"value":466},{"type":32,"tag":160,"props":504,"children":505},{"style":218},[506],{"type":37,"value":507}," (impressions_699 ",{"type":32,"tag":160,"props":509,"children":510},{"style":212},[511],{"type":37,"value":512},"-",{"type":32,"tag":160,"props":514,"children":515},{"style":218},[516],{"type":37,"value":517}," conversions_699))\n",{"type":32,"tag":160,"props":519,"children":521},{"class":207,"line":520},17,[522],{"type":32,"tag":160,"props":523,"children":524},{"style":218},[525],{"type":37,"value":526},"    \n",{"type":32,"tag":160,"props":528,"children":530},{"class":207,"line":529},18,[531],{"type":32,"tag":160,"props":532,"children":533},{"style":270},[534],{"type":37,"value":535},"    # Attente de revenue (prix IAP × conversion)\n",{"type":32,"tag":160,"props":537,"children":539},{"class":207,"line":538},19,[540,545,549,554,558],{"type":32,"tag":160,"props":541,"children":542},{"style":218},[543],{"type":37,"value":544},"    expected_revenue ",{"type":32,"tag":160,"props":546,"children":547},{"style":212},[548],{"type":37,"value":287},{"type":32,"tag":160,"props":550,"children":551},{"style":218},[552],{"type":37,"value":553}," conv_rate_699 ",{"type":32,"tag":160,"props":555,"children":556},{"style":212},[557],{"type":37,"value":456},{"type":32,"tag":160,"props":559,"children":560},{"style":290},[561],{"type":37,"value":562}," 6.99\n",{"type":32,"tag":160,"props":564,"children":566},{"class":207,"line":565},20,[567],{"type":32,"tag":160,"props":568,"children":569},{"style":218},[570],{"type":37,"value":526},{"type":32,"tag":160,"props":572,"children":574},{"class":207,"line":573},21,[575],{"type":32,"tag":160,"props":576,"children":577},{"style":270},[578],{"type":37,"value":579},"    # Sampling\n",{"type":32,"tag":160,"props":581,"children":583},{"class":207,"line":582},22,[584,589,593,598,603,608,613,617,622],{"type":32,"tag":160,"props":585,"children":586},{"style":218},[587],{"type":37,"value":588},"    trace ",{"type":32,"tag":160,"props":590,"children":591},{"style":212},[592],{"type":37,"value":287},{"type":32,"tag":160,"props":594,"children":595},{"style":218},[596],{"type":37,"value":597}," pm.sample(",{"type":32,"tag":160,"props":599,"children":600},{"style":290},[601],{"type":37,"value":602},"2000",{"type":32,"tag":160,"props":604,"children":605},{"style":218},[606],{"type":37,"value":607},", ",{"type":32,"tag":160,"props":609,"children":610},{"style":439},[611],{"type":37,"value":612},"return_inferencedata",{"type":32,"tag":160,"props":614,"children":615},{"style":212},[616],{"type":37,"value":287},{"type":32,"tag":160,"props":618,"children":619},{"style":290},[620],{"type":37,"value":621},"True",{"type":32,"tag":160,"props":623,"children":624},{"style":218},[625],{"type":37,"value":626},")\n",{"type":32,"tag":160,"props":628,"children":630},{"class":207,"line":629},23,[631],{"type":32,"tag":160,"props":632,"children":633},{"emptyLinePlaceholder":260},[634],{"type":37,"value":263},{"type":32,"tag":160,"props":636,"children":638},{"class":207,"line":637},24,[639],{"type":32,"tag":160,"props":640,"children":641},{"style":270},[642],{"type":37,"value":643},"# Intervalle de crédibilité 95 %\n",{"type":32,"tag":160,"props":645,"children":647},{"class":207,"line":646},25,[648,653,658,663,667,672,676],{"type":32,"tag":160,"props":649,"children":650},{"style":290},[651],{"type":37,"value":652},"print",{"type":32,"tag":160,"props":654,"children":655},{"style":218},[656],{"type":37,"value":657},"(pm.summary(trace, ",{"type":32,"tag":160,"props":659,"children":660},{"style":439},[661],{"type":37,"value":662},"var_names",{"type":32,"tag":160,"props":664,"children":665},{"style":212},[666],{"type":37,"value":287},{"type":32,"tag":160,"props":668,"children":669},{"style":218},[670],{"type":37,"value":671},"[",{"type":32,"tag":160,"props":673,"children":674},{"style":424},[675],{"type":37,"value":427},{"type":32,"tag":160,"props":677,"children":678},{"style":218},[679],{"type":37,"value":680},"]))\n",{"type":32,"tag":33,"props":682,"children":683},{},[684],{"type":37,"value":685},"Cette approche vous dit « au jour 3, la conversion à 6,99 $ est entre 2,1 % et 2,8 %, revenue attendu 0,17 $\u002Futilisateur » — et l'intervalle se réduit à mesure que le test progresse.",{"type":32,"tag":55,"props":687,"children":689},{"id":688},"optimisation-par-segment-whale-dolphin-minnow",[690],{"type":37,"value":691},"Optimisation par Segment : Whale, Dolphin, Minnow",{"type":32,"tag":33,"props":693,"children":694},{},[695,697,701],{"type":37,"value":696},"En F2P, tous les utilisateurs ne réagissent pas au même prix de la même façon. Sans estimation ",{"type":32,"tag":40,"props":698,"children":699},{},[700],{"type":37,"value":51},{"type":37,"value":702}," par segment, vous optimisez la conversion moyenne mais sacrifiez le revenue segment-spécifique. Trois segments clés :",{"type":32,"tag":33,"props":704,"children":705},{},[706,711,713,717,719,723,725,729,731,735,737,741,743,747],{"type":32,"tag":136,"props":707,"children":708},{},[709],{"type":37,"value":710},"Whale (top 5 % des dépensiers) :",{"type":37,"value":712}," LTV > 200 $, 8+ IAP, rétention D30 > 85 %. Peu sensible au prix — un IAP à 9,99 $ avec 15 % moins de conversion peut quand même générer 60 % plus de ",{"type":32,"tag":40,"props":714,"children":715},{},[716],{"type":37,"value":70},{"type":37,"value":718},". L'estimation ",{"type":32,"tag":40,"props":720,"children":721},{},[722],{"type":37,"value":51},{"type":37,"value":724}," par segment répond : « Le prix de 9,99 $ est-il optimal pour les ",{"type":32,"tag":40,"props":726,"children":727},{},[728],{"type":37,"value":44},{"type":37,"value":730},", ou 14,99 $ génère-t-il un meilleur LTV ? » Vous isolez les conversions des ",{"type":32,"tag":40,"props":732,"children":733},{},[734],{"type":37,"value":44},{"type":37,"value":736}," et mettez à jour la distribution ",{"type":32,"tag":40,"props":738,"children":739},{},[740],{"type":37,"value":51},{"type":37,"value":742}," whale-spécifique. Exemple : conversion globale à 9,99 $ = 2,8 %, mais chez les ",{"type":32,"tag":40,"props":744,"children":745},{},[746],{"type":37,"value":44},{"type":37,"value":748}," = 6,2 % — testez des prix plus élevés pour ce segment.",{"type":32,"tag":33,"props":750,"children":751},{},[752,757,759,764,766,770,772,776,778,782,784,789],{"type":32,"tag":136,"props":753,"children":754},{},[755],{"type":37,"value":756},"Dolphin (25 % intermédiaires) :",{"type":37,"value":758}," LTV 20-50 $, 2-4 IAP, rétention D30 50-70 %. Sensibilité au prix modérée. Le test Bayésien identifie généralement la fourchette optimale pour les ",{"type":32,"tag":40,"props":760,"children":761},{},[762],{"type":37,"value":763},"dolphins",{"type":37,"value":765}," : entre 4,99 $ et 6,99 $. La distribution ",{"type":32,"tag":40,"props":767,"children":768},{},[769],{"type":37,"value":51},{"type":37,"value":771}," peut être bimodale — certains ",{"type":32,"tag":40,"props":773,"children":774},{},[775],{"type":37,"value":763},{"type":37,"value":777}," se comportent comme des ",{"type":32,"tag":40,"props":779,"children":780},{},[781],{"type":37,"value":44},{"type":37,"value":783}," (pics de dépense le weekend), d'autres glissent vers le segment ",{"type":32,"tag":40,"props":785,"children":786},{},[787],{"type":37,"value":788},"minnow",{"type":37,"value":790},". Un raffinement de segmentation est nécessaire.",{"type":32,"tag":33,"props":792,"children":793},{},[794,799,801,806],{"type":32,"tag":136,"props":795,"children":796},{},[797],{"type":37,"value":798},"Minnow (70 % restants) :",{"type":37,"value":800}," LTV \u003C 10 $, majoritairement non-payeurs. Très sensibles au prix — même 2,99 $ vs 4,99 $ change la conversion de 40 %. Le test Bayésien révèle généralement : le prix le plus bas (0,99-1,99 $) maximise la conversion mais le revenue total chute. Stratégie : utilisez 0,99 $ comme premier IAP pour convertir les ",{"type":32,"tag":40,"props":802,"children":803},{},[804],{"type":37,"value":805},"minnows",{"type":37,"value":807},", puis dirigez-les vers l'échelle 4,99 $.",{"type":32,"tag":33,"props":809,"children":810},{},[811],{"type":37,"value":812},"Modèle Bayésien hiérarchique pour estimation par segment :",{"type":32,"tag":195,"props":814,"children":816},{"className":197,"code":815,"language":199,"meta":16,"style":16},"with pm.Model() as hierarchical_price:\n    # Prior global de conversion\n    global_alpha = pm.Gamma('global_alpha', alpha=2, beta=0.1)\n    global_beta = pm.Gamma('global_beta', alpha=2, beta=0.1)\n    \n    # Conversion segment-spécifique\n    conv_whale = pm.Beta('conv_whale', alpha=global_alpha, beta=global_beta)\n    conv_dolphin = pm.Beta('conv_dolphin', alpha=global_alpha, beta=global_beta)\n    conv_minnow = pm.Beta('conv_minnow', alpha=global_alpha, beta=global_beta)\n    \n    # Vraisemblance (données segment)\n    whale_obs = pm.Binomial('whale_obs', n=200, p=conv_whale, observed=12)\n    dolphin_obs = pm.Binomial('dolphin_obs', n=800, p=conv_dolphin, observed=24)\n    minnow_obs = pm.Binomial('minnow_obs', n=3000, p=conv_minnow, observed=60)\n    \n    trace = pm.sample(3000)\n",[817],{"type":32,"tag":202,"props":818,"children":819},{"__ignoreMap":16},[820,840,848,910,967,974,982,1033,1082,1131,1138,1146,1221,1293,1365,1372],{"type":32,"tag":160,"props":821,"children":822},{"class":207,"line":208},[823,827,831,835],{"type":32,"tag":160,"props":824,"children":825},{"style":212},[826],{"type":37,"value":380},{"type":32,"tag":160,"props":828,"children":829},{"style":218},[830],{"type":37,"value":385},{"type":32,"tag":160,"props":832,"children":833},{"style":212},[834],{"type":37,"value":226},{"type":32,"tag":160,"props":836,"children":837},{"style":218},[838],{"type":37,"value":839}," hierarchical_price:\n",{"type":32,"tag":160,"props":841,"children":842},{"class":207,"line":234},[843],{"type":32,"tag":160,"props":844,"children":845},{"style":270},[846],{"type":37,"value":847},"    # Prior global de conversion\n",{"type":32,"tag":160,"props":849,"children":850},{"class":207,"line":256},[851,856,860,865,870,874,879,883,888,892,897,901,906],{"type":32,"tag":160,"props":852,"children":853},{"style":218},[854],{"type":37,"value":855},"    global_alpha ",{"type":32,"tag":160,"props":857,"children":858},{"style":212},[859],{"type":37,"value":287},{"type":32,"tag":160,"props":861,"children":862},{"style":218},[863],{"type":37,"value":864}," pm.Gamma(",{"type":32,"tag":160,"props":866,"children":867},{"style":424},[868],{"type":37,"value":869},"'global_alpha'",{"type":32,"tag":160,"props":871,"children":872},{"style":218},[873],{"type":37,"value":607},{"type":32,"tag":160,"props":875,"children":876},{"style":439},[877],{"type":37,"value":878},"alpha",{"type":32,"tag":160,"props":880,"children":881},{"style":212},[882],{"type":37,"value":287},{"type":32,"tag":160,"props":884,"children":885},{"style":290},[886],{"type":37,"value":887},"2",{"type":32,"tag":160,"props":889,"children":890},{"style":218},[891],{"type":37,"value":607},{"type":32,"tag":160,"props":893,"children":894},{"style":439},[895],{"type":37,"value":896},"beta",{"type":32,"tag":160,"props":898,"children":899},{"style":212},[900],{"type":37,"value":287},{"type":32,"tag":160,"props":902,"children":903},{"style":290},[904],{"type":37,"value":905},"0.1",{"type":32,"tag":160,"props":907,"children":908},{"style":218},[909],{"type":37,"value":626},{"type":32,"tag":160,"props":911,"children":912},{"class":207,"line":266},[913,918,922,926,931,935,939,943,947,951,955,959,963],{"type":32,"tag":160,"props":914,"children":915},{"style":218},[916],{"type":37,"value":917},"    global_beta ",{"type":32,"tag":160,"props":919,"children":920},{"style":212},[921],{"type":37,"value":287},{"type":32,"tag":160,"props":923,"children":924},{"style":218},[925],{"type":37,"value":864},{"type":32,"tag":160,"props":927,"children":928},{"style":424},[929],{"type":37,"value":930},"'global_beta'",{"type":32,"tag":160,"props":932,"children":933},{"style":218},[934],{"type":37,"value":607},{"type":32,"tag":160,"props":936,"children":937},{"style":439},[938],{"type":37,"value":878},{"type":32,"tag":160,"props":940,"children":941},{"style":212},[942],{"type":37,"value":287},{"type":32,"tag":160,"props":944,"children":945},{"style":290},[946],{"type":37,"value":887},{"type":32,"tag":160,"props":948,"children":949},{"style":218},[950],{"type":37,"value":607},{"type":32,"tag":160,"props":952,"children":953},{"style":439},[954],{"type":37,"value":896},{"type":32,"tag":160,"props":956,"children":957},{"style":212},[958],{"type":37,"value":287},{"type":32,"tag":160,"props":960,"children":961},{"style":290},[962],{"type":37,"value":905},{"type":32,"tag":160,"props":964,"children":965},{"style":218},[966],{"type":37,"value":626},{"type":32,"tag":160,"props":968,"children":969},{"class":207,"line":276},[970],{"type":32,"tag":160,"props":971,"children":972},{"style":218},[973],{"type":37,"value":526},{"type":32,"tag":160,"props":975,"children":976},{"class":207,"line":296},[977],{"type":32,"tag":160,"props":978,"children":979},{"style":270},[980],{"type":37,"value":981},"    # Conversion segment-spécifique\n",{"type":32,"tag":160,"props":983,"children":984},{"class":207,"line":314},[985,990,994,998,1003,1007,1011,1015,1020,1024,1028],{"type":32,"tag":160,"props":986,"children":987},{"style":218},[988],{"type":37,"value":989},"    conv_whale ",{"type":32,"tag":160,"props":991,"children":992},{"style":212},[993],{"type":37,"value":287},{"type":32,"tag":160,"props":995,"children":996},{"style":218},[997],{"type":37,"value":421},{"type":32,"tag":160,"props":999,"children":1000},{"style":424},[1001],{"type":37,"value":1002},"'conv_whale'",{"type":32,"tag":160,"props":1004,"children":1005},{"style":218},[1006],{"type":37,"value":607},{"type":32,"tag":160,"props":1008,"children":1009},{"style":439},[1010],{"type":37,"value":878},{"type":32,"tag":160,"props":1012,"children":1013},{"style":212},[1014],{"type":37,"value":287},{"type":32,"tag":160,"props":1016,"children":1017},{"style":218},[1018],{"type":37,"value":1019},"global_alpha, ",{"type":32,"tag":160,"props":1021,"children":1022},{"style":439},[1023],{"type":37,"value":896},{"type":32,"tag":160,"props":1025,"children":1026},{"style":212},[1027],{"type":37,"value":287},{"type":32,"tag":160,"props":1029,"children":1030},{"style":218},[1031],{"type":37,"value":1032},"global_beta)\n",{"type":32,"tag":160,"props":1034,"children":1035},{"class":207,"line":26},[1036,1041,1045,1049,1054,1058,1062,1066,1070,1074,1078],{"type":32,"tag":160,"props":1037,"children":1038},{"style":218},[1039],{"type":37,"value":1040},"    conv_dolphin ",{"type":32,"tag":160,"props":1042,"children":1043},{"style":212},[1044],{"type":37,"value":287},{"type":32,"tag":160,"props":1046,"children":1047},{"style":218},[1048],{"type":37,"value":421},{"type":32,"tag":160,"props":1050,"children":1051},{"style":424},[1052],{"type":37,"value":1053},"'conv_dolphin'",{"type":32,"tag":160,"props":1055,"children":1056},{"style":218},[1057],{"type":37,"value":607},{"type":32,"tag":160,"props":1059,"children":1060},{"style":439},[1061],{"type":37,"value":878},{"type":32,"tag":160,"props":1063,"children":1064},{"style":212},[1065],{"type":37,"value":287},{"type":32,"tag":160,"props":1067,"children":1068},{"style":218},[1069],{"type":37,"value":1019},{"type":32,"tag":160,"props":1071,"children":1072},{"style":439},[1073],{"type":37,"value":896},{"type":32,"tag":160,"props":1075,"children":1076},{"style":212},[1077],{"type":37,"value":287},{"type":32,"tag":160,"props":1079,"children":1080},{"style":218},[1081],{"type":37,"value":1032},{"type":32,"tag":160,"props":1083,"children":1084},{"class":207,"line":330},[1085,1090,1094,1098,1103,1107,1111,1115,1119,1123,1127],{"type":32,"tag":160,"props":1086,"children":1087},{"style":218},[1088],{"type":37,"value":1089},"    conv_minnow ",{"type":32,"tag":160,"props":1091,"children":1092},{"style":212},[1093],{"type":37,"value":287},{"type":32,"tag":160,"props":1095,"children":1096},{"style":218},[1097],{"type":37,"value":421},{"type":32,"tag":160,"props":1099,"children":1100},{"style":424},[1101],{"type":37,"value":1102},"'conv_minnow'",{"type":32,"tag":160,"props":1104,"children":1105},{"style":218},[1106],{"type":37,"value":607},{"type":32,"tag":160,"props":1108,"children":1109},{"style":439},[1110],{"type":37,"value":878},{"type":32,"tag":160,"props":1112,"children":1113},{"style":212},[1114],{"type":37,"value":287},{"type":32,"tag":160,"props":1116,"children":1117},{"style":218},[1118],{"type":37,"value":1019},{"type":32,"tag":160,"props":1120,"children":1121},{"style":439},[1122],{"type":37,"value":896},{"type":32,"tag":160,"props":1124,"children":1125},{"style":212},[1126],{"type":37,"value":287},{"type":32,"tag":160,"props":1128,"children":1129},{"style":218},[1130],{"type":37,"value":1032},{"type":32,"tag":160,"props":1132,"children":1133},{"class":207,"line":348},[1134],{"type":32,"tag":160,"props":1135,"children":1136},{"style":218},[1137],{"type":37,"value":526},{"type":32,"tag":160,"props":1139,"children":1140},{"class":207,"line":366},[1141],{"type":32,"tag":160,"props":1142,"children":1143},{"style":270},[1144],{"type":37,"value":1145},"    # Vraisemblance (données segment)\n",{"type":32,"tag":160,"props":1147,"children":1148},{"class":207,"line":374},[1149,1154,1158,1163,1168,1172,1177,1181,1186,1190,1194,1198,1203,1208,1212,1217],{"type":32,"tag":160,"props":1150,"children":1151},{"style":218},[1152],{"type":37,"value":1153},"    whale_obs ",{"type":32,"tag":160,"props":1155,"children":1156},{"style":212},[1157],{"type":37,"value":287},{"type":32,"tag":160,"props":1159,"children":1160},{"style":218},[1161],{"type":37,"value":1162}," pm.Binomial(",{"type":32,"tag":160,"props":1164,"children":1165},{"style":424},[1166],{"type":37,"value":1167},"'whale_obs'",{"type":32,"tag":160,"props":1169,"children":1170},{"style":218},[1171],{"type":37,"value":607},{"type":32,"tag":160,"props":1173,"children":1174},{"style":439},[1175],{"type":37,"value":1176},"n",{"type":32,"tag":160,"props":1178,"children":1179},{"style":212},[1180],{"type":37,"value":287},{"type":32,"tag":160,"props":1182,"children":1183},{"style":290},[1184],{"type":37,"value":1185},"200",{"type":32,"tag":160,"props":1187,"children":1188},{"style":218},[1189],{"type":37,"value":607},{"type":32,"tag":160,"props":1191,"children":1192},{"style":439},[1193],{"type":37,"value":33},{"type":32,"tag":160,"props":1195,"children":1196},{"style":212},[1197],{"type":37,"value":287},{"type":32,"tag":160,"props":1199,"children":1200},{"style":218},[1201],{"type":37,"value":1202},"conv_whale, ",{"type":32,"tag":160,"props":1204,"children":1205},{"style":439},[1206],{"type":37,"value":1207},"observed",{"type":32,"tag":160,"props":1209,"children":1210},{"style":212},[1211],{"type":37,"value":287},{"type":32,"tag":160,"props":1213,"children":1214},{"style":290},[1215],{"type":37,"value":1216},"12",{"type":32,"tag":160,"props":1218,"children":1219},{"style":218},[1220],{"type":37,"value":626},{"type":32,"tag":160,"props":1222,"children":1223},{"class":207,"line":397},[1224,1229,1233,1237,1242,1246,1250,1254,1259,1263,1267,1271,1276,1280,1284,1289],{"type":32,"tag":160,"props":1225,"children":1226},{"style":218},[1227],{"type":37,"value":1228},"    dolphin_obs ",{"type":32,"tag":160,"props":1230,"children":1231},{"style":212},[1232],{"type":37,"value":287},{"type":32,"tag":160,"props":1234,"children":1235},{"style":218},[1236],{"type":37,"value":1162},{"type":32,"tag":160,"props":1238,"children":1239},{"style":424},[1240],{"type":37,"value":1241},"'dolphin_obs'",{"type":32,"tag":160,"props":1243,"children":1244},{"style":218},[1245],{"type":37,"value":607},{"type":32,"tag":160,"props":1247,"children":1248},{"style":439},[1249],{"type":37,"value":1176},{"type":32,"tag":160,"props":1251,"children":1252},{"style":212},[1253],{"type":37,"value":287},{"type":32,"tag":160,"props":1255,"children":1256},{"style":290},[1257],{"type":37,"value":1258},"800",{"type":32,"tag":160,"props":1260,"children":1261},{"style":218},[1262],{"type":37,"value":607},{"type":32,"tag":160,"props":1264,"children":1265},{"style":439},[1266],{"type":37,"value":33},{"type":32,"tag":160,"props":1268,"children":1269},{"style":212},[1270],{"type":37,"value":287},{"type":32,"tag":160,"props":1272,"children":1273},{"style":218},[1274],{"type":37,"value":1275},"conv_dolphin, ",{"type":32,"tag":160,"props":1277,"children":1278},{"style":439},[1279],{"type":37,"value":1207},{"type":32,"tag":160,"props":1281,"children":1282},{"style":212},[1283],{"type":37,"value":287},{"type":32,"tag":160,"props":1285,"children":1286},{"style":290},[1287],{"type":37,"value":1288},"24",{"type":32,"tag":160,"props":1290,"children":1291},{"style":218},[1292],{"type":37,"value":626},{"type":32,"tag":160,"props":1294,"children":1295},{"class":207,"line":406},[1296,1301,1305,1309,1314,1318,1322,1326,1331,1335,1339,1343,1348,1352,1356,1361],{"type":32,"tag":160,"props":1297,"children":1298},{"style":218},[1299],{"type":37,"value":1300},"    minnow_obs ",{"type":32,"tag":160,"props":1302,"children":1303},{"style":212},[1304],{"type":37,"value":287},{"type":32,"tag":160,"props":1306,"children":1307},{"style":218},[1308],{"type":37,"value":1162},{"type":32,"tag":160,"props":1310,"children":1311},{"style":424},[1312],{"type":37,"value":1313},"'minnow_obs'",{"type":32,"tag":160,"props":1315,"children":1316},{"style":218},[1317],{"type":37,"value":607},{"type":32,"tag":160,"props":1319,"children":1320},{"style":439},[1321],{"type":37,"value":1176},{"type":32,"tag":160,"props":1323,"children":1324},{"style":212},[1325],{"type":37,"value":287},{"type":32,"tag":160,"props":1327,"children":1328},{"style":290},[1329],{"type":37,"value":1330},"3000",{"type":32,"tag":160,"props":1332,"children":1333},{"style":218},[1334],{"type":37,"value":607},{"type":32,"tag":160,"props":1336,"children":1337},{"style":439},[1338],{"type":37,"value":33},{"type":32,"tag":160,"props":1340,"children":1341},{"style":212},[1342],{"type":37,"value":287},{"type":32,"tag":160,"props":1344,"children":1345},{"style":218},[1346],{"type":37,"value":1347},"conv_minnow, ",{"type":32,"tag":160,"props":1349,"children":1350},{"style":439},[1351],{"type":37,"value":1207},{"type":32,"tag":160,"props":1353,"children":1354},{"style":212},[1355],{"type":37,"value":287},{"type":32,"tag":160,"props":1357,"children":1358},{"style":290},[1359],{"type":37,"value":1360},"60",{"type":32,"tag":160,"props":1362,"children":1363},{"style":218},[1364],{"type":37,"value":626},{"type":32,"tag":160,"props":1366,"children":1367},{"class":207,"line":435},[1368],{"type":32,"tag":160,"props":1369,"children":1370},{"style":218},[1371],{"type":37,"value":526},{"type":32,"tag":160,"props":1373,"children":1374},{"class":207,"line":474},[1375,1379,1383,1387,1391],{"type":32,"tag":160,"props":1376,"children":1377},{"style":218},[1378],{"type":37,"value":588},{"type":32,"tag":160,"props":1380,"children":1381},{"style":212},[1382],{"type":37,"value":287},{"type":32,"tag":160,"props":1384,"children":1385},{"style":218},[1386],{"type":37,"value":597},{"type":32,"tag":160,"props":1388,"children":1389},{"style":290},[1390],{"type":37,"value":1330},{"type":32,"tag":160,"props":1392,"children":1393},{"style":218},[1394],{"type":37,"value":626},{"type":32,"tag":33,"props":1396,"children":1397},{},[1398,1400,1405,1406,1411,1412,1416],{"type":37,"value":1399},"Ce modèle relie les conversions ",{"type":32,"tag":40,"props":1401,"children":1402},{},[1403],{"type":37,"value":1404},"whale",{"type":37,"value":607},{"type":32,"tag":40,"props":1407,"children":1408},{},[1409],{"type":37,"value":1410},"dolphin",{"type":37,"value":607},{"type":32,"tag":40,"props":1413,"children":1414},{},[1415],{"type":37,"value":788},{"type":37,"value":1417}," via un prior global — même avec peu d'observations par segment, vous obtenez des estimées raisonnables.",{"type":32,"tag":55,"props":1419,"children":1421},{"id":1420},"durée-de-test-et-règle-darrêt-décision-par-probabilité-posterior",[1422],{"type":37,"value":1423},"Durée de Test et Règle d'Arrêt : Décision par Probabilité Posterior",{"type":32,"tag":33,"props":1425,"children":1426},{},[1427,1429,1433],{"type":37,"value":1428},"En A\u002FB classique, la durée du test est fixée à l'avance (14 jours, minimum 1000 conversions). Avec l'optimisation Bayésienne, la règle d'arrêt repose sur la probabilité ",{"type":32,"tag":40,"props":1430,"children":1431},{},[1432],{"type":37,"value":51},{"type":37,"value":1434}," : « La probabilité que le variant A surpasse le variant B dépasse-t-elle 95 % ? » Cette pause dynamique raccourcit le test tout en réduisant le risque de faux positif.",{"type":32,"tag":33,"props":1436,"children":1437},{},[1438,1443,1445,1449],{"type":32,"tag":136,"props":1439,"children":1440},{},[1441],{"type":37,"value":1442},"Exemple de règle d'arrêt :",{"type":37,"value":1444}," Test 4,99 $ vs 6,99 $. Chaque jour, vous calculez la probabilité ",{"type":32,"tag":40,"props":1446,"children":1447},{},[1448],{"type":37,"value":51},{"type":37,"value":1450}," :",{"type":32,"tag":195,"props":1452,"children":1454},{"className":197,"code":1453,"language":199,"meta":16,"style":16},"# Échantillons posterior\nsamples_499 = trace.posterior['conv_rate_499'].values.flatten()\nsamples_699 = trace.posterior['conv_rate_699'].values.flatten()\n\n# Comparaison revenue (prix × conversion)\nrevenue_499 = samples_499 * 4.99\nrevenue_699 = samples_699 * 6.99\n\n# Probabilité que 6,99 $ soit meilleur\nprob_699_better = (revenue_699 > revenue_499).mean()\nprint(f\"P(6,99 $ > 4,99 $) = {prob_699_better:.2%}\")\n",[1455],{"type":32,"tag":202,"props":1456,"children":1457},{"__ignoreMap":16},[1458,1466,1493,1517,1524,1532,1558,1583,1590,1598,1625],{"type":32,"tag":160,"props":1459,"children":1460},{"class":207,"line":208},[1461],{"type":32,"tag":160,"props":1462,"children":1463},{"style":270},[1464],{"type":37,"value":1465},"# Échantillons posterior\n",{"type":32,"tag":160,"props":1467,"children":1468},{"class":207,"line":234},[1469,1474,1478,1483,1488],{"type":32,"tag":160,"props":1470,"children":1471},{"style":218},[1472],{"type":37,"value":1473},"samples_499 ",{"type":32,"tag":160,"props":1475,"children":1476},{"style":212},[1477],{"type":37,"value":287},{"type":32,"tag":160,"props":1479,"children":1480},{"style":218},[1481],{"type":37,"value":1482}," trace.posterior[",{"type":32,"tag":160,"props":1484,"children":1485},{"style":424},[1486],{"type":37,"value":1487},"'conv_rate_499'",{"type":32,"tag":160,"props":1489,"children":1490},{"style":218},[1491],{"type":37,"value":1492},"].values.flatten()\n",{"type":32,"tag":160,"props":1494,"children":1495},{"class":207,"line":256},[1496,1501,1505,1509,1513],{"type":32,"tag":160,"props":1497,"children":1498},{"style":218},[1499],{"type":37,"value":1500},"samples_699 ",{"type":32,"tag":160,"props":1502,"children":1503},{"style":212},[1504],{"type":37,"value":287},{"type":32,"tag":160,"props":1506,"children":1507},{"style":218},[1508],{"type":37,"value":1482},{"type":32,"tag":160,"props":1510,"children":1511},{"style":424},[1512],{"type":37,"value":427},{"type":32,"tag":160,"props":1514,"children":1515},{"style":218},[1516],{"type":37,"value":1492},{"type":32,"tag":160,"props":1518,"children":1519},{"class":207,"line":266},[1520],{"type":32,"tag":160,"props":1521,"children":1522},{"emptyLinePlaceholder":260},[1523],{"type":37,"value":263},{"type":32,"tag":160,"props":1525,"children":1526},{"class":207,"line":276},[1527],{"type":32,"tag":160,"props":1528,"children":1529},{"style":270},[1530],{"type":37,"value":1531},"# Comparaison revenue (prix × conversion)\n",{"type":32,"tag":160,"props":1533,"children":1534},{"class":207,"line":296},[1535,1540,1544,1549,1553],{"type":32,"tag":160,"props":1536,"children":1537},{"style":218},[1538],{"type":37,"value":1539},"revenue_499 ",{"type":32,"tag":160,"props":1541,"children":1542},{"style":212},[1543],{"type":37,"value":287},{"type":32,"tag":160,"props":1545,"children":1546},{"style":218},[1547],{"type":37,"value":1548}," samples_499 ",{"type":32,"tag":160,"props":1550,"children":1551},{"style":212},[1552],{"type":37,"value":456},{"type":32,"tag":160,"props":1554,"children":1555},{"style":290},[1556],{"type":37,"value":1557}," 4.99\n",{"type":32,"tag":160,"props":1559,"children":1560},{"class":207,"line":314},[1561,1566,1570,1575,1579],{"type":32,"tag":160,"props":1562,"children":1563},{"style":218},[1564],{"type":37,"value":1565},"revenue_699 ",{"type":32,"tag":160,"props":1567,"children":1568},{"style":212},[1569],{"type":37,"value":287},{"type":32,"tag":160,"props":1571,"children":1572},{"style":218},[1573],{"type":37,"value":1574}," samples_699 ",{"type":32,"tag":160,"props":1576,"children":1577},{"style":212},[1578],{"type":37,"value":456},{"type":32,"tag":160,"props":1580,"children":1581},{"style":290},[1582],{"type":37,"value":562},{"type":32,"tag":160,"props":1584,"children":1585},{"class":207,"line":26},[1586],{"type":32,"tag":160,"props":1587,"children":1588},{"emptyLinePlaceholder":260},[1589],{"type":37,"value":263},{"type":32,"tag":160,"props":1591,"children":1592},{"class":207,"line":330},[1593],{"type":32,"tag":160,"props":1594,"children":1595},{"style":270},[1596],{"type":37,"value":1597},"# Probabilité que 6,99 $ soit meilleur\n",{"type":32,"tag":160,"props":1599,"children":1600},{"class":207,"line":348},[1601,1606,1610,1615,1620],{"type":32,"tag":160,"props":1602,"children":1603},{"style":218},[1604],{"type":37,"value":1605},"prob_699_better ",{"type":32,"tag":160,"props":1607,"children":1608},{"style":212},[1609],{"type":37,"value":287},{"type":32,"tag":160,"props":1611,"children":1612},{"style":218},[1613],{"type":37,"value":1614}," (revenue_699 ",{"type":32,"tag":160,"props":1616,"children":1617},{"style":212},[1618],{"type":37,"value":1619},">",{"type":32,"tag":160,"props":1621,"children":1622},{"style":218},[1623],{"type":37,"value":1624}," revenue_499).mean()\n",{"type":32,"tag":160,"props":1626,"children":1627},{"class":207,"line":366},[1628,1632,1637,1642,1647,1652,1657,1662,1667,1672],{"type":32,"tag":160,"props":1629,"children":1630},{"style":290},[1631],{"type":37,"value":652},{"type":32,"tag":160,"props":1633,"children":1634},{"style":218},[1635],{"type":37,"value":1636},"(",{"type":32,"tag":160,"props":1638,"children":1639},{"style":212},[1640],{"type":37,"value":1641},"f",{"type":32,"tag":160,"props":1643,"children":1644},{"style":424},[1645],{"type":37,"value":1646},"\"P(6,99 $ > 4,99 $) = ",{"type":32,"tag":160,"props":1648,"children":1649},{"style":290},[1650],{"type":37,"value":1651},"{",{"type":32,"tag":160,"props":1653,"children":1654},{"style":218},[1655],{"type":37,"value":1656},"prob_699_better",{"type":32,"tag":160,"props":1658,"children":1659},{"style":212},[1660],{"type":37,"value":1661},":.2%",{"type":32,"tag":160,"props":1663,"children":1664},{"style":290},[1665],{"type":37,"value":1666},"}",{"type":32,"tag":160,"props":1668,"children":1669},{"style":424},[1670],{"type":37,"value":1671},"\"",{"type":32,"tag":160,"props":1673,"children":1674},{"style":218},[1675],{"type":37,"value":626},{"type":32,"tag":33,"props":1677,"children":1678},{},[1679],{"type":37,"value":1680},"Jour 5 : P(6,99 $ > 4,99 $) = 73 % — trop tôt. Jour 9 : 94 % — sous le seuil 95 %. Jour 12 : 96 % — arrêtez, 6,99 $ est optimal. Cette approche économise 2-5 jours par rapport au fréquentiste.",{"type":32,"tag":33,"props":1682,"children":1683},{},[1684,1689,1691,1695],{"type":32,"tag":136,"props":1685,"children":1686},{},[1687],{"type":37,"value":1688},"Durée minimale du test :",{"type":37,"value":1690}," Même si Bayes stoppe tôt, en F2P testez au minimum 7 jours — la première semaine révèle les pics de rétention, le comportement des dépensiers du weekend, l'effet événement. Une pause avant 7 jours biaise le ",{"type":32,"tag":40,"props":1692,"children":1693},{},[1694],{"type":37,"value":51},{"type":37,"value":114},{"type":32,"tag":33,"props":1697,"children":1698},{},[1699,1704,1706,1710],{"type":32,"tag":136,"props":1700,"children":1701},{},[1702],{"type":37,"value":1703},"Minimisation du regret :",{"type":37,"value":1705}," Avec Thompson Sampling, vous attribuez du trafic au variant suboptimal (exploration). Le regret = revenue optimal - revenue réel. Le framework Bayésien minimise le regret car à mesure que le ",{"type":32,"tag":40,"props":1707,"children":1708},{},[1709],{"type":37,"value":51},{"type":37,"value":1711}," se met à jour, l'exploration décroît et l'exploitation s'accroît. Sur un test de 14 jours : premiers 5 jours ≈ 30 % regret, derniers 5 jours ≈ 5 % regret — regret moyen 15 %. En A\u002FB classique avec répartition 50-50 permanente : regret moyen 25-30 %.",{"type":32,"tag":55,"props":1713,"children":1715},{"id":1714},"production-moteur-de-dynamic-pricing-et-raffinement-posterior-continu",[1716],{"type":37,"value":1717},"Production : Moteur de Dynamic Pricing et Raffinement Posterior Continu",{"type":32,"tag":33,"props":1719,"children":1720},{},[1721,1723,1727],{"type":37,"value":1722},"Le test est terminé, 6,99 $ a gagné — mais ce n'est que le début. La vraie puissance de l'optimisation Bayésienne en prix émerge en production avec un raffinement ",{"type":32,"tag":40,"props":1724,"children":1725},{},[1726],{"type":37,"value":51},{"type":37,"value":1728}," continu.",{"type":32,"tag":33,"props":1730,"children":1731},{},[1732,1742,1744,1748,1750,1755,1757,1761,1763,1767,1768,1772],{"type":32,"tag":136,"props":1733,"children":1734},{},[1735,1737,1741],{"type":37,"value":1736},"Architecture du moteur ",{"type":32,"tag":40,"props":1738,"children":1739},{},[1740],{"type":37,"value":112},{"type":37,"value":1450},{"type":37,"value":1743}," À chaque session utilisateur, vous estimez le segment (prédiction LTV, cohorte de rétention, vélocité de dépense). En fonction du segment, vous samplez de la distribution ",{"type":32,"tag":40,"props":1745,"children":1746},{},[1747],{"type":37,"value":51},{"type":37,"value":1749}," pour obtenir le price point optimal. Exemple : nouvel utilisateur, rétention D1 à 80 %, aucun IAP encore — le ",{"type":32,"tag":40,"props":1751,"children":1752},{},[1753],{"type":37,"value":1754},"prior",{"type":37,"value":1756}," ",{"type":32,"tag":40,"props":1758,"children":1759},{},[1760],{"type":37,"value":788},{"type":37,"value":1762}," domine, vous samplez dans la fourchette 0,99-1,99 $. Même utilisateur au jour 7 après 2 IAP pour 8 $ total — le ",{"type":32,"tag":40,"props":1764,"children":1765},{},[1766],{"type":37,"value":51},{"type":37,"value":1756},{"type":32,"tag":40,"props":1769,"children":1770},{},[1771],{"type":37,"value":1410},{"type":37,"value":1773}," se renforce, vous basculez à la fourchette 4,99-6,99 $.",{"type":32,"tag":33,"props":1775,"children":1776},{},[1777,1782,1784,1788,1790,1794,1796,1801,1803,1807],{"type":32,"tag":136,"props":1778,"children":1779},{},[1780],{"type":37,"value":1781},"Raffinement du posterior :",{"type":37,"value":1783}," En production, chaque conversion met à jour le ",{"type":32,"tag":40,"props":1785,"children":1786},{},[1787],{"type":37,"value":51},{"type":37,"value":1789},". Après 30 jours, 1200 conversions supplémentaires à 6,99 $ : prior Beta(125, 4995), nouveau ",{"type":32,"tag":40,"props":1791,"children":1792},{},[1793],{"type":37,"value":51},{"type":37,"value":1795}," Beta(1325, 46995). L'intervalle de crédibilité s'affine : ",{"type":32,"tag":160,"props":1797,"children":1798},{},[1799],{"type":37,"value":1800},"2,7 %, 2,9 %",{"type":37,"value":1802},". Vous avez 95 % de confiance en 6,99 $. Mais le marché change — un concurrent lance une campagne à 4,99 $, la conversion chute — le ",{"type":32,"tag":40,"props":1804,"children":1805},{},[1806],{"type":37,"value":51},{"type":37,"value":1808}," s'élargit à nouveau, un nouveau test se déclenche.",{"type":32,"tag":33,"props":1810,"children":1811},{},[1812,1817],{"type":32,"tag":136,"props":1813,"children":1814},{},[1815],{"type":37,"value":1816},"Intégration bandit multi-armé :",{"type":37,"value":1818}," Si votre échelle IAP contient plusieurs SKU (starter pack 4,99 $, mega pack 19,99 $, ultimate 49,99 $), Thompson Sampling devient un algorithme bandit en production. À chaque impression, vous tirez un échantillon de chaque SKU, présentez celui avec le revenue attendu maximal. Combiné à des efforts d",{"type":32,"tag":1820,"props":1821,"children":1822},"style",{},[1823],{"type":37,"value":1824},"html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}",{"title":16,"searchDepth":256,"depth":256,"links":1826},[1827,1828,1829,1830,1831],{"id":57,"depth":234,"text":60},{"id":117,"depth":234,"text":120},{"id":688,"depth":234,"text":691},{"id":1420,"depth":234,"text":1423},{"id":1714,"depth":234,"text":1717},"markdown","content:fr:gaming:optimisation-prix-bayesienne-f2p-mobile.md","content","fr\u002Fgaming\u002Foptimisation-prix-bayesienne-f2p-mobile.md","fr\u002Fgaming\u002Foptimisation-prix-bayesienne-f2p-mobile","md",1782338701457]