| bayesian inference of a possiblely defected coin flip and gamblers fallacy? I am very confused about this problem, since I am not in school any more, I hope the public could answer me. gambler's fallacy is that a gambler usually see something happens so many times in a row that he would assume the next result is the opposite. I understand the event is unrelevant, do the result of next event still follows the same probability distribution assumed. What if the system is defected , take the coild flip as example, if i see 7 head in a row, can i possibly know that the coin is defected? if so can i calculate the odds of the defect? like p(head)=.5p(defect) or so . but i know if i see 1000 head in a row , i am maybe 100 percent sure the coin is defected. but maybe the coin maybe still good, i am just so lucky to see a miracle.
thank you very much for your help, maybe I made a wrong example. suppose i believe a basketball team has the ability as .5 probability to win a game, after I ovbserve my team lose 10 game in a row, can i adjust my belief with the appearing fact? cause I see somany people try to do analysis work to see whether the team can win or not. Thanks in advace.
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