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 Title: 凱利準則及其在賭博上的應用;Kelly's Criterion and It's Application to Gambling Authors: 張婷容;Ting-jung Chang Contributors: 數學研究所 Keywords: 賭博;凱利準則;gambling;Kelly's criterion Date: 2008-11-11 Issue Date: 2009-09-22 11:09:20 (UTC+8) Publisher: 國立中央大學圖書館 Abstract: 在長期的賭博過程中，賭客若單次將全部賭資下注勢必面臨破產的危機。為了提升獲利的機率，降低破產的可能性，我們必須研究賭客每次下注的最佳比率。凱利準則假設莊家與賭客在賭博的過程中策略不變，且賭客可獲得下注訊息，分別在訊息正確及傳輸受干擾的情形下，求得賭客下注的最佳策略。本篇論文主要在對凱利準則做推廣，在三種不同的賭博遊戲—擲幣模型、輪盤模型、傳輸受干擾下的賭博模型下求取下注的最佳策略。凱利準則假設賭局是公平的，因此賠率皆相同。而我們假設賭客與莊家雙方都不知道真實的機率為何，皆加以猜測。莊家訂定賠率，而賭客則根據這個賠率尋求自己下注的最佳比率。 In the long run of the gambling process, if the gambler bets all his money at one time, he may face the crisis of bankruptcy. To promote the probability of the profit and decrease the possibility of bankruptcy, we must find out the best proportion of every bet. Kelly’s criterion supposes that the banker and the gambler keep the strategy unchanged during all the process, and the gambler can get the information of the game. Under the circumstances of correct information and noisy communication, Kelly gets the best strategy of betting for the gambler. In this paper, we spread Kelly’s criterion to gain the best way to bet in three situations：coin model, roulette model, and gambling model with noisy communication. Kelly’s criterion assumes that the game is fair; therefore, the odds are all the same. We suppose both the gambler and the banker don’t know how much the true probability is, and they guest it. The banker makes the rule of the odds, and the gambler find the best proportion of betting according to the odds. Appears in Collections: [數學研究所] 博碩士論文

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