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In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956. Because the Kelly Criterion leads to higher wealth compared to any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity), it is a scientific gambling method.

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  • Kelly-Formel (de)
  • Criterio di Kelly (it)
  • Kelly criterion (en)
  • Formule de Kelly (fr)
  • 켈리 공식 (ko)
  • Критерий Келли (ru)
  • 凱利公式 (zh)
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  • Die Kelly-Formel, auch Kelly-Kriterium genannt, dient der Gewinnmaximierung von Wetten mit positiver Gewinnerwartung. Sie geht auf den Wissenschaftler John Larry Kelly jr. zurück, der sie 1956 veröffentlichte. Mit einer Wette ist in diesem Zusammenhang das Riskieren eines Geldbetrages (Einsatz) gemeint, der im Gewinnfall mit einem festgelegten Vielfachen des Einsatzes (feste Quote) belohnt wird. Im Verlustfall wird der Einsatz abgegeben. (de)
  • La formule de Kelly est une règle mathématique déterminant la part de fonds à miser ou investir dans une "loterie" répétée, si le joueur / investisseur cherche à maximiser le taux de croissance de son budget, à long terme.Elle est l'application, dans ce cas simple, du critère de Kelly. (fr)
  • Nella teoria della probabilità, il criterio di Kelly (anche strategia di Kelly o puntata di Kelly) è una formula utilizzata per determinare la quantità ottimale del capitale da investire in una scommessa. Nella maggior parte degli scenari di gioco e alcuni scenari di investimento, la strategia di Kelly farà sostanzialmente meglio di qualsiasi strategia diversa nel lungo periodo. (it)
  • 凱利公式、凱利方程、凱利判據、凱利策略(英語:Kelly criterion、Kelly strategy、Kelly bet),是一種根据赌博赢或输的概率,计算出每次下注的资金占所有赌本的最佳比例的公式,由約翰·拉里·凱利於1956年在《》中發表,可用以計算出每次遊戲中應投注的資金比例。除可將長期增長率最大化外,此方程式不允許在任何賭局中,有失去全部現有資金的可能,因此有不存在破產疑慮的優點。方程式假設貨幣與賭局可無窮分割,而只要資金足夠多,在實際應用上不成問題。 (zh)
  • In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956. Because the Kelly Criterion leads to higher wealth compared to any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity), it is a scientific gambling method. (en)
  • 확률론과 시제간(intertemporal) 포트폴리오 선택에서, 켈리공식 (또는 켈리기준, 켈리전략, 켈리베팅)은 반복되는 일련의 베팅에서 최적 베팅규모를 결정하는 공식이다. 단순화된 몇가지 가정 하의 대부분의 도박과 몇몇 투자 시나리오에서, 켈리공식은 장기적으로 다른 어떤 전략보다 우월한 성과를 낸다. (장기란, 관측된 베팅 성공의 비율이 베팅이 성공적일 확률과 동일해지는 기간을 의미한다.) 벨 연구소의 연구원이었던 J. L. Kelly가 1956년 기술하였다. 켈리공식의 현실적 유용성은 검증되었다. 최근 켈리공식은 투자론의 주류의 일부가 되었고, 워렌 버핏과 빌 그로스 등 성공한 투자자들이 켈리공식을 사용한다는 주장이 제기되어왔다. (ko)
  • Критерий Келли (англ. Kelly criterion) — финансовая стратегия ставок, разработанная Джоном Л. Келли в 1956 году. Эта стратегия определяет размеры ставок в процентах от величины ваших денежных средств. Но может возникнуть ситуация когда ставка игрока будет меньше минимальной ставки букмекера. Эта стратегия сложна тем, что требует правильной оценки вероятностного исхода. В 2000-х годах анализ в стиле Келли стал частью основной теории инвестиций, и было заявлено, что известные успешные инвесторы, включая Уоррена Баффета и Билла Гросса, используют методы Келли. Пример: Ставка игрока: . (ru)
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