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- Gamblers_ruin abstract "The term gambler's ruin is used for a number of related statistical ideas: The original meaning is that a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet. Another common meaning is that a gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually go broke against an opponent with infinite wealth. Such a situation can be modeled by a random walk on the real number line. In that context it is provable that the agent will return to his point of origin or go broke and is ruined an infinite number of times if the random walk continues forever. The result above is a corollary of a general theorem by Christiaan Huygens which is also known as gambler's ruin. That theorem shows how to compute the probability of each player winning a series of bets that continues until one's entire initial stake is lost, given the initial stakes of the two players and the constant probability of winning. This is the oldest mathematical idea that goes by the name gambler's ruin, but not the first idea to which the name was applied. The most common use of the term today is that a gambler playing a negative expected value game will eventually go broke, regardless of betting system. This is another corollary to Huygens' result.The ideas have specific relevance for gamblers; however they are also general theorems with wide application and many related results in probability and statistics. Huygens' result in particular led to important advances in the mathematical theory of probability.".
- Gamblers_ruin wikiPageExternalLink TheGamblersRuin.
- Gamblers_ruin wikiPageExternalLink gamblers_ruin.html.
- Gamblers_ruin wikiPageExternalLink ~tom.
- Gamblers_ruin wikiPageExternalLink kmath084.htm.
- Gamblers_ruin wikiPageID "453078".
- Gamblers_ruin wikiPageLength "12508".
- Gamblers_ruin wikiPageOutDegree "24".
- Gamblers_ruin wikiPageRevisionID "701770075".
- Gamblers_ruin wikiPageWikiLink Almost_surely.
- Gamblers_ruin wikiPageWikiLink Blaise_Pascal.
- Gamblers_ruin wikiPageWikiLink Category:Causal_fallacies.
- Gamblers_ruin wikiPageWikiLink Category:Gambling_terminology.
- Gamblers_ruin wikiPageWikiLink Category:Named_probability_problems.
- Gamblers_ruin wikiPageWikiLink Category:Variants_of_random_walks.
- Gamblers_ruin wikiPageWikiLink Christiaan_Huygens.
- Gamblers_ruin wikiPageWikiLink Corollary.
- Gamblers_ruin wikiPageWikiLink Expected_value.
- Gamblers_ruin wikiPageWikiLink Fixed-odds_betting.
- Gamblers_ruin wikiPageWikiLink Gamblers_conceit.
- Gamblers_ruin wikiPageWikiLink Gamblers_fallacy.
- Gamblers_ruin wikiPageWikiLink Gambling.
- Gamblers_ruin wikiPageWikiLink Markov_chain.
- Gamblers_ruin wikiPageWikiLink Martingale_(betting_system).
- Gamblers_ruin wikiPageWikiLink Pierre_de_Fermat.
- Gamblers_ruin wikiPageWikiLink Probability.
- Gamblers_ruin wikiPageWikiLink Problem_of_points.
- Gamblers_ruin wikiPageWikiLink Risk_of_ruin.
- Gamblers_ruin wikiPageWikiLink Statistics.
- Gamblers_ruin wikiPageWikiLink Theorem.
- Gamblers_ruin wikiPageWikiLink Wiener_process.
- Gamblers_ruin wikiPageWikiLinkText "Gambler's ruin".
- Gamblers_ruin wikiPageWikiLinkText "gambler's ruin".
- Gamblers_ruin wikiPageUsesTemplate Template:Citation_needed.
- Gamblers_ruin wikiPageUsesTemplate Template:Cite_book.
- Gamblers_ruin wikiPageUsesTemplate Template:Cite_journal.
- Gamblers_ruin wikiPageUsesTemplate Template:Portal.
- Gamblers_ruin wikiPageUsesTemplate Template:Reflist.
- Gamblers_ruin subject Category:Causal_fallacies.
- Gamblers_ruin subject Category:Gambling_terminology.
- Gamblers_ruin subject Category:Named_probability_problems.
- Gamblers_ruin subject Category:Variants_of_random_walks.
- Gamblers_ruin type Fallacy.
- Gamblers_ruin type Process.
- Gamblers_ruin type Redirect.
- Gamblers_ruin type Variant.
- Gamblers_ruin comment "The term gambler's ruin is used for a number of related statistical ideas: The original meaning is that a gambler who raises his bet to a fixed fraction of bankroll when he wins, but does not reduce it when he loses, will eventually go broke, even if he has a positive expected value on each bet.".
- Gamblers_ruin label "Gambler's ruin".
- Gamblers_ruin sameAs Q660446.
- Gamblers_ruin sameAs Ruin_des_Spielers.
- Gamblers_ruin sameAs Ruine_du_joueur.
- Gamblers_ruin sameAs 도박꾼의_파산.
- Gamblers_ruin sameAs m.02bbm9.
- Gamblers_ruin sameAs Задача_о_разорении_игрока.
- Gamblers_ruin sameAs Задача_про_розорення_гравця.
- Gamblers_ruin sameAs Q660446.
- Gamblers_ruin sameAs 赌徒破产理论.
- Gamblers_ruin wasDerivedFrom Gamblers_ruin?oldid=701770075.
- Gamblers_ruin isPrimaryTopicOf Gamblers_ruin.