Image:Petersburg-Paradox.png

La bildo estas kopiita de wikipedia:en. La originala priskribo estas:

[edit] Summary

Graph of average value per play over approximately 20,000 game plays of the St. Petersburg paradox game. The average value rises from about one to five over the first 500 plays and then slowly rises to an average value of eight between 500 and 20,000 plays.

The graph illustrates the characteristics of the St. Petersburg Paradox game:

• as game play progresses there is a typical slow decline in average value punctuated occasionally be a very large jump in average value

• as game play progresses there is a very, very slow overall rise of the average winning over many game plays because the occasional large jumps are on average slightly larger than the long, slow declines between them.

• although the average winning rises overall, it rises more and more slowly as gameplay progresses.

The graph illustrates the characteristics that make the game seem paradoxical:

• Since, on the whole, the average value continually rises, the average value of a gameplay does indeed go to infinity as the number of gameplays goes to infinity.

• Since the average value rises towards infinity at a very, very slow rate that continues to slow further as gameplay progresses, typical values of a few gameplays, or even a few hundred or a few thousand gameplays, are very small. In order to reach even modestly high average returns, tremendously huge amounts of gameplays are typically required.

The combination of infinitely high average winnings with very low typical winnings from a few gameplays seems paradoxical, but the graph shows how both of these can coexist.

Graph created by Brent Hugh.

[edit] Licensing

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | ‪Norsk (bokmål)‬ | ‪Norsk (nynorsk)‬ | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | ‪中文(简体)‬ | ‪中文(繁體)‬ | zh-yue-hant | +/-

[edit] Historio de la dosiero

Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version.

Click on date to download the file or see the image uploaded on that date.

• (del) (cur) 02:20, 30 September 2005 . . Bhugh ( en:User_talk:Bhugh Talk) . . 829x559 (8294 bytes) (Graph of average value per play over approximately 20,000 game plays of the St. Petersburg Paradox game. The average value rises from about one to five over the first 500 plays and then slowly rises to an average value of eight between 500 and 20,000 pla)

• St. Petersburg paradox