MAKE A MEME
View Large Image
| View Original: | Petersburg-Paradox.png (829x559) | |||
| Download: | Original | Medium | Small | Thumb |
| Courtesy of: | commons.wikimedia.org | More Like This | ||
| Keywords: Petersburg-Paradox.png en wikipedia Maksim page en wikipedia 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 by 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 all but a few gameplays seems paradoxical but the graph shows how both of these can coexist Graph created by Brent Hugh 1 date/time username edit summary ---- 03 05 30 September 2005 en User Bhugh <nowiki></nowiki> ---- 02 44 30 September 2005 en User Bhugh <nowiki></nowiki> ---- 02 20 30 September 2005 en User Bhugh <nowiki> 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 </nowiki> Original upload log 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 Game theory Probability paradoxes | ||||
