Random Bulgarian solitaire
From Wikimanqala
Random Bulgarian solitaire
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| Stochastic Bulgarian solitaire |
| © 2003, Serguei Popov |
| Brazil |
| Used in maths research |
| This game is a solitaire |
| Reverse sowing |
| n holes per row |
Random Bulgarian solitaire was invented by the Brazilian statician Serguei Popov in 2003. He teaches at the Instituto de Matemática e Estatística of Sao Paulo University. It is a generalized variant of deterministic Bulgarian solitaire.
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Rules
The game has almost the same rules as Bulgarian solitaire. However, one card is removed from each pile with a fixed probability p.
- If p = 0, the piles are left intact.
- If p = 1, the game is deterministic Bulgarian solitaire.
- The general case with 0 < p < 1 is known as random Bulgarian solitaire or stochastic Bulgarian solitaire. This is a finite irreducible Markov chain.
- If N is a triangular number (that is N = 1 + 2 + 3 + ... + k, for some k), then it is known that deterministic Bulgarian solitaire will reach a stable configuration in which the size of the piles is 1, 2, 3, ... k. This state is reached in k² - k moves or fewer. If N is not triangular, no stable configuration exists and a limit cycle is reached.
- Popov showed that stochastic Bulgarian solitaire spends "most" of its time in a "roughly" triangular distribution.
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References
- Popov, S.
- (2003) Random Bulgarian Solitaire. [Pdf document]
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External links
 | We publish it as we understand it is a fair use. Although the information posted in this web is under the Creative Commons Attribution ShareAlike 2.5 License this does not imply the game has lost its copyright. You can consider the game and its rules have a copyright, and what is free is this way of explaining them. If you are the copyright holder and don't want to have it published here, please contact us |
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