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This is the definition of ''optimal'' martingale and no c.e. martingale is optimal, see "Algorithmic randomness and complexity". <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:コドボル|コドボル]] ([[User talk:コドボル|talk]] • [[Special:Contributions/コドボル|contribs]]) 09:23, 26 May 2010 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->
== Betting ==
''Martin-Löf randomness has since been shown to admit...random sequences should be incompressible, they should pass statistical tests for randomness, and it should be difficult to make money betting on them.''
The nature of the randomness has no relevance to how easy it is to make money betting on them. This needs to be clearer to be true. I am not going to edit as it is 15 years since I did any algorithmic computer science, but these days, doing finance, i know that statement is untrue.
It is dificult to make money betting on the precise value of a sequence, but a sequence can fall within bounds, bounds that can be discovered and exploited in the sense of gambling, and still the values of the sequence can be random from the POV I understand it (Chaitin: The sequence is un-compressible.)
Gambling strategies are every bit as evolved, sophisticated and complex as AIT these days. So the language needs to be moderated. It may indeed be '''very''' easy to make money by betting on a random sequence.
[[User:Worik|Worik]] ([[User talk:Worik|talk]]) 20:46, 2 November 2010 (UTC)
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