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| visits | member for | 1 year, 9 months |
| seen | 2 hours ago | |
| stats | profile views | 6 |
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Apr 21 |
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Betting on the digits of a real number I've updated the question in response to your comments. |
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Apr 20 |
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Betting on the digits of a real number @joriki: Yes, I see that I formulated the question slightly incorrectly. I think I meant "Is there a strategy such that there is no $x$ that 'defeats' it in the long run". My instinct initially was that there might be choices for $x$ that 'defeat' every strategy (but you have shown that to not be the case), which is why I made the error, I think. |
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Apr 20 |
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Betting on the digits of a real number @carlop: $0.5 - 2|x-0.5|$ is not always greater than zero for $x$ between 0 or 1, take $x=1$, for example. |
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Apr 20 |
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Betting on the digits of a real number @joriki: But there is not a unique $x$ given an initial string of digits, so what does "correct guess" even mean? I see the problem you are bringing up, but I guess when I'm talking about strategy, I mean some rule or algorithm to play this game no matter what $x$ is. |
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Apr 20 |
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Betting on the digits of a real number I see. Does it clarify things if we define strategies to be functions mapping strings of digits (all the $nN$ revealed digits that I know at turn $n$) to guesses $p$? |
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Apr 20 |
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Betting on the digits of a real number Thanks for the comment. $x$ is kept secret, so the choice of $p$ must be made based only on what digits have been revealed in play. I have edited the question to clarify this. |
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Feb 7 |
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An approximate relationship between the totient function and sum of divisors Thanks. I find these kinds of facts remarkable. Do you know what are the prerequisites for Hardy and Wright? |
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Aug 12 |
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Recognizing and Using Chaitin's Constant Great answer, thanks. |
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Aug 11 |
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Recognizing and Using Chaitin's Constant Thank you all for your replies! |
