# JOwen

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|          |                | bio     | visits   |             |                  |
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|          | 170 reputation | website |          | member for  | 1 year, 9 months |
| 8 badges | location       |         | seen     | 2 hours ago |                  |

# 9 Comments

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| Apr21 | comment | Betting on the digits of a real numberI've updated the question in response to your comments.                                                                                                                                                                                                                                                                                                      |
| Apr20 | comment | 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. |
| Apr20 | comment | 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.                                                                                                                                                                                                                                                   |
| Apr20 | comment | 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.                                                                                 |
| Apr20 | comment | Betting on the digits of a real numberI 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 $p$?                                                                                                                                                                                       |
| Apr20 | comment | Betting on the digits of a real numberThanks 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.                                                                                                                                                                              |
| Feb7  | comment | An approximate relationship between the totient function and sum of divisorsThanks. I find these kinds of facts remarkable. Do you know what are the prerequisites for Hardy and Wright?                                                                                                                                                                                                           |
| Aug12 | comment | Recognizing and Using Chaitin's ConstantGreat answer, thanks.                                                                                                                                                                                                                                                                                                                                      |
| Aug11 | comment | Recognizing and Using Chaitin's ConstantThank you all for your replies!                                                                                                                                                                                                                                                                                                                            |
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