Originally Posted by

**Dodo**
No, you need to go up a level in abstraction. The "model" is *not* a simple one (in which every possible number would be equally likely); so, the "weighted average" takes this into account--think about integration in the calculus. And the model would be created uniquely for the seen number--this number is a clue as to the distribution of numbers in the model space that includes the seen and unseen numbers.

Suppose you told me that you wrote down the size of your bankroll on a piece of paper and another number on a second piece of paper. If one of the pieces of paper is revealed to begin with a "9" digit, my guess would be that your bankroll size is written down on the other piece of paper. I reach this conclusion because Benford's law tells me that an arbitary decimal number has less than a 5% chance of starting with a "9" digit. If the seen number started with a "1" or a "2" digit, my guess would be that that number is the size of your bankroll by a similar reasoning process. This "guess which number is my bankroll size" game is much easier than the game described in the article. In that game, arbitrary numbers could be revealed, so no model can be created *a priori*. But upon seeing the first number, you can use it as a clue to the characteristics of the the unseen number and create a model space that reflects all the possibilities with appropriate weightings. I will emphasize that YOU can: this is beyond my abilities or desire to do so.

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