Why so? I really can't understand that. Why we can only select from numbers proposed by players?
4 Answers
You can do what you want to do. However, the thought about choosing the exact numbers that are proposed is that with growing numbers, you cannot estimate small details reliably. That's why with growing numbers, the gaps between numbers become larger.
Once you start giving detailed numbers (like one estimating 8 and the next 13, chosing 11 as a mean) people assume this actually is a detailed estimation. It's not. The method is meant to be a rough guess.

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Behind the idea that people should agree on one number is that everybody should have the same understand of the story. If people pick very different numbers they have a different understanding how much work needed to complete the story or how difficult it will be. The different numbers should start discussions then and finally lead to a shared view of the story.

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The numbers used are spaced far apart on purpose (typically from the Fibonacci sequence). If you get numbers from all across the board from 1 to 23, you're supposed to ask why the person who voted 1 gave it such a low score ("Did you think about testing and deployment? What about these other acceptance criteria?") and why the person who voted 23 gave it such a high score ("Are you aware we already have an existing code base? Did you know that Karen knows a lot about this and can pair up with you?") and then re-vote. If you're really stuck because half the team says 8 and the other half says 13, you can take the 13 and move on with your lives.
The extra precision isn't necessary when your accuracy is not great. My team goes for even less precision and buckets stories into "small" (one person can do a bunch in an iteration), "medium" (one person can handle a few of these), "large" (one person a week or more), and "extra large" (too big and needs to be split).

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You should think to numbers as symbols with none arithmetic meaning, except for a (partially) ordered relation, because they are estimates (of effort need to do done a user story).
If you use math to model an estimate you should provide a way:
- to represent certainty
- to represent uncertainty
- to operate with that representations
- to define an average as a function of certainty and uncertainty
If you use some kind of average which operates on estimates modeled as single numbers you are supposing that certainty and uncertainty can be handle in the same way, and I guess it's a bad assumption.
I think that the spirit of planning poker session is achiving a team-shared estimates by a discussion among human being and not using arithmetic on human being estimates.

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