I am not a Scrum Master or a Ph.D. in math. How do stories with 0 and 0.5 points apply to stories on the Scrum board?
0-point and 0.5-point stories are part of the modified Fibonacci sequence often used in user story estimation, and denote stories that are smaller than the team's standardized baseline.
Sequence Measures Relative Effort
Story points in Scrum often use a standard or modified Fibonacci sequence to estimate the level of effort for stories based on some agreed-upon baseline such as a "typical" one-point story. The sequence is intended to encourage relative estimates of effort, rather than time-based estimates. For example, a 1/2-point story should require half as much effort to complete as a 1-point story, while a 2-point estimate is expected to take twice the effort required by the baseline.
Some people use zero-point estimates for stories that they don't want included in their velocity tracking, or for stories that they consider too small to assign points to individually. For example, some teams might assign a number of zero-point stories an aggregate estimate, where a half-dozen zero-point stories are assigned an aggregate value of five points.
In my professional experience, while 1/2 point stories may have a valid place in Sprint Planning or user story estimates, I have never seen zero-point stories used to good effect. Using them either results in invisible work (a big no-no in effective Scrum implementations) or mis-estimates caused by emergent complexity or disregard of work-in-progress (WIP) limits.
In my own practice, I strongly recommend avoiding zero-point estimates altogether. However, your professional mileage may vary.
Stories with 0 SP means that there is nothing to do in this story. It means that this story has been done in another story, or just someone done it by accident. You can keep them in your product backlog, or with all stories which has been accomplished so you can see what have been already implemented into your product
0,5 SP means that there is a little work to do.
One key objective of modified Fibonacci series in story point is to avoid false impression of precise multiplication between relative sizes. For an example using a series of 1,2,4,8,... implies some preciseness that 4 story point worth of story is exactly 2 times bigger than a story point 2 worth of a story. When keeping that in mind, using 0.5 will also create the same confusion because 0.5 to 1 is exactly the double and 1 to 2 also exactly double the size. Hence avoid using 0.5 in your sizing scale.