Accuracy of short term standard deviation?

[barongreenback]

Let's say I know the standard deviation of my win rate. As I play more hands the SD number may change. This might be due to game conditions or my play changing. However, even if we assume that these variables are consistent my SD should 'settle down' over time, coming closer and closer to the true figure. How do I estimate how close to this 'true figure' my current SD is? In effect what is the SD of my SD?

This is a difficult subject to search for because the search terms are common. If it has been covered before can you provide a link? I do remember a link to a rather deep essay on this a while back but I've lost it. I suspect this could be quite an interesting subject but at the moment I'm mainly looking for a practical answer.

Thanks,
James