Stable Manager is a windows program you run on your computer. When the program opens up you will see a list of your horses. You will be able to click on one of the horses and see the detail of the horse - as you can on TK itself - stats, xp etc.
When the program opens it will show data as you last saw it. To refresh the data you enter your username/securitycode on the settings page and select the Load from Web menu option. The program will then access TK and fetch the latest info about your horses.
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