Well thank you for your effort . But you could have described it in a very simple way , Stake = shares . I really do not see why you made it too complicated.
And to calculate stakes just do what you will do to calculate you shares in any thing . Value of the asset ( pool ) / number of shares ( stake ) = value of 1 share ( stake) .
The sampling you have done has been a very nice, useful and understandable example. Thank you for your good comment and notes.