Please use big square points and slider "Size" for changing shapes of conics. Set number of segments with "n" slider. Start "the game" with small numbers. Dashed segment show distance between start and end points of Poncelet's chain. Try to change shapes of conics and close the chain! Use firstly square points and slider "Size"; than slider "Fine" for fine tuning of inner ellipse' shape.
Switch on "Show centroid" checkbox and explore the mass center behavior.