Pentalpha! How many games can we play on this stellar geometric pattern?

About Lone Star, from BoardGameGeek:

From the game box: "Lots of fun for every one" Lone Star is a game published in the 1940s by the Starcraft / Star Mfg. Company in Lincoln, Nebraska, U.S.A. It's a peg game on a pentagram with 31 holes. It was originally patented and published in 1892 by Charles H. Rickert. The solitaire version is exactly what one would expect: Place a peg in every hole on the board except the center hole. Each turn is then a jump-and-capture move following the lines on the board until no more jumps can be made. The ultimate goal in this game is to leave only one peg on the board and it's in the center hole. The two-player game is set up the same way, and moves are always single jump-and-capture moves, but the objective is to be the last player able to jump a peg. The final variation for Lone Star is a capturing competition. Again, the set up is the same and every move the two players make must be a jump-and-capture move. The major change is that chain jumps are allowed. The winner is the player who captures the most pegs when no more jumps can be made.