Hey, That's my Fish! is a great example of a combinatorial game that is mass-produced and purchasable.
The initial game board is a randomly generated grid of hexagons, each containing an iceberg with 1, 2 or 3 fish on it. Players then take turns putting their penguins on bergs with exactly one fish.
Each turn, a penguin moves any number of spaces in a straight line (in the 6 "hexcardinal" directions) from one iceberg to another. That penguin may not jump any other penguins or any empty hexagons in their path. After moving, the hexagon the penguin left is removed from the board, and that player earns points equal to the number of fish on that tile.
If a player cannot move on their turn, they forfeit their turn. Once no more moves are available to any player, all players pick up the tiles their penguins are on and add those fish to their points. The player with the most points (fish) wins.
There are rules for up to four players, which is excellent for flexibility. Once the board has been created, if there are only two players, the game is combinatorial (assuming adoption for points).
This is a really interesting game because there are greedy strategies that are often used in the beginning, even if they're not the best move down the line!
My Last Visit with John Conway
4 weeks ago