Crokinole
Flick a disc across a board, past eight pegs, into a hole barely wider than the disc. Twelve each.
Pull back from your disc, then let go.
The game
Crokinole comes from Ontario, and the oldest board anyone has found was made in 1876. The rings score five, ten and fifteen from the outside in, and the recessed hole at the centre is worth twenty. You shoot from between your own quadrant lines, with the disc touching the outer ring.
Two rules give it its depth. If the other side has anything on the board, one of your discs must strike one of theirs, either directly or by bumping a disc of yours into it. If their side is clear, at least one of your discs involved in the shot has to finish at least touching the fifteen line, which a twenty satisfies. You are never required to hit your own disc.
Breaking either one costs you the disc you played and every disc of yours the shot struck, including any that had just gone in for twenty. That is what stops the game being a matter of hitting the twenty twelve times, and it is why a wild shot into a cluster of your own discs is worse than a safe one.
Rules follow the World Crokinole Championship wording, which is the National Crokinole Association set.
How the opponent plays
It knows nothing about Crokinole. Because a shot here is a pure function of the board, the opponent can play out a few hundred candidate shots for real, look at where each one left things, and keep the best. That beats any amount of hand-written strategy, and it only works because the simulation is exact and cheap enough to run hundreds of times between your turns.
Difficulty is not a different algorithm. A weaker opponent considers fewer shots and then plays the one it chose slightly wrong, which is how a weaker player actually differs from a stronger one. The three settings are tuned by how often each holes an open twenty: about fifteen, forty and seventy per cent.
The physics contains no trigonometry, which looks like an odd rule until you want two browsers to agree. Arithmetic and square roots give identical answers everywhere; sine and cosine are allowed to differ in the last bit, and one bit is a different board twenty collisions later. Keeping them out means a shot can be sent as four numbers and replayed exactly.