Here is the most useful sentence anyone will tell you about Reversi: in the middle of the game, having more discs than your opponent usually means you are losing. Everything else follows from understanding why.
Every disc you own is a disc that can be flipped. Own a great pile of them in the centre, and you've simply given your opponent a great many targets — and, worse, you've filled the board with squares that you can no longer play into.
Reversi is not scored until the end. What matters during the game isn't how many discs you have; it's how many moves you have, and how few your opponent has. Strong players deliberately keep their disc count low in the midgame, take few, quiet moves, and let the opponent expand into a position with nowhere left to go.
Then, on the last few moves, the whole board flips over. This is normal. It is supposed to happen.
A disc in a corner can never be flipped. There's no line through it that has one of your opponent's discs on both sides — geometry simply doesn't allow it. And a corner anchors the edges leading away from it, making those hard to flip too.
So corners aren't just valuable, they're a different kind of thing from every other square. One corner is worth more than a dozen discs in the middle. Take them. Always take them.
The square diagonally adjacent to a corner — the one players call the X-square — is the most dangerous square on the board. Play there, and you very often hand your opponent the corner, because your disc becomes the thing they can flank through.
The squares directly beside a corner along the edge are nearly as bad. If you find yourself with no choice but to play one, that usually means your opponent has already won the mobility battle.
You can see this in the engine's own weights: it values a corner at +120 and the diagonal square next to it at −40. Not a small penalty. A hefty one.
Mobility is simply how many legal moves you have. Reduce your opponent's to zero and they must pass; reduce it to one or two and they're forced to play a terrible move — usually one that gives you a corner.
This is why a strong Reversi player will make a move that appears to gain nothing. It isn't gaining discs. It's taking away your options. The machine here scores mobility heavily and will happily give up discs to do it.
1 – Take few discs, not many. Given a choice between a move flipping one disc and a move flipping seven, the one-disc move is usually better. Genuinely.
2 – Play towards the centre early. Keep your discs in the middle four-by-four for as long as you can, and let your opponent be the one who commits to the edges.
3 – Never touch the X-squares without a very good reason. If you must, count exactly what happens to the corner afterwards.
Because that's its name — the game dates to 1880s England, and it's been in the public domain for well over a century. The version sold in a box under a similar-sounding trademark came along much later. The rules are the same; only the name is owned.
Because disc count in the midgame means almost nothing. Every disc you hold is one your opponent can flip, and a big lead usually means you've expanded too fast and run out of good moves. The flips come at the end, all at once — that's the game working as designed, not a betrayal.
A corner disc can never be flipped — there is no line through it that can be flanked. It also anchors the edges next to it. One corner is worth more than a dozen discs in the centre, which is why the whole game is really a fight over four squares.
The number of legal moves you have. Strong play is about reducing your opponent's mobility until they're forced into a move that hands you a corner. It's why a good player will sometimes make a move that appears to gain nothing — it's taking your options away, not taking your discs.