How to play REVERSI
There have been many Reversi (or "Othello" - see footnote) programs written, since the rules readily lend themselves to computer implementation. Many programs just seem to play by trying to flip over the maximum number of pieces at each move - but this is a recipe for disaster if used against someone with knowledge of the game. Have a go at playing FLIP-IT like that, then when you have lost by about 60 disks to 4, come back and read how to really play! I believe these weak programs have lead to Reversi being looked down upon a bit by some of the more hardened computer users, and yet Reversi can sometimes compete with Chess, in terms of subtlety and depth!
Let us start with normal Reversi. The game starts with the following board, with Black to start:-
DIAGRAM 1
: A B C D E F G H
1 - - - - - - - -
2 - - - - - - - -
3 - - - - - - - -
4 - - - O X - - -
5 - - - X O - - -
6 - - - - - - - -
7 - - - - - - - -
8 - - - - - - - -
(O = White, X = Black, Black to play. (legal black moves highlighted in red)
The rules that define a legal move are very simple when seen in real play, but they sound complex when written down, so it is a good idea to run FLIP-IT and try playing a few moves, to get the idea. Anyway, you may move to a vacant square if it is adjacent to an opponents piece, and if by moving to that square you bracket a horizontal/vertical/diagonal line of your opponents piece(s) between the square you are moving onto and a square you already occupy. All of the opponents pieces bracketed or trapped in this way are captured and are flipped over to your colour. As I said it is much easier to see this by example - in Diagram 1 above black can move to the squares marked '+' - for instance if he moves to C4 he 'traps' whites piece at D4 between his at C4 and E4, and D4 becomes a black piece. You may only make moves that "Capture" in this way - you are not allowed to just play to any empty square - so in the opening position in Diagram 1 black may only move to D3, C4, F5 or E6.
If a player has no legal moves available he must PASS a turn, allowing his opponent to take another turn. However if he has a legal move available he MUST take it - you may only pass when you have no moves. The game ends when all 64 squares are full up, or when neither player has legal moves available - even though there may be some vacant squares left. Once the game ends, the player with the most pieces wins - or occasionally there is a draw if both players have the same. So, because the object of the is to finish with more disks than your opponent, some people translate this as meaning "Ok, lets flip over as many disks as possible with every move." - leading to disaster. You could imagine that the following diagram has resulted at the end of a game where White has been capturing everything in sight..
DIAGRAM 2 :- (O = White, X = Black, Black to play)
: A B C D E F G H
1 - O O O O O O -
2 O O O O O O O O
3 O O O O O O O O
4 O O O O O O O O
5 O O O X O O O O
6 O O O O O O O O
7 O O O O O O O O
8 - O O O O O O -
Black has only one disk on the board at D5, with the four corner squares empty and white holding the remaining 59 squares. And yet, if you play out the game, you will find that Black in fact wins by 40 disks to 24! IE. Black plays A8, White PASSES, then A1, PASS, H1, PASS, H8. While this is an extreme example, this sort of chaotic turn-about often occurs in the last few moves of a game, particularly when a master player crushes a novice. The critical factor in the above example are the CORNER SQUARES. Whites mass of pieces were totally unstable because he didn't have possession of the corners. These are referred to as STABLE SQUARES - once you have a corner it can never be recaptured by your foe, and also other adjacent pieces of your colour can also become stable, forming an unassailable fortress from which you can attack the rest of the board. So if, for instance, in Diagram 2 White had already occupied, say, A1, the whole mass of 28 pieces up and left of the A8-H1 diagonal become stable white territory, and white would win the game. By implication, it is bad to occupy the squares adjacent to the corner squares before you have captured the corner, because you may be offering your opponent the option to get the corner, either immediately or later. Consider the following position:-
DIAGRAM 3 :- O = White, X = Black, White to play
: A B C D E F G H
1 - - - - - - - -
2 - X - - - - - -
3 - - X O O - - -
4 - - - X O - - -
5 - - - O X - - -
6 - - O - - X - -
7 - - - - - - - -
8 - - - - - - - -
Black has, rather foolishly, just moved to the B2 square. While White cannot capture the corner immediately, all he needs to do is to move to F5 (capturing E5), and wherever black moves he cannot recapture E5, so White will be able to capture A1 on the next turn. The square at B2, and also those at B7, G2 and G7 are referred to in Reversi terminology as the X-SQUARES, and are generally considered very bad to occupy, especially in the early/mid game. While there are some particular positions towards the end-game where an "X-SQUARE SACRIFICE" can actually win you the game, you should avoid these squares unless you know what you are doing. The Edge squares adjacent to the corners, (B1, A2, G1, H2, A7, B8, H7 and G8) are called the C-SQUARES, for rather obscure historic reasons. The position with C-SQUARES is more complex - while they may offer your opponent future access to a corner, there are some positions where it is relatively safe to take these squares, particularly towards the end of a game. However it is still wise to avoid occupying a C-SQUARE unless you are sure it is a safe position. Of course once you actually occupy a corner all this changes, and it becomes desirable to capture the adjacent C and X-SQUARES - these will now be stable and unassailable.
OK, now up to this point I have discussed ideas that may already be known, at least to some extent, to people who have picked up the game from some of the other shareware offerings. I now move to ideas that are less commonly known outside the realm of serious players, and yet are critical to actually winning games against strong opponents. So far, you understand that your ultimate objective is to get stable corner (and then surrounding) squares - but what strategy should you adopt in the early-mid game, before you get near these squares? Well, if you think about it, you want to FORCE your opponent to capture weak squares such as (say) an X-SQUARE, enabling you to capture a corner - after all he probably will not make such moves voluntarily. However if you can engineer a situation where your opponent only has one or two legal moves available, and these moves are to weak squares, he will have no choice! Here we come to an absolutely critical concept in Reversi - MOBILITY. The MOBILITY of a player is simply a count of the number of legal moves he has available - a subset of this, what you could call GOOD-MOBILITY, is a count of legal moves excluding bad C and X-SQUARE moves that result in the opponent getting the corner. Consider the following:-
DIAGRAM 4 :- O = White, X = Black, Black to play
: A B C D E F G H
1 - - O - - - - -
2 - - O O O O - -
3 O O X X X O - -
4 O O X O O O - -
5 O O O O X O - -
6 - - O O X O - -
7 - - O X O O - -
8 - - O O - O - -
Here all black needs to do is move to E8, effectively blocking whites last decent move. Now white has only one move left, and he HAS to move to B2, allowing black to get A1. By capturing a corner this early in the game, black should have no problem in forcing a win. Take a note of the formation after blacks E8 move - all of blacks pieces are surrounded by white ones (except C3), and white occupies all the peripheral or frontier pieces. This is called CENTRAL CONTROL, and it is very desirable to have this sort of formation - the more peripheral squares you have, the more moves you are offering your opponent! While in the above example disaster was just one move away for white, the strategy for whittling away at your opponents stock of good moves holds out for the longer term as well. If you watch a game between a weak player and an expert, and made a note of the mobility after each move, you will often see the expert players mobility creep up, while that of the weak player diminishes to a point where he literally has no decent moves at all.
So what long term strategy increases your mobility? Here we come to one of the most shocking truths about the game - because while the ultimate goal is to get more disks than your opponent, the best way to win is to actually keep your disk count LOW in the early and mid game! This is called EVAPORATION strategy, and can be translated at its simplest as trying to flip over the FEWEST number of opponents disks at each move. The logic behind this is simple - the more disks you have on the board, the more mobility you are ultimately offering your opponent. However we can refine this strategy further, since it is clearly worst to flip over peripheral (rather than central) pieces, because the more peripheral pieces you have, the more moves you are offering your opponent. A move that doesn't flip over many (or any) peripheral squares is called a QUIET move, and this will be illustrated in our next example. Incidentally note that evaporation doesn't apply once you start capturing corners, because your tactics will then be to MAXIMISE your STABLE (ie. unflippable) piece count. Another feature of the Diagram 4 is whites wall of pieces from F2 to F8 - it is considered very bad to form an unbroken peripheral wall like this since white has no options to move into the territory in the G and H columns. Similarly once the wall has been formed, black should avoid breaking up the wall by cutting across it - this would let white off the hook. Consider blacks options in Diagram 5:-
DIAGRAM 5: - O = White, X = Black, Black to play
: A B C D E F G H
1 - - O O O O - -
2 - - O O - - - -
3 - - O O O O - -
4 - - X X O O - -
5 - - X X O O - -
6 - - O O X X - -
7 - - O O - - - -
8 - - - - - - - -
Compare two of blacks moves, E2 and F2. From the point of view of evaporation they are the same - they flip over the same number of disks. However note that E2 only flips over central pieces, and only creates one new white move at F2. By comparison, F2 flips over a whole mass of peripheral squares E3,F3,F4,F5, creating no less than 6 new white move options - and sealing off a similar number of his own move options to boot! What's worse, he has created a wall of pieces from F2 to F6, and is in a pretty bad way. It is important to try and see the effects of tactics like mobility and evaporation at depth. Consider the following:-
DIAGRAM 6 :- O = White, X = Black, Black to play
: A B C D E F G H
1 - - - - - - - -
2 - - - - - - - -
3 - O O - X - - -
4 X O X O O O O -
5 O X X X X X - -
6 O O O O O O - -
7 - - X O O - - -
8 - - X - - - - -
Black can force a corner capture thus:- A7, E2, A3, G6, A2, and white now only has B7, conceding A8 to black. You will need an Reversi board to play this through - or the full version of FLIP-IT, which allows the setting up and playing through of positions. Let us consider another category of squares - the EDGE squares. Even though these squares are peripheral, occupying them does not directly create moves for your opponent, since he cannot move 'beyond' the edge and flip them! So, on the face of it, occupying a wall of pieces along the edge of the board does not seem bad, and to a certain extent this is true. However you should be wary of occupying edge territory too early in the game - it can tend to make subsequent moves 'flip' over more non-edge pieces than you want to, in other words it works against your evaporation and mobility in the long run. As mentioned earlier, the edge squares adjacent to the corner (the C- SQUARES) can be dangerous to occupy, since they sometimes offer your opponent an option to form a tactical trap, allowing him to get a corner. Consider this position:-
DIAGRAM 7 :- O = White, X = Black, White to play
: A B C D E F G H
1 - X - - - - - -
2 - - X X O - - -
3 - - O O O - - -
4 - - O O X O - -
5 - - X O X - - -
6 - - - O - - - -
7 - - - - - - - -
8 - - - - - - - -
Black has just taken an isolated C-SQUARE, B1. If white now takes E1, then whatever black does (he cannot move C1 or D1) white can go C1! Now black must lose the corner - if he goes D1, white can still simply take A1. Isolated C-SQUARES like that are the worse - the situation is not so bad when you already occupy some of the edge squares. Even then there are dangers:-
DIAGRAM 8 :- O = White, X = Black, White to play
: A B C D E F G H
1 - - O O O O O -
2 - - O X O O - -
3 - X X X O O - -
4 X O O O O O - -
5 X X X X X O - -
6 X O O X X O - -
7 - - - - - - - -
8 - - - - - - - -
Here black can play B2! Now if white replies with A1, black can take a toe hold at B1, and no matter where white goes, black can take H1 and not only get a corner, but also a whole edge of stable squares from B1 to H1. Note that blacks B2 move was to a normally dangerous X-SQUARE, and this is one of the occasions when an X-SQUARE and corner sacrifice is a winning tactic. Whites pieces from C1 to G1 are called an UNBALANCED EDGE, and are dangerous because white only occupies one of the C-SQUARES - if he already had B1, he would not be in danger. While unbalanced edges are not always bad, they should still be avoided if at all possible. There quite a lot of different tactical edge traps, along similar lines to the above positions. As the very end of the game approaches, the value of the corner squares diminish and the actual piece count becomes more relevant - particularly stable disk counts. In the last few moves of the game you simply want to flip over the maximum number of disks RELATIVE TO YOUR OPPONENT - trying to see this is called DISK-COUNTING, and is something that humans are bad at, and computers are good at! FLIP-IT can sometimes execute perfect play over the last twenty or more moves of the game, based simply on counting pieces for all possibilities! General rules of thumb for the end-game are hard to come by - sometimes moves are good just because they are!
That concludes this short tutorial on the game - like in all things, the best way to learn is through experience, so try out these ideas against FLIP-IT in real play!
(* The game of Reversi is also marketed as a board game under the trade mark "Othello" - however I use the 100+ year old name for the original game here.)
(This text is (C) PC Solutions 1993-2004. To download a free demo of FLIPIT see http://www.ChessAndCheckers.com)