Strategy Guide for Reversi & Reversed Reversi

While there are many online guides to Reversi or Othello (see links below) there does not seem to have been much written about the reverse game. This guide aims to correct this omission and is also a useful opportunity for me to try to distil my limited understanding of the ordinary game. I used to play both forms of the game online at the MSN Gaming Zone before it closed and, in particular, enjoyed taking part in the ladder tournaments on the Case's MyLeague ZoneReversi Ladder, & Reversed Ladder and the somewhat irregular Zone Reversed Reversi Tournaments.


In the classic game of Reversi you try to end up with the most discs of your colour at the end of the game. In Reversed Reversi the rules are the same but the goal is to end up with the fewest discs. Much of the strategic thinking behind the classic game can also be applied to the reverse game, though sometimes in reverse!


Topics

Home    
 


 
The Rules  











Diagram 1: Starting position
Black, to move, has a choice
of four symmetrically equivalent squares.

Reversi or Othello takes place between two players, black and white, on an 8x8 board of 64 squares. There are 64 discs coloured black on one side and white on the other.
The board is set up initially with two black discs (i.e. a disc with black side uppermost) placed on squares e4 and d5 and two white discs on d4 and e5.
Black always plays first with players then taking alternate turns.
At each turn a player must place a disc with their colour face up on one of the empty squares of the board, adjacent to an opponent's disc such that one or more straight lines (horizontal, vertical or diagonal) are formed from the newly placed disc, through one or more of the opponent's discs and up to other discs of their own colour already on the board. All the intervening discs of the opponent's colour are flipped to the colour of the newly laid disc.
Discs may be flipped from one colour to the other but once played are not moved from one square to another or removed from the board.
Players may not pass unless there is no valid move available to them in which case they must pass.
Play continues until neither player is able to move, usually when all 64 squares have been played.
 

 
The Goal   Reversi   Reversed Reversi










Diagram 2
  The winner is the player with most pieces turned to their colour at the close of play. By convention any empty squares at the end are added to the winners score, thus diagram 2 shows a 35-29 win for black.

If both players have the same number of discs at the end then the game is tied.
  Reversed Reversi (a.k.a. Anti-Reversi) is played with the same rules but the goal is changed. The winner of the game is the the player with least number of discs at the end. These may also be referred to as "suicide rules" with the winner being the player who successfully suicides in what would otherwise be a regular game of reversi. Diagram 2 illustrates a Reversed Reversi victory for white who has 29 discs compared to black's score of 35. Playing badly at the regular game is not enough - you'll have to work hard to force your opponent to take more discs than you if you are to win the game.
 

 
Notation      

North











Diagram 3: Significant squares
  The squares on the reversi board are referred to using coordinate notation in order to record games and allow the discussion of strategy. Certain significant squares are given special names. The corners are a1, h1, a8 & h8. The X-squares are those squares diagonally adjacent to a corner and the C-squares are the other squares adjacent to a corner. Some analysts of the game also refer to A-squares & B-squares as indicated left. The central 4x4 block of squares is  

W
e
s
t

E
a
s
t

South

    referred to as the sweet
sixteen
, while the central 2x2
  Diagram 4
    block of squares initially occupied at the start of the game is called the centre. The four edges of the board maybe referred to as the north, east, south & west edges respectively and it is possible, for example, to talk of the north-west corner of the board meaning the a1 corner and surrounding squares.  

Games can be recorded either by listing the move numbers and coordinates for each player

 

Black
1. c4
3. d3
5. d6
7. f5

White
2. c3
4. c5
6. f4
8. e6

or by recording the move numbers in a grid. Diagram 4 shows a typical move sequence for the Tanida opening overlaid on top of the position arrived at after the first 8 moves.

 

         
Maximum Disks Strategy
or Greedy Algorithm
  Reversi   Reversed Reversi

Diagram 5
: Too much, too soon
(Run mouse over board to see result)
  Beginners usually start by interpreting the requirement to end up with the most discs as a strategy for the whole game. This position illustrates that having the most pieces at one point in time does not necessarily guarantee a final victory. White leads 59-1 but has no valid moves remaining. Black may now play into a1 or h8 followed by the remaining corners in any order. White has to pass each time and thus black ends up winning the game 40-24!

It can also be tempting to try to wipe out your opponent earlier in the game by taking as many of their pieces as possible however unless your opponent is carelessly working the evaporation strategy and not paying attention then it is unlikely that you will succeed. By the time it becomes apparent that you have failed you are likely to have few good moves left and your opponent will be well placed to drive you to defeat.
  In contrast this is an ideal endgame position for white in Reversed Reversi as, like it or not, black is now forced to take all four corners and ends up taking 40 discs to white's 24. In practice however, trying to set up this sort of ideal endgame is dangerous. Taking so many pieces can exhaust your mobility giving control of the game to your opponent. Consider diagram 5 where just one of the X or C squares is black. White will then have to take one of the four corners and, even with black taking the remaining three, the final score will be 24-40 or 21-43 in black's favour!

In reversed reversi you don't have to worry about being wiped out as this too counts as a victory, but this is another argument against wildly grabbing useful looking territory. In one of my early reversed games I was so busy preparing the ground for the big finish that I missed the fact that my opponent was evaporating and I was suddenly forced to take the last of his pieces before half of the discs had even been laid. Needless to say I now try harder to ensure my opponent's survival.

 

 
Stable Discs   Reversi   Reversed Reversi

Diagram 6
(Mouse over to highlight stable discs)

  It should be readily apparent that once a disc has been placed on a corner square it cannot be flipped, The disc is said to be determined or stable. Neighbouring discs of the same colour are also stable if there is no way for the opponent to outflank them through the rest of the game. In diagram 6 black has 23 stable discs while white has just one (d6) that cannot possibly be flipped by subsequent moves. Black needs to take and secure just 10 discs from the 40 available during the remaining play to secure a win.   In the reverse game you want to try to avoid creating stable regions of your own colour while trying to "assist" the creation of the same for your opponent. Creating blocks of your colour with single "holes" into which your opponent must play at some point may prove useful although you have to be wary of any negative side effects that might arise for you when your opponent finally plays there.
 

 
Positional Strategy   Reversi   Reversed Reversi

Diagram 7

  Having seen how useful the corners are and taking into account that each piece you lay may act as a 'stepping stone' for your opponent it is easy to try to assign a fixed worth or fitness to each square. Corners are very good, X & C-squares bad (because they may give your opponent access to corners), A & B-squares OK etc. Since the board has a number of symmetries there are only 10 distinct types of squares. Diagram 7 shows part of the static evaluation table used in the reversi program that was included with past versions of Microsoft Windows. Fortunately the game is deeper than this (otherwise it wouldn't be any fun) and a few games with players of any strength will reveal that a strategy of trying to play in "good" squares and avoiding "bad" ones will soon yield control of the game to your opponent. Nevertheless an idea of static worth may help when it comes to choosing between two moves that would otherwise appear of equal value using other criteria. When planning a move you need to consider your opponents' possible response, then your response to that and so on. At the end of the game it might be possible to calculate all the variations but elsewhere in the game you will need to have some mechanism to avoid having to consider all possible branches more deeply than is practical - e.g. a feeling for the relative worth of particular squares.  

Looking at diagram 5 it should be apparent that if you can force your opponent to take all four corners and edges they are likely to end up with the most discs. Simply inverting the positional values of each square gives a first approximation to a fixed evaluation of the reverse game. Further study shows that while occupying an X-square in the classic game is likely to give away a corner and is therefore usually a bad move, control of both the C-squares and the X-square is required if you are to oblige your opponent to take up the corner. Once a disc has been placed on a C-square it can only be flipped by a move to the corner square. The X-square can be flipped more readily and may be used by your opponent as a stepping stone to a C-square. Likewise taking an early A-square can provide access to C-squares for your opponent so should probably be avoided. At least one A-square will be required to prevent any possibility of your opponent flipping the X-square later in the game however. Compare the south-east & south-west corners of the diagram 8 below. Black will almost certainly have to play to h8 before the game is out, gaining an unwanted corner. However playing b6 will flip the disc on b7 and if white cannot flip b7 again then, depending on the relative mobility during the endgame, there is a possibility that white may have to take the south-west corner before the conclusion of the game. 


Diagram 8

While acknowledging the limitations of pure positional strategy I would suggest the above static table for consideration as a quick guide to the likely relative value of various squares in Reversed Reversi. In short, C-squares are nearly always useful, whereas those adjacent to them should probably be avoided because they provide access to the C-square.

 

 
Mobility   Reversi   Reversed Reversi










Diagram 9: White to play
 

At each stage of the game you will have to chose between the limited number of moves available to you. In diagram 9 white has just 3 available moves or "liberties", two of which hand a corner to black straight away. Assuming white plays to e8 black will have 13 moves available of which 11 will lead to a win with best possible play by both sides thereafter. In this position white has poor mobility having few moves to choose from, all pretty bad at that, while black has good mobility having lots of choice. As long as there is at least one non-disastrous move for each player the game will remain in balance but if you can start to restrict the mobility of your opponent while maintaining your own then you may be able to force them into having to make bad moves.

  The concept of mobility is also key to the reverse game. If you can achieve a position where you can restrict the   availability of moves to your opponent then you are well on the way to victory.
 

 
Evaporation Strategy
or "Less Is More"
  Reversi   Reversed Reversi


Diagram 10: Black to play

  The easiest way to increase your relative mobility compared to that of your opponent is to have fewer pieces on the board - so while you want most pieces at the end of the game it pays to try to keep down your gains in the early stages... of course your opponent knows this as well so they will probably be trying to do the same. You also have to take care not to evaporate altogether. In this position black (to move) can wipe out white by playing at d6 bringing the game to an early conclusion!   The evaporation strategy is also useful in the reverse game as the aim is to try to take control by reducing your opponents available moves or liberties. The lower your disc count, the fewer liberties they are likely to have and the more likely they are to be forced to make poor moves. In contrast to the regular game you don't even have to worry about being wiped out yourself (this too counts as a victory) but you do need to be wary of your opponent evaporating completely.
 

 
Frontiers   Reversi   Reversed Reversi










Diagram 11: Black to play
 

Each move is played to an empty square adjacent to an opponent's disc and flips at least one of their discs. The discs which have empty neighbouring squares form the frontier while those that do not are called interior discs. The more frontier discs you have, the more choices your opponent has and, likewise, a smaller set of frontier discs restricts the number of available moves. It should be clear that minimising one's frontier is key to winning the battle for mobility. In diagram 11 black should play a6 flipping 3 discs (rather than f7 which flips 1) as this keeps the frontier to a minimum. A move like this which does not flip any frontier disks is called a quiet move and often represents good play. This suggests a refinement of the evaporation strategy in which you try to evaporate your frontier discs while not being so concerned with the total numbers of discs flipped at each turn.

  Maintaining a small set of frontier discs will prove just as useful as it does in the regular game as it serves to increase your relative mobility.
 

 
Stoner Traps or
"Heads I Win, Tales You Lose!"
  Reversi   Reversed Reversi











Diagram 12: White to play











Diagram 13: Black to play with white threatening d8.

N.b. The black disc at b5 ensures that black cannot safely respond to d8 with b8. The trap would also fail if white did not fully control the diagonal at this point as black would be able to play a8 and then reply to d8 with b8 winning the southern edge. White must also have access to the attack square d8.

  A Stoner trap (named after John Stoner) is a particular type of forced corner exchange that takes advantage of a weak edge position, that is an edge including a C-square. The attacker first gains control of a diagonal (meaning they have all the discs in that diagonal) by playing to an X-square, then attacks the opponent's weak edge by threatening to take a corner. The opponent cannot respond by taking back the edge since this would flip back the X-square played in the previous move and provide access to the other corner. Whatever response the defendant makes the attacker gains at least one corner square and a number of stable discs.

In diagram 12 white plays b7  threatening d8 on a subsequent move. Looking at diagram 13, black cannot deny access to d8 by playing it themselves as this gives white access to h8. Wherever else black chooses to play white will be able to play d8 on the next move with the threat of h8 to follow. If black then plays b8 to recover the south edge, b7 will be flipped and provide access to a8 for white who may then take all of the southern edge. Once the trap has been set the best that black can hope for is to get access to a8 in exchange for losing the h8 corner.
  The nearest analogy I've come up with is this sort of position. White plays d8 to gain access to at least one C-square with the hope that, having access, black can be obliged to capture the edge later in the game. A black reply to e8 also flips f7giving white access to g7 and the opportunity to take all of the southern edge.
 











Diagram 14

 

 

 
Parity   Reversi   Reversed Reversi











Diagram 15: Black to play

  The last player to move (normally white) has an advantage as any discs they flip in that turn can't be flipped back. This is global parity. Towards the end of the game the remaining empty squares will form distinct regions with either odd or even numbers of squares. Playing last into each such region will usually yield the best results. In general avoid playing first into regions with even local parity (even numbers of empty squares) and play into regions of odd parity. Diagram 15 has three  areas of 1, 2 & 3 squares respectively. White cannot play to g8. Black's best move is to play g2 in an area of odd parity leaving two areas of even parity into which white must play. By replying into the same region as white each time and saving g8 for the final move black wins 36-28. Should black make the wrong initial move white can win 39-25.   Black has the advantage of global parity in the reverse game provided neither player has to pass or there are an even number of passes. White will play last and is likely to lose out by virtue of move order in an otherwise even endgame. If you can force your opponent to be the last to play into each region in the final stages of the game then this too should tip the balance in your favour. It is therefore useful to create odd regions rather than even ones and to play into even regions in preference to playing into odd ones. In diagram 15 black should play to a2 forcing white to either take the west edge or initiate play to the north-east - either way white will lose. Diagram 5 shows a position with 4 singleton regions into which only black may play with inevitable results. Most of my successful Reversed Reversi games finish with my opponent having to move into just such regions for the last two or three moves while I pass each time having no available moves.
 

 

Openings
It is quite easy to lose control of the game in the first few moves. Play the wrong move and your opponent will be able to restrict your choice of moves to those that work in their favour. While the concepts discussed above may help guide your opening moves it is worth looking at some standard openings which appear to preserve the balance of control, at least for a while. The openings page has an illustrated step-by-step guide to some of the more promising opening variations and a list of common named openings. 

 

 

Animated Openings, Tricks & Traps Etc.
In addition to the original openings page the main section of this site now comprises of a JavaScript applet that demonstrates all the standard opening sequences, illustrates some of the potential traps that you can try to set or avoid and includes a selection of short wipe-out games and some complete regular and reversed games. 

 

 

Topics to come... (eventually)
Tempo
Move order
Wedges
Poison
Swindles
Conclusion

 

 

Links

   

Play Online:

MSN Zone Reversi - Free online play with a .Net account
MyLeague Zone Reversi Ladder - For ladder play with regular tournaments
MyLeague Reversed Ladder - For ladder play with regular tournaments, in reversed style...
MSN Zone Reversed Reversi Tournaments - Tournament calendar & results
PlayOK (formerly Kurnik) - Free online play
VOG: Vinco Online Games - You can play online & unrated as a guest for short periods however rated play requires fee-paying membership
   

Reversi Downloads:

Beppi Menozzi's Happy End - Practise your endgame skills
WZebra - The finest freeware Othello/Reversi program available
   

Strategy Guides & Other Links:

British Othello Federation - The home of British Othello

Elements of Strategy - A brief guide accompanying a Java-based Othello program called Ajax
French Othello Federation Booklet - An online English translation at the home of WZebra
Joel Feinstein's Othello Guide - Some interesting topics are covered here, in particular The Art of Sacrificing Four Corners, now graphically illustrated on this site here
Othello: A Minute to Learn, A Lifetime to Master - A 170-page PDF (Acrobat) book from Othello Champion Brian Rose
Othello Club Deutschland Home page of the German Othello Club
Othello Openings - A list of opening variations and their usage frequency
Othello Patterns & Tricks A few interesting sequences (tesuji) are shown here, most of which are now also available on this site here
Othello University - Strategy guide with a trainer applet here that contains a larger list of named openings
The Othello Guide - Sadly missing at present, this site had a great forum together with some useful insights on strategy. A number the tricks & traps presented on this site were originally found there.
Othello World - Another Othello forum
Yahoo! Games - The online game is S L O W (and their board is back-to-front) but the strategy guide is worth taking a quick look at for pointers if you are new to the game
 

 

Acknowledgments
While my notes on Reversed Reversi are all original, parts of this strategy guide have been copied adapted from existing guides found on some of the sites referenced above. As Tom Lehrer put it in his song Lobachevsky:-

Plagiarize,
Let no one else's work evade your eyes,
Remember why the good Lord made your eyes,
So don't shade your eyes,
But plagiarize, plagiarize, plagiarize -
Only be sure always to call it please 'research'

Feedback:
turingtest2@{remove}samsoft.org.uk

Version 1.22 - 04/01/2011