Last updated : July, 2006.

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@F.Pittner

mail@tothello.com

Introduction

Just for those who are not familiar with what the reversed or anti othello means:

• Othello = Reversi: (means the same game type);
• Normal mode: the winner is the player who at the end has the most of discs;
• Anti mode = Reversed mode: the winner is the player who at the end has the least number of discs.

If you follow a game played by a top program you will see that the right strategy in a normal game is to find the equilibrium of the number of own and opponent’s pieces: if you have too many pieces, it can easily happen that you lose mobility and finally the game. In a normal game there are several hidden traps you can encounter. The most evident is not to move into the X- squares (B2, G2, G7, B7) if you don’t have to .

I will skip to explain in detail how one can learn to play Othello (reversi) games. If you are really interested there are many sources available on the internet. I prefer the help files of the WZebra program created by Gunnar Andersson (see the links), but other pages are also very useful. Opening strategies calculated by top programs are a good starting point and help human players too. But as soon as the game stage reaches an unknown position intuition becomes ineffective and brute calculation wins. Just think of the situation when an x-square has to be played because this is the best move. How many human players will risk this move without knowing the exact outcome? Computer programs calculate and make these moves without any fear. My personal opinion is that the reversi game - and especially the normal game type - is not really convenient for human players.

And now after a philosophical aside, let’s come back to the reversed reversi game. The only source I have found on the web about the reversed Othello games is a high level description of Turingtest (http://www.samsoft.org.uk/reversi/strategy.htm), who played several games in the MSN gaming zone’s tournaments.

The range (space) of the game’s result

If you are a beginner in reversi games you can be easily defeated by a program 64:0. The program will flip all your pieces, you will not even be able to play each time you want to, because you will probably have to pass many times. Thus from the normal endgame result’s point of view all results from -64 to 64 are very probabilistic. Of course the better the players are, the closer the final result will be to a draw. So in a normal game the most probable outcome is the draw, but -64 and +64 results appear very often in comparison to the reversed games. In the case of reversed games the situation is more difficult. A beginner will definitely lose, but only extremely rarely will the final difference be -64.  Even a beginner human player can force the opponent to have at least 5-10 discs at the end, thus the average final wipe-out result (disc difference) is between -32 and -44. Of course one can lose by -64 if he really wants to, but with a very minimal strategy this doesn’t happen. This is one of the reasons why I really like reversed games (you are not wiped-out psychically ).

Interestingly from my experience a reversed game position is more difficult to solve perfectly than the same position in the normal game mode. To clarify this have a look at the following two pictures. Both are the “same” board positions, but the first is a normal othello and the second is a reversed othello.

On the left picture in the normal othello, the range of the possible moves’ values is [-26,0], while on the right in case of the reversed othello the range is [-10, +2]. This affects the search algorithm since there are more moves with closer values to the best move, and therefore the pruning needs more calculation.

You will find another example of this on the pages with the exact solution of the normal and anti 6x6 games. There are only a few exact solutions (main lines) of the normal game resulting finally in +4 for white, but just have a look at the third move of the reversed game: after C2 B4 there are already 3 possible moves of black (C5, D5, E5) which are all best moves and lead to +2 for black in the end.

Have a look at the position values in the normal 6x6 game: and in the reversed 6x6 game:

Using search terminology we can state that in general solving a reversed game  is more difficult because the number of cut-offs is less, there are many moves with very close values to the best move, therefore more moves have to be searched.

No subtle traps

In a normal game if a human player plays against a good computer program, the latter will probably force the first player to give up some corners using its full knowledge of mobility and subtle traps (which could be calculated only by an in-depth search). Playing many reversed games I found that - unlike the case of normal games, except the closed corner shown on the next image (A1), there are no other subtle traps that the player should be aware of. This makes the reversed game more “philanthropist” than the normal one.

If you are interested in playing reversed games in comparison to the normal othello, please read Guidline of reversed othello.

The possible perfect outcome of the ANTI 8x8 game

One can ask: okay, now what does Tothello  say about the exact outcome of the reversed 8x8 othello game? Although it has not been proved by a theory, practically the normal 8x8 othello game is a draw. There’s no chance for neither of the parties to win. Of course you need a big opening book to prove this, but according to our best knowledge this is the outcome.

This question can only be answered by building an adequate opening book and trying to solve as many games as possible. Tothello has played about 55000-60000 games in reversed mode with itself and another many games with aSaio. It seems that the outcome of the reversed othello game is +2 (black wins). D3C3C4 seems to lead to +4 for black, while D3C5 seems to lead to +2. There are - of course - many "main lines", one of the best chioces is for example:

C4E3F5E6D3C5D6C6F6F4E7G5D7F3G6F7B4B5G8D8G7C8B7C7E8F8A6C2D2B3B6C3H4H5G3G4H3H6A2E2B8H2G2G1F2A3E1D1A5B2F1A4C1A1H1B1H7H8PAA8A7