My Othello Career
Mostly off topic, but Tyler Cowen sent me a cryptic email asking about it. I can refer him to this essay.from 1998.
With apologies to Robert Fulgum, everything I ever learned about competition I learned by playing Othello(tm owned by Pressman toys). Othello is a board game somewhat like Chess or Go, and it has a small fraternity of competitive players, of which I am one.
When I was at my peak, I might have played at 65 percent of optimality. That is, 65 percent the time I played the correct move for the given position. The 65 percent figure is a guess, because it is impossible to prove that a move is correct (except for positions near the end of the game, when one can use a computer to determine the optimal move by brute force.)
At that time, the world champion of Othello might have played at 75 percent of optimality. If this is correct, and the world champion and I had played 100 games, how many would I have been expected to win?
If you think that 75 percent of optimality vs. 65 percent of optimality should lead to a fairly small difference in games won, you are assuming implicitly that the game only lasts one move. In fact, because each player makes 30 moves, the cumulative effect of a seemingly small difference in accuracy is such that I would be fortunate to win 5 games out of 100 against the world champion.
Suppose that a game lasts N moves. I win when I play correctly for more moves than the world champion. As N becomes large, the small per-move advantage of the world champion compounds until my chances of winning nearly vanish.
…Many people argue that Microsoft wins with inferior software and superior marketing tactics. However, Microsoft software usually is superior in some dimensions, even though it may be inferior in others. My mental model of Microsoft is that, like the world champion in Othello, it makes fewer mistakes than its competitors.
More below the fold, if you are interested. You can also read this interview.Basically, all it took for computers to overtake humans (or at least this human) in Othello was one or two iterations of Moore’s Law back in the late 1980’s. I forget whether it was the 486 or the Pentium that did me in.
It was a real lesson in what happens when you’re up against a rival whose ability is doubling every 18 months or so. I had a copy of a program by David Parsons that I could whip any time on my then out-of-date computer in the late 1980s. Once I got a newer model, I inserted the exact same disk, and with a faster machine I could not win a game. The computer was now looking ahead 7 to 9 moves within the time constraint, instead of 5, and that made all the difference. Parsons himself crushed me during the U.S. nationals in 1988, because he had run my usual openings through his computer program and found lines that refuted them. He was not a better overall player, as I think he would admit.
Parsons’ program was an old-fashioned AI type of program. The next generation used statistics. The computer would have a database of games with positions and outcomes. So, when it looks at a position at move 33, it looks in the database for the most similar sorts of positions and the final scores of those games. Crudely speaking, if the average is a win for Black by 5 discs, then the position is scored as +5 for Black and -5 for White.
So, now, imagine that we are Black, about to make move 25. We create a tree of all possible sequences of moves between now and move 33, and if there is a move 25 (to, say, square c8) that with best play by both sides leads to the position described in the preceding paragraph, then we can score that particular move as +5. If it is the best scoring move, then we go to c8 at move 25.
Except that is looking ahead 8 moves. Zebra Othello used to have no problem looking ahead 15 moves, maybe 20. I have not tried it on any recent computer.
I think the only reason that Othello was not “solved” ten years ago (in the sense that Tic-tac-toe has a solution, which is that optimal play by both sides leads to a draw) is that it turns out that a lot of the openings seem to lead to really close games. I remember having Zebra play out for both sides the result of an opening known as the Rotating Flat, aka the Rose-Kling-Tamenori variation, and the final score was something like 33-31. That was true for a number of other openings as well. What this says is that the tree of optimal Othello games is very bushy, so that humans as currently constructed will never be able to master Othello purely through memorization. So human Othello will remain interesting, even though computer Othello might ultimately be dull, because by now it may be possible to solve the game on the computer.
My career began in 1981 and lasted about 10 years. I never won a U.S. national title. Two rival players, Brian Rose and David Shaman, were better than me. I wrote a lot of good articles for Othello Quarterly, but there is no online archive. If somebody wants a set of old issues to scan in and put on line, I am pretty sure I have a complete set through the early 1990s.
My best tournament was the Internationals in Milan in 1987 (the only international in which I participated). The U.S. sent three players as a “team,” and I came in 6th–behind Brian and David but much better than expected relative to the top players European players. The Japanese sent only one of their top players (who finished first), or else they would almost surely have finished 1-2-3. During the 1980s and 1990s, only a handful of non-Japanese ever came in first. Brian and David won international titles, but they had to become really obsessive in order to do so*. Not that there’s anything wrong with that.
(*by any rational standard, of course, I also was obsessive. But I did manage to hold on to a full-time job and spend time with my children)