Since I have trouble beating the The King Element on even its lowest Normal setting of 1 second, I thought I’d experiment with the Fun and Easy levels to see if they improve my luck.
Easy Levels
The Easy levels range from 0 to 7 and limit the number of nodes searched per move:
Setting a limit on the nodes searched produces a much more natural game than compared to limiting the ply-depth (another Level choice). Also, the Easy levels don’t suppress the search’s check extensions, as I’ve seen mate announcements as high as “Mate in 9” on Easy level 7 (requiring an 18-ply search).
To estimate the ELO’s of the various levels, I setup several mini-tournaments against the King and a few of my older computers: the Fidelity Chess Champion (est. ELO 1475) and the Novag Super Conny (est. ELO 1775). After playing a number of games and adjusting the levels, I estimate the Easy levels work out to about:
These are very rough estimates, especially on the lower levels. You’re welcome to improve this table with your own experiments. (Note: in the matches, I set the Fidelity to 1 min/move and the Novag to 30 secs/move. The King moves instantaneously on the Easy settings).
I then checked into the move accuracies for levels 1, 4, and 7 by comparing them to the King’s Normal setting of 15 secs/move. Here’s a breakdown of the accuracies showing the frequencies of the best move through the 8th best move:
There are a lot of obvious responses in a game of chess, like piece recaptures and checking moves, so even a low setting like Easy 1 can reach 50% accuracy. The real difference is in the non-obvious moves, where stronger settings will reach higher accuracies. Still, even when the search is severely constrained to a few thousand nodes, it’s amazing that the King can play so strongly against these old computers.
Fun Levels
I next experimented with the Fun levels. These work the same as the Easy levels (i.e. same node limits), but add an element of randomness to the move evaluations. In the chart below, the randomness added or subtracted to each move evaluation ranges from -4.0 to +4.0 on Fun level 0 and decreases to -0.25 to +0.25 on Fun level 5 (the maximum setting). In the lowest settings, you can see that outright blunders will be made.
The random elements are “non-randomly” generated, so if you play a game with the King on a Fun level, it will replay the same game if you make the same moves. Also, there are times where the random elements stray from the bounds above, so I can’t state with certitude the exact algorithm that Johan de Koning is employing.
I didn’t bother trying to estimate the ELO for the Fun levels as the play quality is rather crude and it often plays aimless or poor moves. The Easy levels are best if you’re just looking to learn something from a good sparring partner, but don’t want to get killed in the process.
-Eric
