In this section we analyze the differences between agent and human behavior,
according to the 12 ``quantifiable'' behaviors described on the previous
section. Figure 3.40 shows the results. The graphs in this figure
repeat the curves for robot behavior frequency vs. performance (same as in 3.39),
adding the curves for the human case.
Table 3.4 summarizes these results, comparing four categories:
novice agents, advanced agents, novice humans and advanced humans.
These are the differences for each individual behavior:
For humans, doing closed turns with exact precision requires training. As with agents, there is a strong correlation between frequency of tight turns and performance. A top human, on average, performs tight turns as often as a beginner agent.
The opposite is true for agents. Robots develop this strategy in the beginning of robot-robot coevolution scenarios, when most other strategies are random (hence suicidal). Sometimes a whole population may fall into a mediocre stable-state  characterized by most agents doing spirals. The spiral is probably the simplest non-suicidal behavior in terms of GP code.
A search for the shortest robots ever produced by the novelty engine (table
3.5) reveals two minimal behaviors which use just 5 tokens.
One of them, R230007 does a classic tight spiral, and the other, R. 90001, a
more loose spiral.
which translates as:In the end, humans get out of mazes for the exact same reason.
(IFLTE 0.88889 _C _C (LEFT_TURN))
As evolution progresses, agents ``unlearn'' to do spirals, finding better
strategies. The behavior frequency diminishes sharply for more advanced agents,
approaching the human average rate: In the best robots, spiraling has been almost
A human's attention typically shifts between two modes: it either focuses on a narrow region around the present position, in order to perform precise maneuvers and turns, or spreads over a wider region, analyzing the different parts of the arena in an effort to plan the next move.
A move such as the staircase can be performed only in the narrow attention mode. When one switches to the second, ``big picture'' mode of attention, turns stop completely. So humans in general will not perform continuous turns for long periods of time.
Agents, on the other hand, lack attention characteristics altogether, so they can afford to be constantly turning without confusing or delaying their sensors readings or analysis.
The ``filling'' zigzag serves the purpose of making the most out of a confined space and amounts to about half of all zig-zags, in humans and robots alike. The frequency of filling zig-zag, for humans as well as agents, is an order of magnitude larger for expert players as compared to novices.
The reasons for asymmetric behavior on robots are similar to those explained for spiraling above: early on coevolutionary runs, a useful turn is discovered and exploited. The code will spread along the population and everybody will start performing the same type of turn. Later on, more advanced turning patterns are discovered that involve left as well as right turns.
In the end, the best agent strategies have perfectly balanced frequencies of left and right turns: levels of asymmetry are near-zero for advanced robots, and for humans of all levels.
Agents go across edges once every 300 game steps (approximately), whereas the human frequency is closer to one crossing every 500 game steps (a random walk would go across an edge every 256 steps).
A random walk would move along the edges 7.8% of the time. This is about the frequency for novice robots, but expert ones `edge' about 12% of the time. Human rates stay between 2.5% and 5%, increasing slightly for experts.
Even though agents do not perceive edges -- and thus are incapable of defining ``edging'' explicitly -- the better ones do it more often than random. Thus, albeit indirectly defined, agents seem to have found a way to exploit a human weakness.
For humans, being close to an edge is perceived as dangerous: something might come up unexpectedly from the other side, so humans stay away from edges more often than not.
Altogether, we have found that the set of behaviors we have been analyzing has provided us with interesting measures of robot and human evolution and learning. Some of them are typical of the ``robot'' species: more tight turns, more crossings of the screen's edges, diagonals produced by quickly alternating turns.
Zigzag is a unique problem in that it seems about equally important, and equally difficult for agents and humans alike. Zigzagging is fundamental for split endgames, when both players are trying to save space, waiting for the other to make a mistake.
Some behaviors occur mostly at specific levels of expertise: Spiraling and asymmetry are typical of novice agents, whereas in-out spirals and edge following are characteristic behaviors of advanced agents. Among humans, tight turns and edge crossings are common tools of expert players.
None of these behaviors had more frequency on humans than robots. Perhaps our choice of 12 sample behaviors was biased by our observations of how agents behave, rather than humans. But it is also interesting to reflect on the fact that human behavior is more complex, more changing, so it is difficult to find fixed patterns that occur very often. Several behaviors have much larger frequencies amongst agents than humans: staircase, edge following, and frequency of turns.
This last characteristic, lower human frequency of turns, we conjecture is related to a fundamental difference on the way that agents and humans approach the game. Agents are reactive, they read their sensors and act immediately. Humans switch between different attention modes: they exploit safe situations, where they can go straight for a while without interruptions, to look at the opponent's behavior, examine remote areas of the board, study the current topology of the game situation, and make plans for the future. Even though strategically it makes no difference, a human would rarely do a diagonal, quickly pressing the left and right keys while his/her attention is analyzing remote areas of the screen. A person can perform a diagonal with equal efficiency than a robot, but at the cost of concentrating all attention on the narrowest area, maintaining a precise coordination of turns and trajectory.