Experience and insight in the Race game

We study experimentally how subjects learn to plan ahead when they make sequential decisions. The task is the Race game. This game is played on a finite set of m possible positions occupied by a marker, which is initially in the first position. Two players alternate in the role of mover, and each one can move the marker forward by 1,2...,k places. The player who puts the marker in the final position wins.Learning follows a similar pattern for all subjects. The experience of losses in early rounds induces them to switch the mode of analysis to backward analysis, which proceeds from the final position. The game has a simple dominant strategy, so we can calculate the frequency of errors made by subjects in each of the positions. The hypothesis that players follow a backward analysis gives precise predictions on the pattern of errors: for example that errors are more frequent, the further the position is from the end.The experiment demonstrates that individuals are able to learn effective planning for future distant rewards, with a procedure of backward analysis. Their learning process may appear a pure insight, but is derived from evaluation of experience. Subjects are also able to transfer the knowledge they get from playing one game to a related game.