64 Squares and a Grain of Rice

by puneinvestor

Once upon a time in India, a wise man went to his king with a new invention: the game of chess. The king loved this game of queens and knights so much that he offered the poor wise man a year’s supply of rice to feed his family. The wise man, being wise, said, “Your majesty, that is very generous of you but I ask for only a token of your appreciation. Please give me just one grain of rice today representing the first square of the chessboard, and only two tomorrow representing the second. On the third day, I would like just double the number of grains received on the second day, and so on until you have fairly compensated me for the 64 squares of the chessboard. ”

The king thought him a fool to pass up on a year’s supply of rice in exchange for a few grains of rice over two months and immediately agreed to this no-brainer. As the king looked on with sympathy, the poor man walked home to his family holding one grain of rice in his palm.

On the following day, the wise man returned to the king’s palace and collected his two grains of rice for the second square of the chessboard.  On the third night too, his family had virtually nothing to eat. On the fourth day, the man’s wife, getting increasingly worried about their hungry children, pleaded with him to wiggle out of the deal with the king. “Entreat his majesty to forgive our foolishness. Let’s accept just half a year’s supply,” she said to her husband. The wise man risked marital harmony when he brought home eight measly grains of rice that day.

By the eighth day, the wise man had been paid off for one row of the chessboard. He brought home 128 grains, not enough to feed a family of four. Unbeknownst to him, his wife went to the king the same day to beg for cancellation of the deal. The king was a big believer in moral hazard and turned her back, saying, “I intend to enforce the contract your husband has with me. Of what use are promises if they are not kept?”

It took another week before the man had enough to feed his family. His wife was now smiling because she had come to understand what was cooking and it wasn’t just rice. The compensation for the last square of the third row was 8.4 million grains of rice. At the half-way mark, the man owned all the rice in the kingdom. On the 64th day, he was to be paid two thousand Indian “rice-years”, or as much rice as it would take the whole of modern-day India two thousand years to produce.

Moral of the Story:

Like both the king and the wise man’s wife, we are prone to underestimating the exponential nature of compounding. The phenomenon is particularly difficult to appreciate during the early part of the relevant time horizon. In the wife’s situation, it is perfectly normal to want to renege on day eight. While making such a choice, though, it is important to assign appropriate weights to distant rice grains.