The Chess Game Rice Wager Story

In a prior post I told the story of the Thousand Year Trusts of the Middle Ages, where rich merchants would purchase 1,000 year certificates of deposit for their remote descendants, at 3% interest compounded annually.

$1,000 held for 1,000 years at 3% compounded annually = $1,000 x (1.03 to the 999th power) = 6.67 QUINTILLION dollars.

As related, the European courts later struck the notes down essentially for bestowing unlawful amounts of economic power to individuals.

My other favorite story of the same sort, exhibiting the power of geometric progression, is that of the two men playing chess. One says to the other, "If I win, I want you to pay me one grain of rice on the first square of the chess board, two grains on the second square, four on the third square, eight on the fourth, and so on, doubling the number of grains to the 64th square of the chess board."

The other man idly agrees, and loses, and has his servants bring a basket of rice to begin paying-off the wager.

The numbers of grains of rice mount in this fashion

1+
2+
4+
8+
16+
32+
64+
128+
256+
512+
1024+
2048+
4096+
8192+
16384+
32768+
65536+
131072+
262144+
524288+...

You can see what is happening. We are less than one-third of the way through the 64 square board, and the numbers are getting huge.

Years ago I read that by the time we get to the 64th square, the accumulation of rice is equal to about 9 cubic miles.