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Second Half of the Chess Board

Run the Second Half of the Chess Board MicroSim Fullscreen

About This MicroSim

This MicroSim visualizes the classic "rice on the chessboard" story: place one grain of rice on the first square of a chess board, two on the second, four on the third, and keep doubling all the way to the 64th square. Each square holds twice as many grains as the one before it — the same doubling pattern often used to describe exponential growth in AI capabilities.

For the first several squares, the grains are drawn individually so you can count them. Once the count is too large to depict as individual grains, the square instead shows a number, abbreviated with K (thousand), M (million), B (billion), T (trillion), Qa (quadrillion), and Qi (quintillion) once it gets astronomically large. A dashed white line marks the boundary between the first half of the board (squares 1-32) and the second half (squares 33-64) — the point where the totals stop looking manageable and start looking impossible.

By square 32, the board holds about 4.3 billion grains — already a lot of rice, but still something you could picture. By square 64, a single square holds over 9.2 quintillion grains, and the whole board holds 18,446,744,073,709,551,615 grains in total — enough rice to cover the entire Earth. The lesson: a constant doubling rate looks harmless for a long time, right up until it doesn't.

How to Use

Drag the Doubling Step slider to reveal the board one square at a time, starting at square 1 (upper left) and moving left-to-right, top-to-bottom through square 64 (lower right). The panel below the board shows the exact grain count and running total for the currently revealed square.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

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<iframe src="https://dmccreary.github.io/tracking-ai-course/sims/second-half-of-chessboard/main.html"
        height="632px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

Adult professional / executive education (organizational AI-tracking course)

Duration

10-15 minutes

Prerequisites

None — a foundational visualization for discussing exponential growth before applying it to AI capability trends.

Key Insight

Something growing exponentially can stay economically unremarkable for a long stretch, then abruptly become one of the largest forces in the economy — with no change in the growth rate, only in how far along the curve it already is. Slide to square 32, the last square of the first half, and the panel shows that square alone is worth about $85,900 at today's rice prices — real money, but nowhere near strategically significant. Slide to square 64, the last square of the board, and that single square is worth about $369 trillion — over 4 billion times more than square 32, and more than nine times the entire U.S. national debt (roughly $40 trillion as of 2026). Both squares follow the exact same doubling rule; only the square number differs. Strategically, almost none of the impact shows up until deep in the second half.

Activities

  1. Prediction (2 min): Before moving the slider, ask learners to guess how many grains will be on square 20, then on square 40. Reveal the actual values and compare.
  2. Exploration (5 min): Have learners slide to square 32 and read the estimated dollar value shown in the green line of the panel. Then continue to square 64 and read it again. Ask: how many times larger is the second number?
  3. Discussion (5 min): Connect the metaphor back to AI: ask learners where they think we currently sit on this "board" for AI capability growth, what it would look like for a capability to still be "in the first half" (measurable, but not yet strategically significant), and what evidence would tell them a capability has crossed into the second half.

Assessment

Learners should be able to (a) state the grain count and estimated dollar value at any given square, (b) explain why square 32 is worth about $85,900 while square 64 is worth hundreds of trillions of dollars — despite both following the exact same doubling rule, and (c) articulate why this means an exponential trend can be safely ignored for a long time and then become urgent almost overnight, with implications for how organizations should monitor early-stage AI capabilities.

References

  1. Wheat and chessboard problem — Wikipedia — the traditional story this MicroSim visualizes.
  2. Exponential growth — Wikipedia — background on the underlying mathematical concept.