Artificial Intelligence / Unit 2 AI 0068 worked example, 60 to 90 seconds
Pricing a Tree by Hand
The idea
An exponent too large to compute directly is priced by walking it in squaring steps: multiply a few times, name the magnitude reached, and repeat.
In practice
Invent a board game — Grid — with exactly 30 legal moves in every position, and price its plans 40 moves deep. Start small: 30 squared is 900. Square again: 30 to the fourth is 900 times 900 — 810,000, call it nearly a million. So every additional 4 moves multiplies the plan count by nearly a million. Forty moves is ten such multiplications: a million, times a million, ten times over — a 1 followed by roughly fifty-nine zeros. Now weigh that against hardware: a computer checking a trillion plans per second, running since the universe began, would have examined fewer than one plan in every billion billion billion of them. The tree wins, and it is not close.
Where people slip
Grid is invented so the arithmetic stays exact; real games branch unevenly, and the conclusion survives every such variation.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
Unlocks
- Nothing yet depends on this.
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