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In the classic book Winning Ways for Your Mathematical Plays, volume 4, 2nd edition, p. 818, Berlekamp, Conway and Guy write about the use of pagoda functions to study peg solitaire like games. The authors observe: pagoda functions are known to few.

A pagoda function is any real-valued function $pag$ on peg-positions that has the property that if a move replaces pegs at positions $r$ and $s$ by a peg at position $t$, then $pag(t) \le pag(s) + pag(r)$.

What is the origin of the term pagoda? Does it refer to those tiered towers in Asia?

Humberto José Bortolossi
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    The concept used e.g., to show that solitair pegs cannot esacep 5 steps into the "desert", does involve something reminding of the shape of a pagoda ... I suspect this was coined by Berlekamp/Conway/Guy. – Hagen von Eitzen May 11 '20 at 11:39

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Never heard of it before but a quick search revealed this. From the book, slightly abbreviated "Computers and Games: Second International Conference, CG 2001, Hamamatsu, Japan, October 26-28, 2000 Revised Papers"

A real valued function $\mathbb{N}\to \mathbb{R}$ defined on the set of holes is a pagoda ("pag") function if for every consecutive three holes $(x,y,z)$, the pagoda function ${pag(x), pag(y), pag(z)}$ satisfies $$pag(x)+pag(y)\ge pag(z)$$

EDIT

Apparently, the definition first appeared in this two-volume work by Berlekamp, Conway and Guy. "Winning Ways for your Mathematical Plays"

MathematicianByMistake
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