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Equation 18 · Part 2 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

Symbol p

DKL(p ∥ q)=∑ipilog⁡2(pi/qi)D_{\mathrm{KL}}(p \,\|\, q) = \sum_i p_i \log_2(p_i/q_i)
pp

What this part means

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

p is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

Scoring the fit with Kullback–Leibler divergence, DKL(p ∥ q)D_{\mathrm{KL}}(p \,\|\, q) = ∑i\sum_i pip_i log⁡2(pi/qi)\log_2(p_i/q_i) , from the observed August distribution to each candidate: the solved game scores 10.15 bits, the uniform null scores 0.045 bits, and July’s raw persistence scores 0.00068 bits. On a chi-square test against the eight species’ actual August battle counts (summing to 2,137,239 team-appearances, treating each candidate distribution as the expected shares), the solved game scores approximately 2.3×\times10^{13} — a figure that large only because the model assigns four real, frequently-played species an expected share of essentially zero, and squaring a large real count against a near-zero…

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