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Equation 18 · Part 8 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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