← All parts of this equation

Equation 7 · Part 4 · The Type Chart Is a Payoff Matrix, and the Metagame Only Half-Solves It

Symbol E

U(i,j)=log⁡2 ⁣(E(i,j)/E(j,i))U(i,j) = \log_2\!\big(E(i,j)/E(j,i)\big)
EE

What this part means

E is an input to the expression that computes the quantity on the left.

Its job in the formula

E is an input to the expression that computes the quantity on the left.

The passage around this formula

A matrix of pairwise advantages is an invitation to ask what a population that only cared about that matrix would converge on. Convert E into a genuine zero-sum payoff by taking a log-ratio: U(i,j) = log⁡2\log_2\!(\big(E(i,j)/E(j,i))\big) , which is antisymmetric by construction ( U(i,j) = -U(j,i) ) and reads in doublings of relative advantage — U(i,j)=2 means i ’s best attack into j outclasses j ’s best attack into i by a factor of…

Read this part in the article →

Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

Open the illustrated functions: inputs become outputs guide →

See this notation across published equations →

The article lists its research sources here.