i made an extremely simple algorithm to play weighted rock paper scissors (regular rps, except you win 5 for winning with rock and 1 for winning with paper, for instance). it's producing really weird curves and i'm trying to figure out why.
[3, 2, 1] weights means +3 for winning with rock, +2 for winning with paper, +1 for winning with scissors
mathematically the algorithm is roughly defined by x'(t) = az-by, y'(t) = bx-cz, z'(t) = cy-ax, where [a, b, c] is the list of weights, and x y and z are the chance of the algorithm playing rock, paper, and scissors respectively. sevag told me to integrate this using eigenvectors but that gave me a bunch of imaginary numbers and i got mad. i dont even know what eigenvectors are i just watched a 20 minute lecture only to use wolfram alpha anyway.
so mostly we get this stuff that's kind of like a sine wave but not really. i have no idea what the equation for a curve like this would be.
ok??????
if it starts with the optimal strategy it just chills there
if the weights are too high then this happens. looks like some logarithmic curve or something, idk
with a polar graph we get flowers like this one
the flowers keep growing if left unchecked
my current plan is to represent this in terms of a 3d vector where it's like <rock chance, paper chance, scissor chance> with respect to t. if any math people have better ideas please let me know
[3, 2, 1] weights means +3 for winning with rock, +2 for winning with paper, +1 for winning with scissors
mathematically the algorithm is roughly defined by x'(t) = az-by, y'(t) = bx-cz, z'(t) = cy-ax, where [a, b, c] is the list of weights, and x y and z are the chance of the algorithm playing rock, paper, and scissors respectively. sevag told me to integrate this using eigenvectors but that gave me a bunch of imaginary numbers and i got mad. i dont even know what eigenvectors are i just watched a 20 minute lecture only to use wolfram alpha anyway.
so mostly we get this stuff that's kind of like a sine wave but not really. i have no idea what the equation for a curve like this would be.
ok??????
if it starts with the optimal strategy it just chills there
if the weights are too high then this happens. looks like some logarithmic curve or something, idk
with a polar graph we get flowers like this one
the flowers keep growing if left unchecked
my current plan is to represent this in terms of a 3d vector where it's like <rock chance, paper chance, scissor chance> with respect to t. if any math people have better ideas please let me know
