ROCK PAPER SCISSORS HELL!!!!!!!!!!!!

cityscapes

cityscapes

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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.
unknown.png

General_Behavior_of_Algorithm_B_with_5_1_1_weights.png

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.
General_Behavior_of_Algorithm_B_with_11_10_10_weights.png

ok??????
Convergence_of_Algorithm_B_with_2_1_1_weights.png

if it starts with the optimal strategy it just chills there
General_Behavior_of_Algorithm_B_with_10_1_1_weights.png

if the weights are too high then this happens. looks like some logarithmic curve or something, idk
Rock on a Polar Graph.png

with a polar graph we get flowers like this one
unknown.png

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
 
earl said:
maybe to you
Click to expand...
ok ill explain

so the algorithm stores 3 values, which start out as the same number. lets say [100, 100, 100]

think of this like a bag that has 100 rocks, 100 papers, and 100 scissors, and one of those is picked randomly

so the algorithm plays a game against itself, let's say scissors is picked against paper and gets +1 as a result

the values are updated with this and become [100, 99, 101]. scissors gets +1, paper gets -1

the algorithm plays another game with this new set of values

etc
 
0aLKWeg.png


i'm the head scout from moneyball rockpaperscissorsball who doesn't believe in the statistical approach. in the movie i'm gonna be all like:

"you can't use math to win rock paper scissors, we have experience that you can't replace. some yale graduate kid with google sheets and wolfram alpha can't just tell us what rock paper scissors is about. what we need to look for is a pretty swing when our player chooses rock, and i know what swings that make it to the big leagues look like. do you really think that a bunch of statistics and eigenvectors can replace us as scouts? we've been around the game for 40 years."
 
cityscapes said:
https://erin-online.github.io/projects/spiral/

op delivers etc etc
Click to expand...
perhaps next you can look at whether King's Rock Cloyster is better than Choice Band Cloyster for beating Tapu Fini? There has been some controversy about this matter among mathematicians on this website, so maybe as a fresh set of eyes you could craft a proof to settle the matter once and for all.
 
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