Why the RPS game is of so much interest to me? Because RPS represents one of the simplest models (two players with three probabilistic states each) in fact RPS game
is used by researches in game theory, statistics and chaos theory to study phenomena in non-linear dynamics.

In the game theory  the simplest goal is to improve payout matrix (as its in the lottery which is a type of probabilistic game, albeit very extreme case of one!)

One thing RPS game has in common with lottery is its random probability distribution between game iterations, of course RPS probability states are only 3 where else in a typical lottery game let say mega lottery, there are 56 different  probability states between each iteration, nevertheless its still of value to study simpler models
(possible reduction of large dimensional probabilistic state game (such as lottery) to simpler model is unknown at this stage, I don't even know if at all possible!)

With RPS game, 3 different trials were run, each iterating 4 times across 500 game runs and each run was divided to one of two bets:

1. blind bets, using RPS game learning algorithm that at best yields > 0.333% improvement over statistical medium

2. using Local Lyapunov Threshold to consistently (and selectively) bet on Local Lyapunov Threshold bands

Both 1 and 2 game outcome were collected and are displayed below (note that consistent improvement has been made of 2 over 1, yielding some credibility to the fact that using Local Lyapunov Threshold can in fact improve game's outcome matrix.

This in fact is really surprising to me, to recall RPS game probabilistic states are chosen from the random numbers! So in short, Lyapunov strategy compensates for the random!

There are many things not done as yet such as introduction of:

1. adaptive threshold (to inject statistical inference to Local Lyapunov Threshold)

2. entropy filtering

Below is output from rps_game.cpp, improved trials (using LLE threshold) were marked witth "GAIN" label, there were 12 trials run resulting in 10 improved (GAIN) payouts with LLE over 2 that did not use LLE Threshold.

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Strategy without(-)
Total Game Iterations: 2525....

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