Found this incredibly fascinating paper (ref. 1) (I usually do research during the week, given time and energy, and try to verify theoretical results on the weekend!)
One of key observations right away is the fact that one of the authors (Paolo Patelli) works at T-13 Complex System Group, Theoretical Division, CNLS Los Alamos National Laboratory which gives it a strong level of credibility and correctness.
Paper main motivation is to study popular but basic game of Rock-Paper-Scissors, and via using ideas from Chaos Theory (Local Lyapunov Exponent LLE and entropy) provide a player with an advantage (which accounts to the same thing as predicting game's future outcome).
Although this particular game is of limited rule type, nevertheless its temporal behavior enters chaos in its probability space.
From our end, we are interested in adding yet another tool, namely LLE (Local Lyapunov Exponent) and Entropy and Entropy Filtering and exploring possibility of its use in the lottery game systems (neither of these concepts were known to the author of this blog previously)
We can think of an idea where 2 abstract players are arranged to engage in a competition play, drawing from a pool of lottery numbers, one employing LLE the other entropy and subject this game to the same type of analysis.
Paper ends with the following statement :
"Our preliminary results are encouraging and show that by accepting intermittency in playing it is possible to decide the best moment to play and consequently to improve the performance of a simple and nai¨ve strategy. Filtering based on the Entropy appears more effective than that based on the LLE, and embedding the trajectory in order to compute the Entropy slightly degrades performance while increasing robustness. The effectiveness of a method for automatically adapting the threshold is proven to be effective. "
The best moment to play is one of the key parameters in win/loose strategy in games based on probabilistic theory such as found in lottery games.
1. Chaotic time series prediction for the game, Rock-Paper-Scissors by Franco Salvetti, Paolo Patelli and Simone Nicolo
2. T-13 Complex System Group, Theoretical Division