# gst: Parrondo paradox revisited, a chaotic switching approach

<< Parrondo's paradox is a phenomenon where the switching of two losing games results in a winning outcome. >>

<< Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this final outcome?" (..) In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic. >> Joel Lai.

<< This led to the idea of incorporating chaotic sequences as a means to perform the switching. The authors discovered that using chaotic switching through a pre-generated chaotic sequence significantly enhances the work. For an observer who does not know parts of the information required to generate the chaotic sequence, deciphering the sequence of tosses is analogous to determining a random sequence. However, for an agent with information on how to generate the chaotic sequence, this is analogous to a periodic sequence. According to the authors, this information on generating the chaotic sequence is likened to the keys in encryption. >>

Using quantum Parrondo's random walks for encryption. Singapore University of Technology and Design. Oct15, 2021.

https://phys.org/news/2021-10-quantum-parrondo-random-encryption.html

Joel Weijia Lai, Kang Hao Cheong. Chaotic switching for quantum coin Parrondo's games with application to encryption. Phys. Rev. Research 3, L022019. June 2, 2021. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022019

Also

<< usando l'output di una logistica (per certi valori dei parms) un ipotetico Donald potrebbe avere il vezzo di ottenere stessi risultati con serialita' numerica generata meccanicamente anziche' in modalita' casuale; >>️

#POTUS race: Donald, what he can do (with less than four lines ...). FonT. May 23, 2016. 

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

Also

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, games, life, chaos, Parrondo, Parrondo chaotic switching approach

# gst: switch to three players within the Parrondo game

<< Parrondo's paradox indicates a paradoxical situation in which a winning expectation may occur in sequences of losing games. There are many versions of the original Parrondo's games in the literature, but the games are played by two players in all of them. (AA) introduce a new extended version of games played by three players and a three-sided biased dice instead of two players and a biased coin in this work.  >>️

<< Figure 11 shows the result of combination switches A and B for the fair probabilities in set S_5. The simulation results are performed so on until 100 steps were done, and each step is averaged over 10000 repeats. This strategy, different from the others and even the original Parrondo's paradox, produces a fair expectation from two noisy switches in which the combination of two fair switches is fair. >>

️

Atiyeh Fotoohinasab. A new generalization of Parrondo's games to three players and its application in genetic switches.  arXiv: 2101.11401v2 [q-bio.PE]. Feb 2, 2021. 

https://arxiv.org/abs/2101.11401 

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

keyword 'three-body' in FonT

https://flashontrack.blogspot.com/search?q=three-body

Keywords: gst, games, parrondo, three-body

# game: apropos of Parrondo's paradox, winning with losses driven by reputation and reciprocity

AA << investigate two such social behaviors, reputation and reciprocity, and their role in explaining Darwin’s survival of the fittest, examining how these fundamental principles govern individual interactions and shape broader social dynamics. >>

<< Current theories hint at two main facets of social interaction, reputation and reciprocity, as potential drivers behind this cooperative evolution. Reputation revolves around building and sustaining trust, social worth, and overall community standing. Conversely, reciprocity governs the mutual exchange of actions or benefits, influencing our choices. >>

<< One intriguing concept explored in this domain is Parrondo’s paradox: combining or switching between two losing strategies might surprisingly achieve a winning outcome. The role of Parrondo’s paradox in complex systems has sparked key research into chaotic many-body, quantum, and algorithmic network applications, where combining elements yields opposing beneficial results. Similarly, social physicists aim to uncover hidden mechanisms that govern societal phenomena by integrating the paradox’s counterintuitive principles. >>️

<< The game-theoretic Parrondo’s paradox emerges through multiple iterations of these interactions (..) A naive observation might conclude that in either scheme the chance of individuals losing to the environment is higher than gaining from the environment. For the reputation scheme, one is rewarded with a singular capital from the environment but is punished with two. Similarly, the reciprocity scheme only allows for the redistribution of capital or loss of capital. In reality, diverse schemes can be adopted by different individuals. Thus, (AA) suggest two forms of switching: (1) stochastic switching, where the individual randomly selects one of two schemes to employ with equal probability, and (2) rule-based switching, where the individual only selects the reputation scheme if it passes the reputation threshold ρ; otherwise, it employs the reciprocity scheme. >>

AA << also performed simulations on other network topologies (..) Parrondo’s paradox is strongly observed in small-world networks, weakly in the Erdős-Rényi network, and absent in scale-free networks. >>

To conclude, some of these observations << underscore the profound capability of rule-based switching mechanisms inherent in Parrondo’s paradox to emulate and forecast key aspects of real-world social phenomena. Such insights are invaluable for developing sophisticated models and strategies in various fields, ranging from social sciences to policy making, where accurate predictions of social behavior and dynamics are crucial. >>

Joel Weijia Lai, Kang Hao Cheong. Winning with Losses: The Surprising Success of Negative Strategies in Social Interaction Behavior. Phys. Rev. Lett. 133, 167401. Oct 16, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.167401

Also: Parrondo, tit-for-tat, game, behav, network, in https://www.inkgmr.net/kwrds.html 

Keywords: Parrondo, tit-for-tat, game, behavior, behaviour, network

# game: 'pulsing' Parrondo to jump (and win) between two losing games

<< Parrondo’s paradox, in which losing strategies can be combined to produce winning outcomes, has received much attention in mathematics and the physical sciences; >>

<< In this review paper, the authors examine a large range of recent developments of Parrondo’s paradox in biology, across ecology and evolution, genetics, social and behavioral systems, cellular processes, and disease. >>

Kang Hao Cheong, Jin Ming Koh, Michael C. Jones. Paradoxical Survival: Examining the Parrondo Effect across Biology. BioEssays. Volume 41, Issue 6. doi: 10.1002/bies.201900027. May 27,  2019.   https://onlinelibrary.wiley.com/doi/abs/10.1002/bies.201900027  

Paradoxical Survival: Examining the Parrondo effect across biology. Singapore University of Technology and Design. Aug 5, 2019.   https://www.sciencedaily.com/releases/2019/08/190805134043.htm 

Also

"Parrondo" in: "Notes" & "FonT"

https://inkpi.blogspot.com/search?q=parrondo

https://flashontrack.blogspot.com/search?q=parrondo

# game: Parrondo's paradox reveals counterintuitive wins in biology and decision making in society.

<< 

• Parrondo's paradox illustrates how combining two losing strategies can result in a winning outcome.

• Its applications extend across various disciplines, particularly in understanding ecosystems at different scales.

• The paradox is explored in multiple fields, highlighting adaptability as a key factor in evolutionary survival.

• Future directions are outlined, emphasizing the potential to enhance our understanding of the natural world and society.

 >>️

Tao Wen, Kang Hao Cheong. Parrondo's paradox reveals counterintuitive wins in biology and decision making in society. Physics of Life Reviews. 51, 33-59. Dec 19, 2024. 

https://www.sciencedirect.com/science/article/abs/pii/S1571064524000940 

Also: Parrondo, game, tit-for-tat, in https://www.inkgmr.net/kwrds.html 

Also: 'Parrondo paradox', in Pubmed  https://pubmed.ncbi.nlm.nih.gov/?term=parrondo+paradox&sort=date&size=50

Keywords: gst, Parrondo, game, tit-for-tat

FonT: as mentioned elsewhere in this blog, from my point of view, if well modulated, the two paired strategies "Stochastic Tit-For-Tat" and "Parrondo" are deadly, regardless of the aims of the objectives (cooperative purposes, parasitism, resurfacing of hypothetical clusters of failed entities, ... )

# game: pulsating as a Toffoli gate: Parrondo's paradox with a three-state coin (heads, tails, and a side)

<< Parrondo's paradox - an apparent paradox in which two losing strategies combine to make a winning strategy - can emerge as a coin game with a single coin in the quantum realm, but only when the coin has three states (heads, tails, and a side) rather than the conventional two. >>

<< In the new study, [AA] have demonstrated a Parrondo's game using a three-state coin, which they represent with a qutrit, a quantum system with three states. >>

Lisa Zyga. Parrondo's paradox with a three-sided coin. Phys.org. July 11, 2018.

https://m.phys.org/news/2018-07-parrondo-paradox-three-sided-coin.html

Jishnu Rajendran, Colin Benjamin. Playing a true Parrondo's game with a three-state coin on a quantum walk. EPL. 2018; 122(4). June 28.

http://iopscience.iop.org/article/10.1209/0295-5075/122/40004/meta

https://arxiv.org/abs/1710.04033

Also

"Toffoli gate"

# qubit: three-qubit operation with the Toffoli gate for scalable semiconductor quantum processors. Mar 4, 2018.

https://flashontrack.blogspot.com/2018/03/qubit-three-qubit-operation-with.html

FonT

quando lessi per la prima volta in bibliografia circa il "Parrondo Game"  mi venne in mente una strategia che avevo immaginato e piu' volte usato a suo tempo - da meta'  anni '70 a tutti gli anni '80 (e oltre) - composta da una sorta di "tit-for-tat stocastico" cioe' una strategia di gioco di  "cooperazione/ defezione" con decisioni di scelta pilotate da "lancio di moneta" all'interno di due (e poi anche tre) scenari riconducibili al tipo Parrondo ... in pratica la generazione di scenari senz'altro di  "frontiera", evolutivi,  immediatamente generabili all'interno di situazioni (se-si-puo-dire ... or, namely, "sire-die-soup") del tipo "standard", supposte "lineari".  Anzicheforse.

1668 - ramificata tinnula (di carmina fluitantia). Jun 9, 2005.

https://inkpi.blogspot.com/2005/06/1668-ramificata-tinnula-di-carmina.html

"charlie"

https://inkpi.blogspot.com/search?q=charlie

# game: noise-induced Parrondo's paradox in discrete-time qu-walks

<< Parrondo's paradox refers to the apparently paradoxical effect whereby two or more dynamics in which a given quantity decreases are combined in such a way that the same quantity increases in the resulting dynamics. >>

AA << show that noise can induce Parrondo's paradox in one-dimensional discrete-time quantum walks with deterministic periodic as well as aperiodic sequences of two-state quantum coins where this paradox does not occur in the absence of noise. >>️

Zbigniew Walczak, Jarosław H. Bauer. Noise-induced Parrondo's paradox in discrete-time quantum walks. Phys. Rev. E 108, 044212. Oct 11, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.044212

Also: parrondo, walk, noise, in: https://www.inkgmr.net/kwrds.html

Keywords: games, parrondo, walk, noise

# game: aperiodic Parrondo (behavior based on the binary Fibonacci, Thue–Morse and Rudin–Shapiro sequences); persistence and heterogeneity effects.

AA << study the effectiveness of employing archetypal aperiodic sequencing -- namely Fibonacci, Thue-Morse, and Rudin-Saphiro -- on the Parrondian effect. From a capital gain perspective, (their) results show that these series do yield a Parrondo's Paradox with the Thue-Morse based strategy outperforming not only the other two aperiodic strategies but benchmark Parrondian games with random and periodical (AABBAABB…) switching as well. The least performing of the three aperiodic strategies is the Rudin-Shapiro. >>

AA << analyze the cross-correlation between the capital generated by the switching protocols and that of the isolated losing games. This analysis reveals that a pronounced anti-correlation (below -0.95) with both isolated games is typically required to achieve a robust manifestation of Parrondo's effect. >>

About << the influence of the sequencing on the capital using the lacunarity and persistence measures (AA) observe that the switching protocols tend to become less performing in terms of the capital as one increases the persistence and thus approaches the features of an isolated losing game. >>

Respect to << lacunarity, a property related to heterogeneity, (AA) notice that for small persistence the performance increases with the lacunarity with a maximum (..). In respect of this, (AA) work shows that  the optimisation of a switching protocol is strongly dependent on a fine tune between persistence and heterogeneity. >>

Marcelo A. Pires, Erveton P. Pinto, et al. Parrondo's effects with aperiodic protocols. arXiv: 2410.02987v1 [physics.soc-ph]. Oct 3, 2024.

https://arxiv.org/abs/2410.02987

Also: Parrondo, tit-for-tat, game, behav, network, in https://www.inkgmr.net/kwrds.html 

Keywords: Parrondo, tit-for-tat, game, behavior, behaviour, network

# life: call for four Parrondo's paradox peacekeeper players

<< US President Joe Biden has said world history is at "an inflection point" as he made the case for a "smart investment" of ... >> Ukraine, Israel, Taiwan.

️

Holly Honderich, Sarah Smith. Biden seeks 'vital' (..) aid for Israel and Ukraine. BBC News, Oct 20, 2023. 

https://www.bbc.co.uk/news/world-us-canada-67164900

Also: Switch to three players within the Parrondo game. FonT. Jun 11, 2022.

https://flashontrack.blogspot.com/2022/06/gst-switch-to-three-players-within.html

Also: Parrondo, in https://www.inkgmr.net/kwrds.html

Also: "Parrondo"[TIAB], in https://pubmed.ncbi.nlm.nih.gov/

Also: Parrondo, in https://arxiv.org/search/?query=Parrondo&searchtype=abstract&abstracts=show&order=-announced_date_first&size=50

Keywords: life, game, Parrondo, Potus, war, nfulaw

# game: apropos of Parrondo's game, how a flexible parasite can outsmart its hosts for evolutionary dominance.

<< Antagonistic coevolution between hosts and parasites substantially impacts community structure, with parasites displaying fluctuating selection or arms race dynamics during coevolution. The traditional matching alleles (MA) and gene-for-gene (GFG) models have been used to describe the dynamics and interaction of host-parasite coevolution, with these models assuming that parasites adopt a single strategy when competing with other parasites. >>

AA << present a nonlinear dynamic population model that challenges this assumption, showing how a parasite that is disadvantaged under either the MA or the GFG model can win the competition by switching between the two losing strategies based on an external environmental cue, internal processes, or stochastic decision-making. >>

<< This counterintuitive outcome is analogous to Parrondo's paradox, a game-theoretic concept that shows how alternating between two losing strategies can result in a winning outcome. >>

Tao Wen, Eugene V. Koonin, Kang Hao Cheong. How flexible parasites can outsmart their hosts for evolutionary dominance. Phys. Rev. Research 6, 023104. Apr 30, 2024.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.023104 

Also: game, Parrondo, evolution, in https://www.inkgmr.net/kwrds.html 

Keywords: game, Parrondo, evolution

FonT: from my point of view, if well modulated, the two paired strategies "Stochastic Tit-For-Tat" and "Parrondo" are deadly, regardless of the aims of the objectives (cooperative purposes, parasitism, etc)

# gst: transitions by coupled instabilities

AA << present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. (They)  show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. >>

Valeri Frumkin, Shreyas Gokhale. Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves. Phys. Rev. E 108, L012601. July 17, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.L012601

Also: parrondo, tit-for-tat, game, transition, chaos, in https://www.inkgmr.net/kwrds.html

Keywords: parrondo, tit-for-tat, game,  transition, chaos