Stewart Ethier, Professor Emeritus (retired in 2016)

• Department of Mathematics, University of Utah, 155 S. 1400 E., JWB 233, Salt Lake City, UT 84112, USA.
• ethier@math.utah.edu.
• 801-581-6851 (dept. office, JWB 233), 801-581-4148 (dept. fax).

Papers since 2009 (arXived):

Parrondo's paradox:

• Limit theorems for Parrondo's paradox with Jiyeon Lee. Electronic Journal of Probability 14 (2009) 1827-1862.
• A Markovian slot machine and Parrondo's paradox with Jiyeon Lee. Annals of Applied Probability 20 (2010) 1098-1125.
• A discrete dynamical system for the greedy strategy at collective Parrondo games with Jiyeon Lee. Dynamical Systems 26 (2011) 401-424.
• Parrondo's paradox via redistribution of wealth with Jiyeon Lee. Electronic Journal of Probability 17 (2012) (20) 1-21.
• Parrondo games with spatial dependence with Jiyeon Lee. Fluctuation and Noise Letters 11 (2012) (1250004) 1-22.
• Parrondo games with spatial dependence, II with Jiyeon Lee. Fluctuation and Noise Letters 11 (2012) (1250030) 1-18.
• Parrondo games with spatial dependence and a related spin system with Jiyeon Lee. Markov Processes and Related Fields 19 (2013) 163-194.
• Parrondo games with spatial dependence and a related spin system, II with Jiyeon Lee. Markov Processes and Related Fields 19 (2013) 667-692.
• Parrondo games with spatial dependence, III with Jiyeon Lee. Fluctuation and Noise Letters 14 (2015) (1550039) 1-20.
• Parrondo games with two-dimensional spatial dependence with Jiyeon Lee. Fluctuation and Noise Letters 16 (2017) (1750005) 1-23.
• The flashing Brownian ratchet and Parrondo's paradox with Jiyeon Lee. Royal Society Open Science 5 (2018) (171685) 1-13.
• The tilted flashing Brownian ratchet with Jiyeon Lee. Fluctuation and Noise Letters 18 (2019) (1950005) 1-19.
• How strong can the Parrondo effect be? with Jiyeon Lee. Journal of Applied Probability 56 (2019) 1198-1216.
• How strong can the Parrondo effect be? II with Jiyeon Lee. In Stochastic Processes and Functional Analysis: New Perspectives (RJ Swift, A Krinik, JM Switkes, and JH Park, eds.) Contemporary Mathematics 774 (2021) 25-35. American Mathematical Society.

Gambling/game theory:

• A world record in Atlantic City and the length of the shooter's hand at craps with Fred M. Hoppe. Mathematical Intelligencer 32 (2010) (4) 44-48.
• A game-theoretic analysis of baccara chemin de fer with Carlos Gamez. Games 4 (2013) 711-737.
• On the three-person game baccara banque with Jiyeon Lee. Games 6 (2015) 57-78.
• The evolution of the game of baccarat with Jiyeon Lee. Journal of Gambling Business and Economics 9 (2015) (2) 1-13.
• Optimal conditional expectation at the video poker game Jacks or Better with John Jungtae Kim and Jiyeon Lee. UNLV Gaming Research & Review Journal 23 (2019) 1-18.
• Teaching a university course on the mathematics of gambling with Fred M. Hoppe. UNLV Gaming Research & Review Journal 24 (2020) 1-35.
• Snackjack: A toy model of blackjack with Jiyeon Lee. UNLV Gaming Research & Review Journal 24 (2020) 49-82.
• Gambler's ruin and the ICM with Persi Diaconis. Statistical Science 37 (2022) (3) 289-305.
• A game-theoretic analysis of baccara chemin de fer, II with Jiyeon Lee. Games 14 (2023) 1-24.
• Bertrand's analysis of baccarat, In Frontiers of Dynamic Games: Proceedings of the International Conference "Game Theory and Applications" 2022 (LA Petrosyan, V Mazalov, and NA Zenkevich, eds.) Birkhäuser (2024) 15-26.
• Testing for dice control at craps. UNLV Gaming Research & Review Journal 29 (2025) 173-196.
• Does the first-serving team have a structural advantage in pickleball? with Daryl R. DeFord. Contemporary Math., to appear.
• Variance reduction in Texas hold'em and in video poker. Contemporary Math., to appear.
• Long-term behavior of casino games with Lorenzo Stefanello.

Diffusion processes/population genetics:

• A property of Petrov's diffusion. Electronic Communications in Probability 19 (2014) (65) 1-4.
• Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion with C. Costantini, P. De Blasi, M. Ruggiero, D. Spano. Annals of Appl. Probab. 27 (2017) 1923-1950.

Combinatorics:

• Counting toroidal binary arrays. Journal of Integer Sequences 16 (2013) (13.4.7) 1-8.
• Counting toroidal binary arrays, II with Jiyeon Lee. Journal of Integer Sequences 18 (2015) (15.8.3) 1-12.

Books:

• Markov Processes: Characterization and Convergence with Thomas G. Kurtz (paperback edition), 2005. Wiley.
• Optimal Play: Mathematical Studies of Games and Gambling (edited with William R. Eadington), 2007. Institute for the Study of Gambling and Commercial Gaming.
• Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz (edited with Jin Feng and Richard H. Stockbridge), 2008. Institute of Mathematical Statistics.
• The Doctrine of Chances: Probabilistic Aspects of Gambling, 2010. Springer.