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Full-Text Articles in Applied Mathematics
A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio
A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio
All HMC Faculty Publications and Research
In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …
Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91
Optimal Blackjack Strategy With "Lucky Bucks", Arthur T. Benjamin, Eric Huggins '91
All HMC Faculty Publications and Research
In the casino game blackjack or "21," mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a "blackjack"). However, many casinos offer the player "lucky bucks" that pay the player either 3-to-2 or 2-to-1. In the usual game, the player's expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet.