Book contents
- Frontmatter
- PREFACE
- Contents
- 1 On some Electromagnetic Phenomena considered in connexion with the Dynamical Theory
- 2 On an Electromagnetic Experiment
- 3 On the values of the Integral being Laplace's Coefficients of the orders n, n', with an application to the Theory of Radiation
- 4 Remarks on a paper by Dr Sondhauss
- 5 On the Theory of Resonance
- 6 Note on the explanation of Coronas, as given in Verdet's Leçons d'Optique Physique, and other works
- 7 Some Experiments on Colour
- 8 On the Light from the Sky, its Polarization and Colour
- 9 On the Scattering of Light by small Particles
- 10 On Double Refraction
- 11 On the Reflection of Light from Transparent Matter
- 12 On a Correction sometimes required in Curves professing to represent the connexion between two Physical Magnitudes
- 13 On the Vibrations of a Gas contained within a Rigid Spherical Envelope
- 14 Investigation of the Disturbance produced by a Spherical Obstacle on the Waves of Sound
- 15 Notes on Bessel's Functions
- 16 On the Reflection and Refraction of Light by Intensely Opaque Matter
- 17 Preliminary note on the Reproduction of Diffraction-Gratings by means of Photography
- 18 On the Application of Photography to copy Diffraction-Gratings
- 19 On the Diffraction of Object-Glasses
- 20 An Experiment to illustrate the Induction on itself of an Electric Current
- 21 Some General Theorems relating to Vibrations
- 22 On the Nodal Lines of a Square Plate
- 23 Note on a Natural Limit to the Sharpness of Spectral Lines
- 24 On the Vibrations of Approximately Simple Systems
- 25 On the Fundamental Modes of a Vibrating System
- 26 Vibrations of Membranes
- 27 Harmonic Echoes
- 28 Note on the Numerical Calculation of the Roots of Fluctuating Functions
- 29 A History of the Mathematical Theories of Attraction and the Figure of the Earth from the time of Newton to that of Laplace
- 30 On the Manufacture and Theory of Diffraction-Gratings
- 31 Insects and the Colours of Flowers
- 32 A Statical Theorem
- 33 Mr Hamilton's String Organ
- 34 General Theorems relating to Equilibrium and Initial and Steady Motions
- 35 On the Dissipation of Energy
- 36 On the Work that may be gained during the Mixing of Gases
- 37 Vibrations of a Liquid in a Cylindrical Vessel
- 38 On Waves
- 39 On the Approximate Solution of Certain Problems relating to the Potential
- 40 Our Perception of the Direction of a Source of Sound
- 41 Questions from Mathematical Tripos Examination for 1876
- 42 On the Resistance of Fluids
- 43 Notes on Hydrodynamics
- 44 On the Application of the Principle of Reciprocity to Acoustics
- 45 On a Permanent Deflection of the Galvanometer-Needle under the influence of a rapid series of equal and opposite Induced Currents
- 46 Acoustical Observations. I
- 47 On Progressive Waves
- 48 On the Amplitude of Sound-Waves
- 49 Absolute Pitch
- 50 On Mr Venn's Explanation of a Gambling Paradox
- 51 On the Relation between the Functions of Laplace and Bessel
- 52 Note on Acoustic Repulsion
- 53 On the Irregular Flight of a Tennis-Ball
- 54 A simple Proof of a Theorem relating to the Potential
- 55 The Explanation of certain Acoustical Phenomena
- 56 Uniformity of Rotation
- 57 On the Determination of Absolute Pitch by the Common Harmonium
- 58 On the Instability of Jets
- 59 The Influence of Electricity on Colliding Water Drops
- 60 On the Capillary Phenomena of Jets
- 61 Acoustical Observations. II
- 62 Investigations in Optics, with special reference to the Spectro-scope
- 63 On Reflection of Vibrations at the Confines of two Media between which the Transition is Gradual
- 64 On the Minimum Aberration of a Single Lens for Parallel Rays
- 65 Acoustical Observations. III
- 66 On the Stability, or Instability, of certain Fluid Motions
- 67 On the Resolving-Power of Telescopes
- 68 On the Resultant of a large number of Vibrations of the same Pitch and of arbitrary Phase
- 69 Note on the Theory of the Induction Balance
- 70 On a New Arrangement for Sensitive Flames
- 71 The Photophone
- 72 On Copying Diffraction-Gratings, and on some Phenomena connected therewith
- 73 On Images formed without Reflection or Refraction
- 74 On the Electromagnetic Theory of Light
- 75 On the Velocity of Light
- 76 On a Question in the Theory of Lighting
- 77 Experiments on Colour
- 78 On the Infinitesimal Bending of Surfaces of Revolution
50 - On Mr Venn's Explanation of a Gambling Paradox
Published online by Cambridge University Press: 05 July 2011
Book contents
- Frontmatter
- PREFACE
- Contents
- 1 On some Electromagnetic Phenomena considered in connexion with the Dynamical Theory
- 2 On an Electromagnetic Experiment
- 3 On the values of the Integral being Laplace's Coefficients of the orders n, n', with an application to the Theory of Radiation
- 4 Remarks on a paper by Dr Sondhauss
- 5 On the Theory of Resonance
- 6 Note on the explanation of Coronas, as given in Verdet's Leçons d'Optique Physique, and other works
- 7 Some Experiments on Colour
- 8 On the Light from the Sky, its Polarization and Colour
- 9 On the Scattering of Light by small Particles
- 10 On Double Refraction
- 11 On the Reflection of Light from Transparent Matter
- 12 On a Correction sometimes required in Curves professing to represent the connexion between two Physical Magnitudes
- 13 On the Vibrations of a Gas contained within a Rigid Spherical Envelope
- 14 Investigation of the Disturbance produced by a Spherical Obstacle on the Waves of Sound
- 15 Notes on Bessel's Functions
- 16 On the Reflection and Refraction of Light by Intensely Opaque Matter
- 17 Preliminary note on the Reproduction of Diffraction-Gratings by means of Photography
- 18 On the Application of Photography to copy Diffraction-Gratings
- 19 On the Diffraction of Object-Glasses
- 20 An Experiment to illustrate the Induction on itself of an Electric Current
- 21 Some General Theorems relating to Vibrations
- 22 On the Nodal Lines of a Square Plate
- 23 Note on a Natural Limit to the Sharpness of Spectral Lines
- 24 On the Vibrations of Approximately Simple Systems
- 25 On the Fundamental Modes of a Vibrating System
- 26 Vibrations of Membranes
- 27 Harmonic Echoes
- 28 Note on the Numerical Calculation of the Roots of Fluctuating Functions
- 29 A History of the Mathematical Theories of Attraction and the Figure of the Earth from the time of Newton to that of Laplace
- 30 On the Manufacture and Theory of Diffraction-Gratings
- 31 Insects and the Colours of Flowers
- 32 A Statical Theorem
- 33 Mr Hamilton's String Organ
- 34 General Theorems relating to Equilibrium and Initial and Steady Motions
- 35 On the Dissipation of Energy
- 36 On the Work that may be gained during the Mixing of Gases
- 37 Vibrations of a Liquid in a Cylindrical Vessel
- 38 On Waves
- 39 On the Approximate Solution of Certain Problems relating to the Potential
- 40 Our Perception of the Direction of a Source of Sound
- 41 Questions from Mathematical Tripos Examination for 1876
- 42 On the Resistance of Fluids
- 43 Notes on Hydrodynamics
- 44 On the Application of the Principle of Reciprocity to Acoustics
- 45 On a Permanent Deflection of the Galvanometer-Needle under the influence of a rapid series of equal and opposite Induced Currents
- 46 Acoustical Observations. I
- 47 On Progressive Waves
- 48 On the Amplitude of Sound-Waves
- 49 Absolute Pitch
- 50 On Mr Venn's Explanation of a Gambling Paradox
- 51 On the Relation between the Functions of Laplace and Bessel
- 52 Note on Acoustic Repulsion
- 53 On the Irregular Flight of a Tennis-Ball
- 54 A simple Proof of a Theorem relating to the Potential
- 55 The Explanation of certain Acoustical Phenomena
- 56 Uniformity of Rotation
- 57 On the Determination of Absolute Pitch by the Common Harmonium
- 58 On the Instability of Jets
- 59 The Influence of Electricity on Colliding Water Drops
- 60 On the Capillary Phenomena of Jets
- 61 Acoustical Observations. II
- 62 Investigations in Optics, with special reference to the Spectro-scope
- 63 On Reflection of Vibrations at the Confines of two Media between which the Transition is Gradual
- 64 On the Minimum Aberration of a Single Lens for Parallel Rays
- 65 Acoustical Observations. III
- 66 On the Stability, or Instability, of certain Fluid Motions
- 67 On the Resolving-Power of Telescopes
- 68 On the Resultant of a large number of Vibrations of the same Pitch and of arbitrary Phase
- 69 Note on the Theory of the Induction Balance
- 70 On a New Arrangement for Sensitive Flames
- 71 The Photophone
- 72 On Copying Diffraction-Gratings, and on some Phenomena connected therewith
- 73 On Images formed without Reflection or Refraction
- 74 On the Electromagnetic Theory of Light
- 75 On the Velocity of Light
- 76 On a Question in the Theory of Lighting
- 77 Experiments on Colour
- 78 On the Infinitesimal Bending of Surfaces of Revolution
Summary
Two players, A and B, toss for pennies. A has the option of continuing or stopping the game at any moment as it suits him. Has he, in consequence of this option, any advantage over B?
From one point of view it would seem that A has an advantage; for, as the game proceeds, the balance of gains must pass backwards and forwards from one side to the other, and if A makes up his mind to continue until he has won (for example) 10, the time must come when he will have an opportunity of carrying off his gains. On the other hand, it seems obvious à priori that no combination of fair bets can be unfair, and that A's option is of no value to him, inasmuch as at any point it is a matter of perfect indifference to him whether he risks another penny or not.
In order to examine the matter more closely, let us suppose that A has originally 1000 pennies, and that he proposes to continue the game until he has won 10, and then to leave off. Under these circumstances, it is clear that in no case can B lose more than 10, whereas A, if unlucky, may lose his whole stock before he has an opportunity of carrying off B's. The case is in fact exactly the same as if B had originally only 10 pennies, and the agreement were to continue the game until either A or B was ruined.
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- Chapter
- Information
- Scientific Papers , pp. 336 - 337Publisher: Cambridge University PressPrint publication year: 2009First published in: 1899