Calculate the expected value of the following game. If you win the game, your wealth will increase by 100,000,000 times your wager. If you lose, you lose your wager amount.
The probability of winning is 
.
Definitions:
NMR
Nuclear Magnetic Resonance, a spectroscopic technique used to observe local magnetic fields around atomic nuclei, providing detailed information about the structure, dynamics, and chemical environment of molecules.
Singlet
A term used in quantum mechanics and spectroscopy to describe a state in which all electrons in an atom or molecule are spin-paired, showing no magnetic field external to the system.
Doublet
In spectroscopy, a pattern indicating two closely linked energy levels or particles, often seen in NMR or EPR spectroscopy.
NMR
Nuclear Magnetic Resonance, a spectroscopic technique used to study the structure of molecules by observing the interaction of nuclear spins with magnetic fields.
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