$1.$ In year $20$X$0,$ Elyse is employed as a ticket vendor at an off$-$track betting parlor in New York. No credit is extended to customers, and employees are not allowed to bet on races. Elyse is a compulsive gambler and occasionally places bets without paying for them. In the past, she has always managed to cover her bets without being detected by her employer. Earlier this year,

Elyse ran up $$80,000$ in bets that she did not pay for and won only $$33,000.$

She was unable to cover this large loss and turned herself in to her employer. Elyse was convicted of grand larceny and sentenced to five years of probation, required to perform $200$ hours of community service and pay a $$500$ fine. Her employer was liable to the racetrack for the bets she had made and obtained a judgment against her for the $$47,000$ shortfall it had to pay because of her indiscretions. How much, if any, gross income must Elyse recognize from her illegal betting? May she deduct the losses for her gambling winnings? Please explain.