How is it possible for the expected value of a game to be losing 65 cents of the only outcomes are win $2 or lose $1

Let x be the probability of winning and let y be the probability of losing. Then we can write the following equation:

2x - y = - 0.65 ... (1)

the sum of the probabilities of winning and losing must equal 1.

x + y = 1 ... (2)

Rearranging (2), gives:

y = 1 - x ... (3)

Plugging the expression for y from (3) into (1), we get:

2x - 1 + x = - 0.65

which simplifies to:

3x = 0.35

Therefore x = 0.117 and y = 0.883.

The expected value of the game will be a loss of 65 cents if the probability of winning is 0.117 and the probability of losing is 0.883.