Step 1 :First, we need to calculate the probability of rolling two even numbers. The probability of winning is 1/4 and the probability of losing is 3/4.
Step 2 :Next, we calculate the expected value of the game. The expected value is the sum of the possible outcomes each multiplied by their respective probabilities. In this case, the expected value is \(0.25 \times 13 + 0.75 \times -4 = \$0.25\).
Step 3 :We should not expect to win or lose an amount equal to the expected value in the first game, as the outcome of one game cannot be predicted.
Step 4 :If we play 200 times, we can calculate the expected value over 200 games by multiplying the expected value by 200. This gives us \(0.25 \times 200 = \$50\).
Step 5 :Averaged over 200 games, we should expect to win \$50.
Step 6 :\(\boxed{\text{Final Answer: The expected value of this game to you is \$0.25. If you play 200 times, you can expect to win \$50.}}\)