The probability that you win the game is 50%.
The game is symmetrical for you and your opponent. Thus, your probability of winning is as good as your opponent's, so, you have a 50% of winning.
What does symmetric mean in probability?
Symmetry goes into play in probability theory in this way: if different outcomes are equivalent, they would have the same probability.
A symmetrical distribution happens when the values of variables come at regular frequencies and usually the mean, median, and mode all happen at the same point.
In general, if there are N symmetrical outcomes, the probability of any given one of them happening is taken to be 1/N.
Learn more about probability at: https://brainly.com/question/11234923
#SPJ4