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At Amps Arcade, Anne is about to play her favorite game, Road Dash. She comes in first place half of the time. If she comes in first place for every race in a tournament, she will get her name added to the winners' board. Anne will play a $4$-race tournament today. How likely is it that her name will be added to the winners' board? Anne simulates the situation by rolling a six-sided die $4$ times. Each time an even number appears, it represents Anne coming in first place. This table shows the results of $100$ trials: Number of even numbers rolled $0$ $1$ $2$ $3$ $4$ Number of trials $5$ $27$ $4$$0$ $4$$1$ $4$$2$ Based on Anne's results, what is the probability that her name will be added to the winner's board?