The expected number of heads that Archie can get when flipping a coin $80$ times is $40.$ This is because the probability of getting heads on a single coin flip is $\frac{1}{2}=0.5$, assuming a fair coin. The expected value of a binomial distribution, which models the number of heads obtained in a given number of coin flips, is given by the product of the number of trials and the probability of success in each trial. In this case, the expected number of heads is:

$$80 \cdot 0.5 = 40.$$

Therefore, we can expect Archie to get $40$ heads on average when flipping a coin $80$ times. [1]