You are essentially asking a very interesting question: should I predict using "MAP Bayesian" Maximum a posteriori estimation or "Real Bayesian".
Suppose you know the true distribution that $P(H)=0.2$, then using the MAP estimation, suppose you want to make 100 predictions on next 100 flip outcomes. You should always guess the flip is tail, NOT guessing $20$ head and $80$ tail. This is called "MAP Bayesian", basically you are doing
$$\arg\max_ \theta f(x|\theta)$$
It is not hard to prove that by doing so you can minimize the predicted error (0-1 loss). The proof can be found in ~page 53 of Introduction to Statistical Learning.
There is another way of doing this called "Real Bayesian" approach. Basically you are not trying to "select the outcome with highest probability, but consider all the cases probablistically" So, if someone ask you to "predict next 100" flips, you should pause him/her, because when you given 100 binary outcomes, the probabilistic information for each outcome disappears. Instead, you should ask, what you want to do AFTER knowing the results.
Suppose he/her has some Loss Function (not necessary to 0-1 loss, for example, the loss function can be, if you miss a head, you need to pay \$1, but if you miss a tail, you need to pay \$5, i.e., imbalanced loss) on your prediction, then you should using your knowledge about the outcome distribution to minimize loss over the whole distribution
$$\sum_x \sum_y p(x,y) L(f(x),y)$$
, i.e., incorporate your knowledge about the distribution to loss, instead of "stage-wised way", getting the predictions and do next steps.
What's more, you have a very good intuition about what will have when there are many possible outcomes. MAP estimation will not work well if the number of outcome is large and the probability mass is widely spread. Think about you have a 100 side-dice, and you know the true distribution. Where $P(S_1)=0.1$, and $P(S_2)=P(S_3)=P(S_{100})=0.9/99=0.009090$. Now what you do with MAP? You will always guess you get the first side $S_1$, since it has largest probability comparing to others. However you will get wrong $90\%$ of the times!!