Calculating accuracy of prediction Suppose I have a bag of marbles containing blue and red marbles. I guess/predict that my chance of drawing a red marble is 60%.
If the actual distribution turns out to be 80% blue/20% red, how can I best quantify the accuracy of my initial prediction?
Is it possible to restrict such a quantification to a range between 0 and 100%, such that a correct prediction (20%) would evaluate to a 100% accuracy?


Is it possible to restrict such a quantification to a range between 0 and 100%, such that a correct prediction (20%) would evaluate to a 100% accuracy?

I don't believe so.  What you're asking is "is there a way to know when my prediction is equal to the truth" and that just can't be done.  That is the entire reason we need statistics.
There are ways to estimate what the prediction should be after having seen data. These methods find the prediction which would minimize an appropriate error metric, and so the prediction would be the best prediction you could make conditioned on the data you had seen so far.
As an example, suppose you pull 10 marbles, 3 of which are red.  One way to measure your error is through the cross entropy loss.
$$ \ell(\theta) = - \sum_i y_i \ln(\theta) + (1-y_i)\ln(1-\theta) $$
Here, $\theta$ is your prediction, $y_i=1$ is the event you get a red marble, and $y_i=0$ is the event you get a blue marble. Smaller numbers are preferable here.  Using your 60% initial prediction your error would be approximately 8.  Is that number bad?  Is that number good?  Tough to say,  we need something to contrast against.
Let's use that data to create a new prediction.  We saw that 30% of the marbles were red, so let's devise a new prediction: 30% of the samples are red.
We pull a new sample: 2 reds 8 blues.  Now, let's compare the loss values of our initial prediction of 60% with our new prediction of 30%.
Error for 60% prediction: 8.345
Error for 30% prediction: 5.26
Our new prediction is much much better because it resulted in smaller error(in fact, it is the best prediction we could make having only seen those first 10 draws).
