Hello. Yes, I understand your confusion. p(x)=p(y)=1/2 would be true if you roll the dice an infinite amount of times. For only N=300 this might not be necessarily the case since the number of observations is so small.
I wanted to show this by choosing different values of p(x) and p(y) and to make calculations a little bit more complicated.
But I see now, that 2/3 is actually too much and might be confusing. I will change the conditions of the experiment a little bit. It will be (1,2,3,4) for one bowl and (5,6) for the other.