I agree doing the experiment won't explain WHY the probabilities are not as you expect, but it should be enough (given enough trials - 10 might be too few) to show the probability is (something like) 2/3 if you change and 1/3 if you do. Once that is clear, you will see that the 'obvious' 50:50 solution can't be right. Then go slowly though your logic to see where you assume it is 50:50 and that's where you are going wrong ...