Re: problem 51, a friend of mine made an interesting observation: if the probabilities are different, but always in the same ranking, i.e. Alice is always worst

Re: problem 51, a friend of mine made an interesting observation: if the probabilities are different, but always in the same ranking, i.e. Alice is always worst, Bob is always better than Alice, and Cheris always the best shot, there is a mix of probabilities where Alice's most successful strategy changes from the solution to the original puzzle. What are those probabilities? The easy version is to describe the general circumstances. The hard version is to do the math and describe them exactly.