Hi, I try to experiment a bit with toy games, but I am very bad at maths.

If I am given one of 3 cards : A, K, Q equally often, and I bet all my A, and I bet 1/3 of my Q, and I check all my K.

Then, I really don't see how is my range after I check.

I understand I have no more A, I have 2/3 of the Q I had, and all my K. But what would be the formula to find out which proportion is Q or K ?

I guess I could simplify things and say like 33.33 (the number of Q I had before) * 2/3 + 33.33 (the number of K I had and still have), and then my range is 22.22/66.66 Q, so 1/3 Q and 2/3 K, but it's kind of hard for my brain to process. There should be to just use a formula to find the answer ?

Thank you