To recap my point:
When you start the game, if you played 30 times and things were perfectly distributed statistically, the answer would be:
A = 10 times
B = 10 times
C = 10 times
Okay? When you start, there's a 33% chance it'll be in each. So that's how many it will be in each.
According to my analysis, if you keep your box, you should win 10/30 times. According to your analysis, you should win 15/30 times.
Let's try it out:
Answer in A (10 times)
Choose A, host kills B [50% - 5 times] or C [50% - 5 times]
You're going to win 10/10 times if you keep A.
Answer in B (10 times)
Choose A, host kills C [100%]
You're going to win 0/10 times if you keep A.
Answer in C (10 times)
Choose A, host kills B [100%]
You're going to win 0/10 times if you keep A.
So, if you keep A, you'll win 10/30 times - 33%.
Let's try reverse engineering:
According to your analysis, you're going to win 50% of the time. Let's run your scenario 36 times (distributing answers as you expect them to be), and see what happens.
Okay, Legion's scenario:
You choose your box. You keep your box. You win 50% of the time, and lose 50% of the time.
50% of the time the answer is in your box (because you kept it and won 50% of the time):
A = 18
50% of the time [18] the answer is not in your box (divided equally among the other two)
B = 9
C = 9
So, according to your plan, legion, the answer is in A 50% of the time, B 25% of the time, and C 25% of the time. This is, assuming you start with A, and keep A the entire game.
In other words, in order for you to be correct, Legion, the prize would have to be placed in your box twice as often as either of the others.
JadeKnight's scenario:
You choose your box. You keep your box. You win 33% of the time and lose 66% of the time.
33% of the time the answer is in your box (because you chose it and kept it and won 33% of the time):
A =12
66% of the time [24] the answer is not in your box (divided equally among the other two)
B = 12
C = 12
So, according to this plan the answer is in A 33% of the time, B 33% of the time, and C 33% of the time. And it doesn't matter which box you choose and keep the entire game (it works as well for A as it would for C).