No you don't. Only the peeker see's the dice. Only the peeker can eliminate one die, and that peeker could eliminate probability completely because he knows the full outcome.
Unless YOU can see through the cup, you cannot eliminate the red die, or blue die or left die or right die or big die or small die. All dice faces are in play and unknown to you.
First re-read the wager offered in post 1 of this thread !!!
Take on the damned wager. Big stakes or little stakes or roll the dice yourself. This is not about English. Just damned well do it. Try two dice of different size or colour. After you've rolled the dice a dozen times you will realise that you were abjectly wrong to eliminate one die. Unless you are the kind of idiot who would just roll one die. That's why I said re-read post 1 !!!
If you want to use identical dice the outcome will still tend towards 1/11 it will just be a tiny bit harder to visualise why.