The original problem was stated thusly:
If I have a 52 card deck, equal red and equal black, shuffled to together randomly, and I start to reveal cards to you one at a time...:
You may tell me to stop at any time, and guess what the color the bottom card will be. Can you ever increase your odds better than 50% that it will be black? What if I show you the NEXT card instead?
-- Against intuition, the answer is NO. It is always 50/50, because those odds were determined with initial information input of 26/26 - and even as you remove cards, and the total remaining may change, it doesn't change the initial odds on any GIVEN card from the remaining to be 50/50.
You have to be very carefull with probabilities, small changes in the conditions can change a lot.
But as stated here, I tell you the answer is yes, because I will just wait 51 cards and count and thus know what the last card will be.
If, as I can not read in post, but anyway, the cards are not a equal number of red and blacks, but
equally likely red or black, that's a completely different situation, and it's also a different situation than we have here. Because the cards of a Dominion deck are not Copper with 70% and Estate with 30%, but there are
exactly 3 Estates and 7 Coppers. In the first case, if you know the first 9 cards, you don't know more about the 10th card, it is still 30% Estate and 70% Copper. In the second case, if you know the first 9 cards, you know the 10th, its Copper if you've just found 6 Coppers and Estate if you have found 2 Estates.
But in the first case that would also mean that the startung deck could consist of 10 Estates with probability 0.3^10.