Edited simple Blackjack game in Python 3.4
My first tip would be to get rid of the Game class. It serves no value. Rather, it should be a method, appropriately named main. If you want a few tips for determining whether to write a class or not, here are a some instances where you should avoid classes:


If the class only contains two methods, __init__, and another.
If the class never refers to self. (Credit to @jonrsharpe)

Secondly, those comments underneath your function declarations should be docstrings. A typical function docstring would look something like this,

def my_func(args):
    """
    A detailed description of the function
    and its arguments.
    """

The below statement in Game.__init__ is not needed, and does nothing. It can be removed.

else:
    pass

You have some odd naming in places. For example, logic could be renamed to check_for_soft_17 or something along those lines, and total could be renamed to determine_winner.
The two for loops underneath the VAL = [] could be shortened to generator expressions. Here's how that would be done.

VAL = [[a + 2] * 4 for a in range(9)] + [[10] * 4 for _ in range(3)]

Preferably, the variable a in the above example should also be renamed to something a little more descriptive, and you should apply some of those "magic numbers" to variables as well.
As mentioned by @Josay, you're using globals in a lot of your functions. Rather than assigning a value to a global, try returning a value instead. It makes things a whole lot easier to manage.


Anyways, that's about all I can think of. If there's anything else that you want me to cover, just mention it in the comments, and I'll see what I can do. I hope this helps!