ZFR: He than randomly selects an envelope and then randomly selects 3 cards from that envelope.
rtcvb32: That certainly can change the chance of what is drawn, but not the odds of what kind of cards are drawn.
Yes it does change the odds.
Consider this: He puts LLLF in one envelope and the rest (8F, 1L) in another.
The odds of drawing at least 2L becomes exactly 0.5. He needs to select the envelope with the 3 liberal policies (in which case he's guaranteed to get at least 2L). If he selects the other one, he definitely fails.
Now consider he puts LLLFFF in one and the rest (6F, 1L) in another. The odds of drawing at least 2L become
smaller than 0.5. Not only he needs to draw the one envelope with 3Ls (0.5 chance), he then needs to make sure out of the 6 cards inside it he draws at least 2L.
So as you can see dividing those cards in different ways does change the odds of what kind of cards are drawn.
So, how should zeo divide the cards between the envolopes to get the highest probability of at least 2L being drawn?