Seeing additional cards in the shoe

21 is an information game. I'd argue that a keen eye can often see 2 (or 3) additional cards, if they pay attention:

1) the burn card. Sometimes dealers will expose the burn card, sometimes not. I've found that the dealer is more than happy to show it, if you request. If it's a loose shop, shouldn't be a problem to see it.

2) the final card in the deck. Obviously, this will be after the cut card, so it won't be played. If you're sitting on the right half of the table, you can usually see this card easily.

3) Possibly the last card BEFORE the cut card is put in. If you control the cut, obviously you'd attempt to cut such that the Lo/Hi card is out/in play. Taking advantage of this is not the easiest thing. If you think an Ace/10 is coming around card #50, it's reasonable to up your bet for that round. As for how much additional EV that is, someone else can weigh in.

I would never ask to see the cut card! Why would you ask to see it, unless you are counting cards? The dealers and pit avoid showing the card because they don't want players/counters to see it. I could ask to see it if it were the last shoe I would be there for and if I were not going back to this particular casino.

I guess you are referring to single and double deck. Otherwise it's impossible to see the cards you are referring to.

I would never ask to see the cut card!

It's not unusual for a regular player to ask to see the burn card. I've been asking to see it. After once, dealer often shows it w/o asking. In loose shop, I see no harm in asking.