Customarily, every card that is being played during a hand should eventually be turned up as the bets are settled.
In every situation there is a valid reason for the dealer to examine each hand. And the obvious and practical way to do so is turn up the cards up on the table in full view of everyone.
Of course, when neither the player nor the dealer has broken, the hands must be exposed for comparison. But even when the dealer breaks, he needs to examine each hand.
Obviously, any hand that has drawn cards must be inspected before being paid, to be sure that the hand did not break also. But even a hand that did not draw, and thus must win, must be inspected to be certain it was not a blackjack that an inexperienced player failed to turn up.
This is necessary because the payoff for blackjack is greater than for a win. For a similar reason, the dealer must inspect each hand when he himself has a blackjack; a blackjack by a player would tie.
In addition, the dealer will not accept a player's cards and money if the player simply declares his hand broken and throws the cards in face down.
The dealer is responsible for seeing that no player cheats himself (or the casino) through ignorance of the rules or failure to add a hand correctly.
The one time when there is no obviously valid reason to turn a face-down card is when every player at the table has broken and the dealer's hand is therefore no longer of any relevance.
In this case there is no compelling reason for the dealer to show his hole card, but he customarily does so. For one thing, it is a courtesy to the broken players who may simply be curious about what strength hand they were drawing against.
Also, it is mechanically convenient to turn up the card in order to add it to other cards the dealer may be holding prior to placing them with the discards.
The dealer may fail to show his hole card if all players break. When he has a blackjack, he may pick up the player's hands, look at them while keeping their backs to the players, and retire them to the discards.
When he breaks, he may check the pat hands for a blackjack in the same manner, never exposing them to view. Or, he may not inspect for players' blackjacks at all.
Some casinos claim that Ace, 10, is not blackjack unless declared promptly.
When a dealer adopts these methods of hiding cards, you should counter as much as possible by counting or estimating the hidden cards by inference, as explained--- provided you stay at the table with him at all.
If the dealer has an Ace and no blackjack, his other card must be a non-10. A player's pat hand may be estimated as minus 1. But be sure the hand was actually being played pat; do not attempt to estimate a simple two-card hand unless the owner gives an indication of its composition.
Also, whenever an unbroken hand has drawn a 10 or a combination of small cards totaling ten or more, the hole cards must be non-10s.
Of course, if your play is unduly compromised by a dealer who hides cards, it may be expedient to change tables or casinos.