Of the hard hands, the stiff hands are the most difficult to play in blackjack because it feels like you are already going to lose before you have even really started the round. In such instances the best you can do is minimalize your potential losses. In terms of blackjack strategy it means making the play with the least possible chances of losing, even if the difference of losing between two plays is not great, it will impact your overall blackjack odds.
In most cases novice blackjack players will stand on a hard 12 if the dealer has a 2 through 6. This is done most likely because all of the other hard hands will stand against those dealer up cards.
But a hard 12 is a little bit different from the other stiff hands. When the dealer shows a 2 or a 3 you should hit.
Standing against a 2 or 3 with a hard 12 will cause you to lose 65% of the time and win 35% of the time. But if you were to hit against those two up cards, then you would have a 63% shot of losing and a 37% shot of winning.
Even though there is only a 2% difference, losing 63% of the time is better for your blackjack odds overall than losing 65% of the time. If you want to look at it in a more positive light then think of your blackjack odds in these terms: if you stand you will only win 35% of the time, and if you hit you will win 37% of the time.
Think of hitting a hard 12 against a 2 or 3 as a way of improving your blackjack odds on a stiff hand, even if it is only a little improvement—some is better than none.