How to read the chart
Find your hand in the left column and the dealer's face-up card along the top. The letter where they meet is the best move. The chart has three blocks. Hard totals have no ace, or an ace that has to count as 1. Soft totals have an ace counting as 11, so A,6 is a soft 17. Pairs are two cards of the same value, and that includes any two ten-value cards.
The letters mean: H hit, S stand, D double (hit if you can't double, for example with three cards), Ds double (stand if you can't double), P split, and R surrender (hit if the table doesn't allow it). Rs and Rp appear in a few cells when the dealer hits soft 17: surrender, or stand or split if you can't.
Rules the chart assumes
The chart opens set for six decks, the dealer standing on all 17s, double after split allowed, late surrender allowed and blackjack paying 3 to 2. You can change the soft 17 rule, surrender, double after split and the blackjack payout above the chart, and every cell is worked out again. The deck count stays at six, and you can split up to four hands.
The soft 17 rule moves the most cells. If the dealer hits soft 17, you double 11 against an ace, double A,7 against a 2, and surrender 15 and 17 against an ace (stand on 17 if you can't surrender). If you can't double after splitting, 2,2 and 3,3 are split only against a 4 through 7, 6,6 only against a 3 through 6, and 4,4 is never split. Without surrender, each R cell falls back to its second move.
Why each cell says what it says
Every cell is the move that wins the most, or loses the least, on average for that hand against that dealer card. Tap a cell to see the reason. To see the numbers behind any hand in full, including how much worse the second-best move is, put it into the blackjack hand calculator and solver.