Q:B10  What is the correct basic strategy for single deck Blackjack?
A:B10 (Steve Jacobs)

   The following basic strategy is for single deck games without
   DAS (double-after-splits).

   +--  Player's hand
   |
   |     dealer         dealer
   |   <-might bust-><-might stand->
   V   2  3  4  5  6  7  8  9  X  A  <------- dealer's upcard
  ---+-------------------------------
  XX | S  S  S  S  S  S  S  S  S  S   never, ever, ever split
  99 | P  P  P  P  P  S  P  p  s  s   split if (d <= 9), except 7
  88 | P  P  P  P  P  P  p  p  p  p   always split
  77 | p  p  P  P  P  p  h  h  s  h   split if (d <= 7), stand against 10
  66 | p  p  p  P  p  h  h  h  h  h   split if (d <= 6)
  55 | D  D  D  D  D  D  D  D  H  h   never split, treat like hard 10
  44 | h  H  H  DH DH H  h  h  h  h   never split, double against 5, 6
  33 | h  h  P  P  P  p  h  h  h  h   split if (d >= 4) and (d <= 7)
  22 | h  p  P  P  P  p  h  h  h  h   split if (d >= 3) and (d <= 7)
  AA | P  P  P  P  P  P  P  P  P  p   always split
  ---+-------------------------------
  A9 | S  S  S  S  S  S  S  S  S  S   always stand
  A8 | S  S  S  S *DS S  S  S  s  s   double against a 6
  A7 | S  DS DS DS DS S  S  h  h  h*  double 3-6, hit against 9, 10, A
  A6 | DH DH DH DH DH H  h  h  h  h   double low, hit high
  A5 | h  H  DH DH DH h  h  h  h  h   \
  A4 | H  H  DH DH DH H  h  h  h  h    \ double against 4,5,6
  A3 | H  H  DH DH DH H  H  h  h  h    /
  A2 | H  H  DH DH DH H  H  h  h  h   /
  ---+-------------------------------
  21 | S  S  S  S  S  S  S  S  S  S   always stand
  20 | S  S  S  S  S  S  S  S  S  S   always stand
  19 | S  S  S  S  S  S  S  S  S  S   always stand
  18 | S  S  S  S  S  S  S  s  s  s   always stand
  17 | s  s  s  s  s  s  s  s  s  s   always stand on HARD 17 or above

  16 | s  s  s  s  s  h  h  h  h  h   \
  15 | s  s  s  s  s  h  h  h  h  h    \
  14 | s  s  s  s  s  h  h  h  h  h     > hit if dealer might stand,
  13 | s  s  s  s  s  h  h  h  h  h    /    stand if dealer might bust
  12 | h  h  s  s  s  h  h  h  h  h   /   (special case against 2, 3)

  11 | D  D  D  D  D  D  D  D  D  D   always double
  10 | D  D  D  D  D  D  D  D  h  h   double if (d < 10)
   9 | DH DH DH DH DH H  H  h  h  h   double if dealer might bust
   8 | h  H  H  DH DH H  h  h  h  h   double only against 5, 6
   7 | h  h  h  H  H  h  h  h  h  h
   6 | h  h  h  H  H  h  h  h  h  h   (4-2)
   5 | h  h  h  H  H  h  h  h  h  h   (3-2)
   4 | h  h  h  H  H  h  h  h  h  h   (this hand is really 2-2 pair)
  ---+-------------------------------
  S=stand H=hit D=double P=pair(split)
  DH= double if allowed, otherwise hit
  DS= double if allowed, otherwise stand
  <uppercase> = "strong" hand, favorable to player
  <lowercase> = "weak" hand, favorable to house

  (*) notes:
     Playing A7 against dealer's ace:
        hitting gains 3.63% if dealer must hit on soft 17
        standing gains 0.32% if dealer must stand on soft 17

     Playing A8 against dealer's 6:
        doubling gains 1.96% if dealer must hit on soft 17
        doubling gains 0.03% if dealer must stand on soft 17
        (this rule may be ignored to simplify the strategy)