3pips logo_double  THE MATHEMATICS OF DOUBLE HOLD'EM


Number of Possible Starting Hands

In regular Texas Hold’em

There are (52 × 51)/2 = 1,326 distinct possible combinations of two hole cards from a standard 52-card deck in hold 'em, but since suits have no relative value in poker, many of these hands are identical in value before the flop. For example, A♥ J♥ and A♠ J♠ are identical, because each is a hand consisting of an ace and a jack of the same suit. There are 169 nonequivalent starting hands in hold 'em (13 pocket pairs, 13 × 12 / 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169). (source: Wikipedia.com)


In Double Hold’em

There are (52 × 51 × 50)/6 = 22,100 distinct possible combinations of three hole cards from a standard 52-card deck in double hold 'em, but since suits have no relative value in poker, many of these hands are identical in value before the flop. For example, A♥ J♥ 9♥ and A♠ J♠ 9♠ are identical, because each is a hand consisting of an ace, a jack and a 9 of the same suit. There are 1,755 nonequivalent starting hands in Double Hold’em.  This includes:

  • 13 pocket trips,
  • 13 × 12 = 156 pairs with a suited third card,
  • 156 pairs with an unsuited third card,
  • 13 × 12 × 11 / 6 = 286 distinct cards all suited,
  • 286 distinct cards all unsuited,
  • 286 distinct cards with the two highest suited,
  • 286 distinct cards with the two lowest suited,
  • 286 distinct cards with the lowest and highest suited;

13 + 156 + 156 + 286*5= 1,755.

Best 50 Starting Hands

Note: Math for Double Hold'em which can be played at PartyPoker, Mathematics for Double Texas Hold'em which can be played at TableBrain