Hand strength for pre-flop play has been extensively studied in the poker literature. For example,  attempts to explain strong play in human understandable terms, by classifying all the initial two-card pre-flop combinations into nine betting categories. For each hand category, a suggested betting strategy is given, based on the strength of the hand, the number of players in the game, the position at the table (relative to the dealer), and the type of opponents. For a poker program, these ideas could be implemented as an expert system, but a more general approach would be preferable.
For the initial two cards, there are
combinations, but only 169 distinct hand types (13 paired hands,
suited hands and
For each one of the 169 possible hand types, a
simulation of 1,000,000 games was done against each
of one, three and six random opponents
(to cover the 2, 3-4 and 5 or more player scenarios5.1).
Each opponent was simple and always called to the end of the hand.
This produced a statistical measure of the approximate income rate
(IR) for each starting
hand; income rate measures the return on investment.