There are only 6 choices for A, so the probability is 6 / 7776 = 0.08%. In the following, to find the odds of plain old poker dice hands, I will simply count the number of ways each can happen and then divide by 7776. Some differences are inevitable since the number of possible 5 card poker hands is (52 5) = 52! / (5! (52-5)! ) = 2,598,960 and the number of possible 5-die rolls is only 6 to the power of 5 = 7776.
Ranking poker dice hands by odds mostly follow the same order as poker hands dealt from a standard 52 card deck (except for 5 of a kind which doesn’t exist in a standard poker hand of course). But in any case, a good starting point is to calculate the relative probabilities of getting one of the basic poker hands on one roll. Often there is an opportunity to improve the hand by selectively re-rolling the dice, and sometimes there are constraints added to what hands can be scored.
Many dice games like Yahtzee or Yamslam are based on making the best poker hand out of a roll of 5 dice.
