Using Fractions

Most card problems can be done by using the intuitively more obvious method of parlays or multiplying fractions, without bringing in permutations and combinations. Take the problem of determining the chance of flopping two pairs with no pair on board. Say you have QJ.


The probability that the first card is a queen or a jack is 6/50. If it is, the probability that the second card is the other card (Q or J) is 3/49. If it is, the probability that the third card is something else is 44/48. Multiplying, we get 792/117600. But that is the chances assuming the off card comes last. Since it could also be first or second, we triple these results to 2376/117600 or about 2.02%. Feel free to ask me how to do other poker problems avoiding combinations.