This Probability of Full House Losing (fraction) equation defines the probability that another hand can beat your Full House and this probability is expressed as a fraction.  The Full House can be beaten by all the hands of greater value: four of a kind, straight flush, and royal flush. So the probability that an opponent has a hand that can beat your hand is the sum of all the higher value hands'  probabilities, plus the probability that your opponent has a Full House with a higher three of a kind card value, plus the probability that your opponent has a Full House with a higher pair card value.  See Notes Page for further explanation.

Notes

The probability that you can be beat is the sum of the probabilities of any hand that can beat your Full House. Each of those probabilities is based on the ratio of the combinations of ways to be dealt those winning hands to the number of five card hands possible,`((52),(5))`. The total number of five card hands possible is computed as `((52),(5))` (see the constant defining number of five card hands).

The probabilities that must be summed are:

• The probability of being dealt four of a kind
• The probability of being dealt a straight flush
• The probability of being dealt a royal flush
• The probability of being dealt a full house with a higher three of a kind
• The probability of being dealt a full house with a higher pair