Probability of Two Pair losing (percentage)

This Probability of Two Pair losing (percentage) equation defines the probability that another hand can beat your two pair and this probability is expressed as a percentage.

INPUTS

• High Card - card value of the highest card that is not you highest pair card.
• Pair Cards - card value of the highest pair in your hand

NOTES

The Two Pair hand can be beaten by all the hands of greater value: three of a kind, straight, flush, full house, 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 Two Pair hand with a higher pair than one or both of your pairs, plus the probability that your opponent has an identical card value Two Pair hand with a more valuable high card than you have.  See Notes Page for further explanation.

The probability that you can be beat is the sum of the probabilities of any hand that can beat your Two Pair hand. 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 three of a kind
• The probability of being dealt a straight
• The probability of being dealt a flush
• The probability of being dealt a full house
• 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 higher pair than your highest pair
• The probability of being dealt a two pair of the same card value with a greater value high card