Probability of Straight losing (fraction)

This Probability of Straight losing (fraction)  equation defines the probability that another hand can beat your straight and this probability is expressed as a fraction.  

INPUTS

• Highest Card - the highest card if your straight
  

NOTES

The Straight can be beaten by all the hands of greater value: 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 Straight hand with a higher high card value, plus the probability that your opponent has an identical straight but their high card's suit beats your high card's suit.  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 Straight. 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 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 straight with a higher top card value

** note that if two straights have the same value, for example, 4,5,6,7,8 and 4,5,6,7,8, they split the pot.