Probability of Straight Flush losing (fraction)

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

INPUTS

• Highest Card Value - highest value card of the straight flush series
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NOTES

The Straight Flush hand can be beaten by a hand of greater value: 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 Flush hand with a higher highest card card value.

The Straight Flush hand can be beaten by all the hands of greater value: 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 Flush hand with a higher card value.

The probability that you can be beat is the sum of the probabilities of any hand that can beat your Straight Flush. 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 straight flush with a higher card value
• The probability of being dealt a royal flush