I have a program that runs through all possible boards when holding a specific starting hand in NLHE and classifies the poker hands that result.
The table below shows the results for AKs and AKo. The rows at the bottom of the table show the percentages of boards that result in One Pair or Better and High Card Only respectively in the two cases.
Category | AKs starting hand | AKo starting hand |
---|
Royal Flush | 1,084 | 94 |
Straight Flush | 78 | 122 |
Four of a Kind | 2,668 | 2,668 |
Full House | 47,124 | 47,124 |
Flush | 138,296 | 41,562 |
Straight | 65,508 | 69,954 |
Three of a Kind | 92,004 | 93,808 |
Two Pair | 469,092 | 480,080 |
One Pair | 916,776 | 965,568 |
High Card | 386,130 | 417,780 |
. | | |
Total Boards | 2,118,760 | 2,118,760 |
. | | |
One Pair or Better Count | 1,732,630 | 1,700,980 |
High Card Only Count | 386,130 | 417,780 |
. | | |
One Pair or Better Pct | 81.78% | 80.28% |
High Card Only Pct | 18.22% | 19.72% |
Of course, the above methodology may not be ideal for OP's inquiry since, for example, it classifies boards such as AQ973 (resulting in a pair of Aces) together with Q9722 (resulting in a pair of Deuces) into the "One Pair" bucket which is probably not what OP had in mind or what Card Player calculated. I will leave it to others to pursue if they want further clarity into this question.
Bottom line: many of these types of questions are amenable to combinatoric or brute force calculations which are often fairly straightforward to perform.