The hand that contains a sequential rank of five same-suited cards, for example, Q♥ J♥ 10♥ 9♥ 8♥, is called a straight flush. Another rule that applies here is that under the ace-to-six rule, an ace consistently ranks low. With that being said, a king-high flush would be something like A♥ K♥ Q♥ J♥ 10♥.
Now that you know what a king-high straight flush is, the only gateway to losing to one of those is a same-suited royal flush. This indicates that the cards “K Q J T” should belong to the community cards. The last of the community cards belong to the 9 or your pocket card.
Let’s get into the details of the scenarios.
Possible Scenarios
Here are the two possible scenarios to deal with where you have the chances of losing to a king-high straight flush.
Scenario 1:
The board has 9 on it. The odds are similar to that of a royal flush in a 5-card stud.
Mathematically,
20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 1/64970
Scenario 2:
The board does not contain 9. The odds are calculated similarly. The only exception here is that all the 9s are excluded, and you choose from 16 cards first. The last card should not be a 9 or an Ace of that particular suit. Thus, you multiply by 46/48.
Mathematically,
16/52 * 3/51 * 2/50 * 1/49 * 46/48 = 23/1624350 = 1/70624
There are 2/47 odds of getting the 9. However, you do not want to get an Ace here. Therefore,
2/47 – 2/47 * 1/47 = 91/2162
The odds of having the 9 except for the non-occurrence of an Ace and the “K Q J T” on the board are
91/2162 * 23/1624350 = 1/1677900
Therefore, the odds of such occurrences is calculated as:
1/649740 + 1/1677900 = 163/76344450 = 1/468370
If you had an idea of such an occurrence, the odds would be:
163/76344450 * 2/45 = 163/1717750125 = 1/10538344
Depending on certain factors, the odds would differ. The odds of having an Ace against 8 opponents are:
163/76344450 * 16/45 = 1304/1717750125 = 1/1317239
Endnotes
The odds of an opponent having a similar suited Ace or the chances of one of the above scenarios appearing depends on the number of players dealt in the hand.
There are minimum chances of such happenings. However, it has happened enough in the past to believe that it may still occur in unforeseen situations.
