3-04 Notes on combining hands
Do you know why No Honors does not combine with All Chows? Or why No Honors does not combine with All Simples? The reason is that both All Chows and All Simples are already defined as having no honors. That which is implied by a hand is not scored. Similarly, Mixed Triple Chow does not score additional points for the Mixed Double Chows that form its parts, and All Pairs does not score additional points for Concealed Hand.
A non-repetitive rule governs the scoring of multiple patterns. According to this rule, after scoring sets in a combination, any sets not already scored may be combined with only one of the already-scored sets to form additional combinations.
That may seem a bit wordy, so let's look at an example.
The hand in Figure 1 is a combination of Mixed Straight, All Chows, a Short Straight in dots, and a 789 Mixed Double Chow. When scoring, first count All Chows (2 pts.). Next, score Mixed Straight (8 pts.). At this point, you have combined three of your chows to form Mixed Straight. This is your first combination. You have one chow remaining (789 in dots), and since "after scoring sets in a combination, any sets not already scored may be combined with only one of the already-scored sets to form additional combinations," you may combine the chow with only one set that has been used in the Mixed Straight. Combine it with to create a Short Straight (1 pt.). Alternatively, you can combine it with to form a Mixed Double Chow. But you cannot do both.
See Figure 2 for another example. This hand includes a 234 Pure Double Chow as well as a 234 Mixed Double Chow. Score the as your first combination. Now score the remaining . But you can only combine it with one of the already-scored sets. Combine it with for a Pure Double Chow, or with the for a Mixed Double Chow.