COUNT THE POSSIBILITIES
Pure and Mixed Sequence Probability
The Hub standard profile has 48 pure sequences and 720 mixed-suit sequences among 22,100 hands. Twelve valid rank triples each support 64 suit assignments. Four assignments use one suit throughout, leaving sixty mixed assignments per triple. These category counts depend on the declared valid triples while their comparison order is a separate rule.
The rule, precisely
The Hub standard profile has 48 pure sequences and 720 mixed-suit sequences among 22,100 hands. Twelve valid rank triples each support 64 suit assignments. Four assignments use one suit throughout, leaving sixty mixed assignments per triple. These category counts depend on the declared valid triples while their comparison order is a separate rule.
For a fixed rank triple such as seven-eight-nine, each rank can appear in four suits. The product 4 × 4 × 4 gives 64 assignments. Exactly four use a single suit for all three ranks. The other sixty belong to the mixed-suit sequence category.
The valid triples are the ordinary consecutive triples from 2-3-4 through Q-K-A, plus A-2-3. This gives twelve triples. Moving A-2-3 above or below A-K-Q changes ranking order while preserving the same set of valid triples and category counts.
Original Practice Hand
One rank triple appears as a suited example and a mixed-suit example. Use it to count all possible suit assignments before scaling to the twelve valid triples. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Work through the cards
Fix the ranks as seven, eight and nine. Give each rank four possible suit choices, producing 64 assignments. List the four uniform assignments: all spades, all hearts, all diamonds and all clubs. These are pure sequences. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Fix the ranks as seven, eight and nine. Give each rank four possible suit choices, producing 64 assignments.
List the four uniform assignments: all spades, all hearts, all diamonds and all clubs. These are pure sequences.
Classify the remaining sixty assignments as mixed-suit sequences. Keep the two categories separate.
Multiply each category count by twelve. Divide 48 and 720 respectively by the 22,100-hand sample space.
Result and next variation
Pure sequence has frequency 48/22,100, approximately 0.2172%. Mixed sequence has frequency 720/22,100, approximately 3.2579%. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation. The following steps make that reasoning reproducible for independent study.
Combine the counts to obtain 768 sequence-shaped hands across both categories. Then split them again to check 48 + 720 = 768. This is a useful audit because a suited sequence belongs in the pure category exactly once.
Sources and editorial method
The source note separates published card-rule conventions from the Hub’s own worked examples and mathematical enumeration. Read the declared profile when a convention affects a comparison. Exact cards and calculation steps make the original analysis reproducible, while the editorial policy explains authorship, review scope and the method used to maintain each learning page.
Study convention: The Hub study profile uses one 52-card pack, six standard categories and suit-neutral comparisons. It places A-K-Q above A-2-3, then K-Q-J down to 4-3-2. Practice points count complete explanations within the current page. Read the named convention beside every worked comparison and keep rummy transfer lessons within their own rule system.
Rule reference: Teen Patti rule reference. The Teen Patti reference uses an A-2-3-first ordering; this worksheet uses the declared Hub order. Analysis: fixed teaching deal GH-15; review method by Teen Patti Games Hub Editorial Desk.