COUNT THE POSSIBILITIES
Pair Probability: Rank, Suits and Kicker
Exactly one pair occurs in 3,744 of the 22,100 standard three-card hands, approximately 16.9412 percent. Choose the repeated rank, choose two of its suits, then choose a different kicker rank and one of its suits. The product 13 × 6 × 12 × 4 counts each pair hand exactly once.
The rule, precisely
Exactly one pair occurs in 3,744 of the 22,100 standard three-card hands, approximately 16.9412 percent. Choose the repeated rank, choose two of its suits, then choose a different kicker rank and one of its suits. The product 13 × 6 × 12 × 4 counts each pair hand exactly once.
The repeated rank identifies the pair uniquely, so it supplies thirteen choices. Two of four suits can be selected in six ways. The kicker uses one of the twelve other ranks, with four suits available at each rank.
This construction keeps trail hands in their own category because the kicker rank is selected from the other twelve ranks. It also gives a clean method to generate teaching examples: fix the pair rank and vary its suits and kicker independently.
Original Practice Hand
The hand contains a queen pair and a nine kicker. Use its structure as a label for each stage of the counting product. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Work through the cards
Choose queens as one of thirteen possible repeated ranks. Record the repeated-rank choice. Select spades and hearts as one of six two-suit combinations for that rank. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Choose queens as one of thirteen possible repeated ranks. Record the repeated-rank choice.
Select spades and hearts as one of six two-suit combinations for that rank.
Choose nine as one of twelve kicker ranks and diamonds as one of its four suit choices.
Multiply all independent choices to obtain 3,744 hands. Divide by the 22,100-hand denominator for the category frequency.
Result and next variation
The exact count is 3,744 and the resulting percentage is approximately 16.9412%. Each completed pair hand has one repeated rank and one distinct kicker. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Hold the queen pair rank fixed and count 6 × 12 × 4 = 288 hands. Multiplying those 288 possibilities by thirteen rank choices returns the full count. The two-stage calculation provides a second route to the same answer.
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-17; review method by Teen Patti Games Hub Editorial Desk.