COUNT THE POSSIBILITIES
Why Teen Patti Has 22,100 Three-Card Hands
A standard 52-card pack contains 22,100 unordered three-card hands. The calculation is 52 choose 3, or 52 × 51 × 50 divided by 3 × 2 × 1. Division removes the six dealing orders for each set of three cards. This sample space supports every standard-hand frequency in the Hub probability studio.
The rule, precisely
A standard 52-card pack contains 22,100 unordered three-card hands. The calculation is 52 choose 3, or 52 × 51 × 50 divided by 3 × 2 × 1. Division removes the six dealing orders for each set of three cards. This sample space supports every standard-hand frequency in the Hub probability studio.
The counting unit is one three-card set from a thoroughly mixed single pack, with every set treated equally. This is a mathematical model. A fixed practice hand demonstrates classification, while the sample space describes all possible hands under that model.
Order matters when describing a dealing history but leaves a final hand unchanged. A♠ K♥ Q♦ and Q♦ A♠ K♥ contain the same three cards. Counting the six permutations separately would make the denominator six times too large for unordered hand frequencies.
Original Practice Hand
Take the three displayed cards and list their possible reading orders. This small exercise exposes the exact factor removed by the combination formula. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Work through the cards
Label the three cards A, B and C for the counting exercise. List ABC and ACB. Continue with BAC and BCA, then CAB and CBA. Each ordering contains the same physical set. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Label the three cards A, B and C for the counting exercise. List ABC and ACB.
Continue with BAC and BCA, then CAB and CBA. Each ordering contains the same physical set.
Count ordered three-card selections as 52 × 51 × 50 = 132,600.
Divide by the six listed orders to obtain 22,100 unordered hands. Use that denominator for the category table.
Result and next variation
There are 132,600 ordered selections and 22,100 unordered hands. The factor of six is exactly the number of arrangements of three distinct cards. Keep the stated worksheet assumptions beside the cards and record the specific property that supports the worked explanation.
Repeat the idea with two cards. There are 52 × 51 ordered selections and two orders per pair, giving 1,326 unordered two-card sets. The smaller example helps verify why combinations, rather than ordered selections, suit a hand-frequency table.
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-13; review method by Teen Patti Games Hub Editorial Desk.