Choose 3 cards from 52: C(52,3) = 22,100. Category counts come from disjoint card patterns and sum to the complete sample space.
The standard Teen Patti model starts with a precise question: how often does each category occur in one unordered three-card hand from 52 natural cards? Every count on this page can be derived, enumerated and compared with the exported CSV.
Define the sample space
Choose three distinct cards from a standard 52-card deck. There are C(52,3) = 52 × 51 × 50 ÷ 6 = 22,100 unordered hands. Dividing by six accounts for the six orders of the same three physical cards.
The model recognises twelve sequence rank patterns: A23, 234 through JQK, and QKA. The chosen Ace profile changes the order of the recognised sequences while preserving the category counts.
| Category | Hands | Calculation | Percent |
|---|---|---|---|
| Trail / Trio | 52 | 13 × C(4,3) | 0.235294% |
| Pure sequence | 48 | 12 rank runs × 4 suits | 0.217195% |
| Sequence | 720 | 12 × (4³ − 4) | 3.257919% |
| Color / Flush | 1096 | 4 × C(13,3) − 48 | 4.959276% |
| Pair | 3744 | 13 × C(4,2) × 12 × 4 | 16.941176% |
| High card | 16440 | 22,100 − the five categories above | 74.389140% |
Derive Trail and pair
A Trail chooses one of thirteen ranks and three of the four suits: 13 × 4 = 52. A pair chooses its rank, two suits for that rank, another rank and one suit for the kicker: 13 × 6 × 12 × 4 = 3,744.
These categories are disjoint: a Trail contains three equal ranks; a pair contains exactly two equal ranks and an unmatched card.
Derive the two sequence categories
Twelve recognised rank runs each have four single-suit choices, giving 48 pure sequences. Each rank run has 4³ = 64 suit assignments. Four assignments are single-suit pure sequences, leaving sixty mixed-suit assignments: 12 × 60 = 720 ordinary sequences.
Derive color and high card
Choose three ranks within one suit: C(13,3) = 286. Across four suits that gives 1,144 same-suit hands. Removing the 48 pure sequences leaves 1,096 colors.
The six categories cover the complete model. Subtracting 52 + 48 + 720 + 1,096 + 3,744 from 22,100 leaves 16,440 high-card hands. Their percentages sum to 100%.
Interpret the percentage with its question
The Trail frequency is 52 ÷ 22,100, approximately 0.235294%. This is the frequency of a single-hand category in the stated deck model. A multi-player result also depends on the other hands, shared card removal and the room convention.
Keep single-hand category frequency and a particular game outcome as distinct questions. The comparison tool answers a rank-order question about the exact input hands.
Download the exact hand-count CSV →
Reproduce the calculation
The supplied hand-engine test enumerates all 22,100 hands under three explicit Ace profiles, giving 66,300 category evaluations and matching permutation checks. The exported CSV uses the same denominator and six counts.
Use guided hand practice to connect the arithmetic to concrete examples. 18+ only: learn with practice cards and planned breaks.
Source references
Read each source within its stated product, rule or file scope.