Teen Patti Probability: The Odds of Each Three-Card Hand

Quick answer: A standard 52-card deck can form 22,100 different three-card hands. A trail is 52 of them (about 0.24%), a pure sequence 48 (0.22%), a sequence 720 (3.26%), a colour 1,096 (4.96%), a pair 3,744 (16.94%) and a high card 16,440 (74.39%).

Knowing the odds does not make you win, but it explains why the hands rank the way they do and helps set realistic expectations.

Where 22,100 comes from

Three cards from 52 can be chosen in C(52,3) = 52 × 51 × 50 ÷ 6 = 22,100 ways. Every probability below is a count of hands divided by 22,100.

The full table

How each count works

• Trail: 13 ranks × 4 ways to pick three suits = 52.
• Pure sequence: 12 possible sequences (A-2-3 up to Q-K-A) × 4 suits = 48.
• Sequence (not pure): 12 sequences × 64 suit combinations = 768, minus the 48 pure ones = 720.
• Colour (not pure): 4 suits × C(13,3) = 1,144, minus 48 pure sequences = 1,096.
• Pair: 13 ranks × 6 pairs of suits × 48 other cards = 3,744.
• High card: everything left, 16,440.

Cumulative odds: how often is a hand "good"?

What the table tells you

• Most hands are weak. About three hands in four are just a high card.
• Rank follows rarity, with one traditional exception. Pure sequences (48) are very slightly rarer than trails (52), yet the standard ranking puts the trail on top. See trail vs pure sequence.
• A pair is a decent hand. A pair is about one hand in six, and a pair or better is roughly one in four (25.6%).

A worked example

Imagine you are dealt Q♣ 9♦ 4♠. That is a high-card hand, the most common type. Now imagine J♥ J♦ 6♣, a pair, which about 17% of hands are. Neither tells you whether you will win, because the other players hold hands drawn from the same deck at the same time.

What probability does not tell you

• It describes the deal, not your results. A rare hand can arrive twice in a row, and a common hand can lose to a rare one.
• It does not account for other players' cards, betting or folds.
• It changes with variations. In AK47 or Joker games, wild cards make strong hands much more common.
• It does not predict streaks. Cards have no memory. Getting no pairs in twenty hands does not make a pair more likely next time.

The gambler's fallacy

A common trap is believing a rare hand is "due". Because each deal is independent, the chance of a trail on the next hand is always 52 in 22,100, however long you have waited. This is a major reason limits and stop points matter. See responsible Teen Patti gaming.

Nothing in these numbers can make a win certain. Treat Teen Patti as entertainment and set a spending limit before you play. For how the hands rank, see hand rankings, and for whether the game is mostly skill or chance, read Is Teen Patti skill or chance?

18+ only. Educational content; no outcome is promised.