Understanding the pure sequence probability can transform how you evaluate hands in Teen Patti and similar three-card games. In this article I’ll walk through what a pure sequence (straight flush) actually is, show a step-by-step probability calculation, give practical interpretations (how often you’ll see one at the table), and explain how that knowledge should influence betting and risk management. Along the way I’ll share a short personal anecdote about learning to count hands at a real-money table and point to a reliable resource for practice: pure sequence probability.
What is a pure sequence?
In three-card games like Teen Patti, a "pure sequence" is three consecutive ranks all of the same suit. Examples: 6♠-7♠-8♠ or Q♥-K♥-A♥ (many rule-sets treat A-2-3 and Q-K-A as valid sequences). It is one of the stronger hands — above a normal sequence (three consecutive ranks of mixed suits) and below a trail (three of a kind) depending on the house rules. Knowing the exact frequency of a pure sequence is essential because its rarity defines its relative strength and how aggressively you might play it.
Counting the deck: the basics
Start with the standard 52-card deck: 13 ranks (A,2,3,...,K) × 4 suits. For three-card hands the total number of distinct 3-card combinations (unordered) is the binomial coefficient C(52, 3), which equals 22,100. That denominator is where all probability calculations begin.
How many pure sequences exist?
We need to count distinct unordered hands that are three consecutive ranks all in the same suit. Two important subtleties here:
- Which rank runs count? In most Teen Patti rules you have 12 valid rank-runs for three-consecutive-card sequences: A-2-3, 2-3-4, ..., J-Q-K, Q-K-A. (Ace may act low or high, but sequences like K-A-2 are not normally allowed.)
- For each of those 12 rank runs there are 4 suits. All three cards must share that suit to be a pure sequence.
So the raw count of pure sequences is 12 rank-runs × 4 suits = 48 distinct hands.
Pure sequence probability — the math
With 48 favorable hands and 22,100 possible hands:
Pure sequence probability = 48 / 22,100 ≈ 0.0021724.
As a percentage this is about 0.2172% — roughly two-tenths of a percent. In other words, on average you'd expect a pure sequence about once every 460 hands (1 / 0.0021724 ≈ 460). That frequency is low enough to justify strong betting when you land one, but not so low as to be mythically rare.
Quick checks and related probabilities
It often helps to compare the pure sequence to the broader category of sequences (any suits). For any given rank run, there are 4 choices of suit for each of the three ranks, so 4^3 = 64 possible suit combinations per run. That means:
- Total sequences (any suits) = 12 runs × 64 = 768.
- Pure sequences (all same suit) = 12 runs × 4 = 48.
- So pure sequences are 48 / 768 = 1/16 = 6.25% of all sequences; the rest are mixed-suit sequences.
Probability of any sequence = 768 / 22,100 ≈ 0.03475 ≈ 3.475%.
Putting the numbers into real-world context
When I'm playing, I like to translate probabilities into frequencies players can remember. At a casual table that deals 60–100 hands per hour, expect a pure sequence roughly once every 4–8 hours of continuous dealing (given the ~460-hand average). For a busy online room running thousands of hands a day, you’ll see many pure sequences, but still comparatively few vs. lower-ranked hands like pairs or high cards.
Another useful conversion is odds against: the odds of not getting a pure sequence are about 459:1. That is, for every one pure sequence you expect 459 non-pure-sequence hands.
Why the probability matters for strategy
Understanding these probabilities helps you make informed in-play choices:
- Value betting: Because pure sequences are rare and usually beat most opponent hands, you should consider value-betting more aggressively when you hold one — but watch for board texture or visible betting patterns that suggest a higher hand (trail/three-of-a-kind in some rare combinations).
- Bluffing and deception: If pure sequences are rare, representing one with bluffs can be powerful — but only against opponents who can fold. Against callers who chase pairs or ordinary sequences, deception is less effective.
- Bankroll and variance planning: A hand that wins big but appears infrequently increases variance. Use the probability to size your bets and avoid overleveraging on long-shot expectations.
Variations and rule differences that change the numbers
Any change to deck composition or allowed sequences can affect the math:
- Wildcards/jokers: Adding jokers or wildcards increases many hand probabilities because those wildcards can complete sequences or trails more often. You must recompute combinatorics when jokers are in play.
- Alternate Ace rules: If a rule set treats Ace strictly as low (only A-2-3 allowed) or strictly as high (only Q-K-A), the count of rank runs changes and the number of pure sequences changes accordingly.
- Different deck sizes / stripped decks: Some poker variants remove low cards (e.g., 32- or 36-card decks). Any change in rank count alters the combinatorics from the ground up.
Examples and quick simulations you can run
If you want hands-on verification, run a small Monte Carlo simulation. Draw random three-card hands from a virtual 52-card deck and count the fraction that are pure sequences. With just 100,000 simulated hands you'll see results converge close to the theoretical ~0.217% mark.
Example pseudo-logic for a simple test:
- Create a standard 52-card deck as (rank, suit) pairs.
- Shuffle and sample 3 cards (without replacement) repeatedly.
- Check if the ranks form one of the 12 consecutive patterns and all suits match.
- Tally and divide by total simulations.
Personal anecdote: the lesson that sticks
Early in my Teen Patti days I saw an opponent confidently push in a large amount and called with what I thought was a safe sequence. He opened a pure sequence on the showdown and swept the pot. At first it felt unlucky until I ran the numbers at home — discovering that while a pure sequence is rare, it isn’t vanishingly so. That realization changed my approach: I started treating pure sequences as an event with an understandable frequency, not superstition. When you recognize the math, you make fewer emotion-driven mistakes.
Practical takeaways
- Pure sequence probability (standard deck, common rules) = 48 / 22,100 ≈ 0.2172%.
- Expect roughly one pure sequence every 460 hands on average.
- Pure sequences are strong hands — size bets for value but remain mindful of relative positions and opponent ranges.
- Rule variations (wildcards, Ace handling, deck size) change the numbers; always adapt calculations to the rules in play.
Want to practice or check live tables?
If you’re studying probabilities and want to apply them at live or online tables, start by tracking hands and outcomes during practice sessions. For an accessible playing environment and additional rules references, consider checking out resources that cover Teen Patti gameplay and hand rankings such as pure sequence probability.
Summary
Knowing that the pure sequence probability is about 0.217% equips you to evaluate hand strength, size bets more intelligently, and manage variance prudently. The math is straightforward when you break it down into rank runs and suits: 12 possible rank runs × 4 suits = 48 favorable hands out of C(52,3) = 22,100 total hands. Use that foundation to build strategy, simulate outcomes, and make consistent, probability-based decisions at the table.
