Teen Patti hand odds: all 22,100 three-card hands counted

A Teen Patti deal is three cards from a 52-card deck, and that gives exactly 22,100 possible hands. Count them by type and the ranking makes sense at once: a trail comes up 52 times in those 22,100, a plain high card 16,440 times. Sorted by type, those 22,100 hands are the whole game in numbers, and they explain why a pair is a stronger hand than it feels.

The count: 22,100 hands sorted by rank

The number of three-card hands is 52 × 51 × 50 divided by 6, because the order of the cards does not matter. That is 22,100. Each rank below is counted directly, and the six lines add back to the same total.

Pair or better adds up to 5,660 hands, or 25.61%. Three deals out of four give you nothing but a high card.

How each line is counted

A trail needs three cards of one rank. There are 13 ranks and 4 ways to choose three suits from four, so 13 × 4 = 52. Trail of aces, the top hand, is 4 hands out of 22,100, or 1 in 5,525.

A pure sequence is three consecutive ranks in one suit. With A-K-Q at the top and A-2-3 counted as a run, there are 12 possible runs of ranks, and each can come in 4 suits: 48 hands.

A sequence is the same 12 runs in any suits. Each card can be any of 4 suits, so 12 × 64 = 768, minus the 48 that are all one suit: 720.

A colour is three cards of one suit that are not a run. One suit gives 286 three-card combinations, four suits give 1,144, and taking out the 48 pure sequences leaves 1,096.

A pair is 13 ranks for the pair, 6 ways to pick two suits, and 48 cards left for the third card that do not make a trail: 13 × 6 × 48 = 3,744. Everything else, 16,440 hands, is high card.

The odd one out: trail beats pure sequence

By pure counting, a pure sequence (48 hands) is slightly rarer than a trail (52 hands), yet the trail ranks higher. That is a tradition of the game, not a mistake in the maths, and most rule sets keep it. The difference is 4 hands in 22,100, so it changes almost nothing at the table.

Some home games and a few tables rank A-2-3 as the second-best run, just below A-K-Q. That changes who wins a tie between two runs, not how often runs appear. Check the rules panel of any live table before you play; ranking details are printed there.

What this means when you hold a pair

A pair of sevens beats about 81% of single hands: the 74.39% that are high card plus the five lower pairs. Against one opponent that is a strong position. Against a full table it is weaker than it looks.

A rough sum shows why. The chance that one opponent does not hold pair or better is about 74.4%. For five opponents, multiply it five times: about 22.8%. So in a six-player game, roughly 77 times out of 100 at least one other player holds a pair or better. Your pair is still often good, but plenty of those hands are higher pairs or better.

The same arithmetic explains why blind players stay in so long in home games. With three out of four hands being high card, most showdowns are decided by the highest card, and a K-high or A-high hand wins more often than beginners expect.

Live Teen Patti is a different bet

Many live Teen Patti tables in casino lobbies are not a game between players. The dealer deals hands to two positions, and you bet on which one wins, or on side bets such as a pair or better appearing. Your opponent is the paytable, and the house edge sits in how each bet pays against the counts above.

That is where this table becomes useful. If a side bet pays on "pair or better", you now know the hand turns up about 25.6% of the time for a single hand. Compare that with the payout printed on the table and you can see how much the house keeps. As a made-up example, a bet paying 2 to 1 on an event that happens 25.6% of the time would return on average 3 × 0.256 = 0.768 of the stake, a cost of 23.2%. Real side bets are worded differently, such as needing the hand on one position or counting the best of several cards, so redo the sum with the table's own wording and payouts.

What no count can do

Every deal starts from a fresh shuffle or a fresh shoe position you cannot see, so these numbers describe the long run, not the next hand. No pattern of recent results changes them. Predictors and "signal" groups that claim to know the next hand are selling a story; the deck does not remember.

Play Teen Patti for the cards and the table, with an amount you have decided in advance. If it has stopped feeling like a game, call Tele-MANAS: 14416, free, any hour. Nobody under 18 should play.