All these probabilities are described

There are 52 cards in the deck. The sequence in which the cards are dealt does not matter, it is the combination of the three cards that matters. The total number of combinations of any elements, taken r at a time, from a set of n elements is given by the combination formula nCvar>r (COMBIN(n,r) in Microsoft Excel and compatible spreadsheet ). Thus, the total number of three-card hands, from a deck of 52 cards, is calculated by the formula 52C3 = 22,100.

Although the probability of being dealt a pure sequence is slightly less than that of a trio, trios are considered higher hands in most versions of the game. Because of this variance from strict rarity, a popular house rule is to treat 2-3-5 of the same suit as a straight flush, thereby increasing the number of possible straight flushes to 52, the same as a trio, bringing the probabilities even.

The probabilities of the various ranking combinations are described below. All these probabilities are described for 52-card teen patti, without the two Joker cards. In Joker versions, the probabilities change widely, most importantly for pairs.

HandFrequencyProbabilityCumulative ProbabilityOdds
Three of a kind/trio520.24%0.24%424.00:1
Straight flush/pure sequence480.22%0.45%459.42:1
No pair/high card1644074.39%100.00%0.34:1

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