Indian rummy, a skill-based card game, is an excellent example of how multiple mathematical concepts can coexist. In this game, you must use certain skills which include analytical thinking, mathematical skills, logical reasoning, observational skills and quick decision-making. The objective of the game is to arrange or form a set of cards into valid sequences and sets. A standard deck contains 52 cards having 13 cards each and 1 printed joker. The chances of obtaining a pure sequence of 4 cards from the same suit are quite low. A skilled rummy player can carve out a win by forming sequences and sets based on Permutation and Combination.

Forming sequences and sets is extremely important as they are the basic elements of the game. Understanding the probability can be an excellent option as it helps in analysing which cards need to be picked and which needs to be discarded.

Consider the following example: If you are dealt with 2, 4, and 6 of Hearts and to complete the sequence, you must have either a 5 of Hearts or a 3 of Hearts. What makes you pick 5 of Hearts over 3 of Hearts is the understanding that additional combinations are possible. Another key factor to remember is that if you have a 3 of Hearts and an 8 of Hearts, do not keep them if you see your opponent discarding a 5 of the same suits.

By observing the discarded cards, one can calculate the probability of the joker card of the opponent. If you are playing rummy on a 2-player table then 5 joker cards (1 printed joker and 4 wildcard joker) are used. If you have 1 joker card, there are 4 joker cards available elsewhere. It increases the chances of getting a joker card from the closed deck. It is based on the assumption that the opponent has either one or two joker cards.

Let us examine rummy with a mathematical gaze. Rummy's basic calculations and formulas are based on Probability Theory and the concepts of Permutation and Combination.

## How Permutation and Combination are Associated with Rummy

Take a look at the basic permutation and combination algorithm. The total number of permutations of N things, taken R at a time, is given by:

NPr = N!/(N - R)!

It's interesting how many of us already have this formula mastered as we play this skill-based card game of forming sequences and sets. Even a novice who is familiar with playing rummy will find mathematics far more comprehensible when studied in school.

### How Probability is Associated with Rummy

Let's start with the basics, a deck of 52 cards is used in the game if played on a 2-player table. There are four suits (Hearts, Diamonds, Clubs and Spades) with 13 cards each. Each suit has three face cards (J, Q, K), low-value cards ( 2 to 9) whose point value is equal to their rank and high-value cards ( 10, J, Q, K and A) whose point value is equal to 10 points. Therefore the probability of picking one card out of 52 is equal.

**The Probability of getting a favourable card →(1/52)**

**The Probability of not getting a favourable card →(1-1/52)**

The above results show that the chances of a positive outcome is on the lower side. This result also factually states that "Rummy is a skill-based game, and the chances of changing the outcome of a game is entirely dependent of the level of skill present in the players."

So, what happens in a game when the chances of getting a pure sequence are low? There are a few compelling elements that can entirely change the game. For one thing, if more decks are used, the chances of swiftly making a pure sequence improve. Second, a player's selection of picked and discarded cards will immediately change the game's outcome. A player's ability to judge their opponents' cards based on the cards they are discarding also makes them a strong player.

## Conclusion

In the end, keep in mind that you only need one pure sequence and the remaining cards can be combined to form impure sequences and sets to declare the game before their opponents.

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