The skill based card game of Indian rummy is the perfect example of how multiple mathematical concepts can work at the same time. Let us take a look at rummy with a mathematical eye. The fundamental calculations and formulas associated with Rummy are from Probability Theory and the concept of Permutation and Combination.
How Permutation and Combination are associated with Rummy
The game is all about arranging or forming a sequence depending on the cards you are dealt. There is a higher probability of the favorable event not happening. A standard card deck contains 52 cards and the chances of getting a pure sequence of 4 cards of same suite remains extremely low. Knowing this mathematical reality, a skilled Indian Rummy player is able to carve out a win by manipulating cards based on Permutations
Consider the basic permutation and combination algorithm. Number of all permutations of N things, taken R at a time, are given by:
NPr = N!/(N - R)!
It is quite amazing that most of us are already using this formula in our heads as we play this skill based card game of forming sequences and sets. Even a lay person who is somewhat familiar with playing rummy will find mathematics a lot friendlier when he or she studied it in school.
How Probability is associated with Rummy
Lets understand the game with a standard deck of 52 cards. There are a total number of four suits (♠,♥,♦,♣) with an equal number of 13 cards each. Each suite further has four face cards (J, Q, K, A), so considering the equal probability of picking one card out of 52 cards is
The Probability of getting a favorable card →(1/52)
The Probability of not getting a favorable card →(1-1/52)
From, the above results it is obvious that the probability of a favorable event 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 how do things change in a game if the probability of getting a pure sequence is low? Well, there are several compelling factors which can completely turn the game. For one, if there are more decks in use, chances of quickly making a pure sequence improve. Secondly, a player’s choice of picked cards and discarded cards will quickly alter the end outcome of the game. Also, a player’s ability to judge their opponents cards by the cards they are discarding also makes them strong at the game. And finally, remember that you only need one pure sequence for finishing the game successfully. Rest of the cards can be melded into impure sequences or sets.