In the card game of Rummy, all players start with the same number of cards and the aim is to fill your hand such that all cards are in exactly one meld. Each individual meld is composed of 3 or 4 cards and can each can be completed two ways: cards of the same number/court or consecutive cards of the same suit. (This would mean you have a meld of 3 and a meld of 4 in 7 card rummy and 2 melds of 3 and a meld of 4 in 10 card rummy.) Each individual ace can count as higher than a king or lower than a 2, but not both. (This means K, A, 2 is not allowed.)

What are the probabilities of being dealt a winning hand when: (Note that all decks are without jokers)

- Playing seven card rummy with one deck?
- Playing seven-card rummy with two decks?
- Playing ten-card rummy with one deck?
- Playing ten-card rummy with two decks?
- One of the cards was inadvertantly dropped on the floor before dealing for seven-card rummy?

It would be good to run a simulation.  But to do so requires an algorithm for evaluating a hand.  The mere presence of 3 or 4 of a given denomination, and/or of 3 or 4 runs is not enough as they might overlap instead of including all the cards.

And the algorithm should not take too long to evaluate, as we need a lot of trials.

Posted by Charlie on 2005-01-07 20:27:08