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?

- Playing seven card rummy with one deck?

Please say this isn't the easiest way:

There are four winning hands-

A set of 3 and a set of 4

A set of 3 and a run of 4

A run of 3 and a set of 4

A run of 3 and a run of 4

They need to enumeralted separately, then summed.

The combination hands are trickiest - having one changes the probability of the other.

I'll work on this later if I have time.

The other parts of the problem are just variations.

-Jer

Posted by Jer on 2005-01-07 17:29:01