09-08-09, 09:55 PM #1
How many possible bridge hands?
For those not familiar with Bridge, Whist, & similar card games all you need to know is that these games are played with a standard 52-card deck & 13 cards are dealt to each of 4 players.
Some easy warmup questions.
- How many possible hands can a player hold? Answer: 52! / 39! * 13! = 635 013 559 600
- How many deals to 4 players are possible? Answer: 52! / (13!)4 This is 5.36 * 1028
- How many different holdings are there in a Particular suit? 213 = 8192
Considering some cards as equivalent brings to mind some more difficult problems.
- How many hands are possible if the 2 through the ten are considered to be equivalent? How many deals are possible? How many holdings in a particular suit? For the last question, the answer is 10*24 = 160, which is obviously a lot less than 8192
- The ten & nine are often important in the play of a hand. How many hands are possible if the 2 through the 9 are considered to be equivalent? How many deals? How many holdings in a suit? 9*25 = 288 for the last question.
- Suppose the 2 through the 8 are considered to be equivalent. How many hands? How many deals? 8*26 = 512 for the number of possible suit holdings.
Does anyone have answers to the above?
I might take the time to write a program to answer these questions.
By darksidZz in forum Art & CultureLast Post: 11-19-08, 06:34 PMReplies: 33
By OilIsMastery in forum Human ScienceLast Post: 11-10-08, 01:56 PMReplies: 41
By draqon in forum Human ScienceLast Post: 02-22-08, 07:43 PMReplies: 9
By madanthonywayne in forum World EventsLast Post: 08-09-07, 11:51 PMReplies: 65
By reasonmclucus in forum General Science & TechnologyLast Post: 08-07-07, 12:14 AMReplies: 5