BridgeNinja.com

Poker Card Games Directions

September 24th, 2008 |

Author: Bryan

poker card games directions
Probability question involving cards?

Using a standard 52 card poker deck, a player is dealt 13 cards. What is the total probability of the player receiving 11 clubs and 2 non-clubs?

I really would like to know this because if you can be dealt that hand in the game of Hearts, and you also pass the 2 non-clubs and receive the other 2 clubs, you will have an unbeatable, perfect hand! (I only want to know the probability mentioned in the question above, because the final answer that I am looking for involves multiplying by the probability of the rotation of passes to be in the correct direction so that the player who receives the other 2 clubs is in line to pass them to the one with the other 11 clubs. I am not sure how to calculate the total, since player who passes the 2 clubs must also be DEALT them. If anyone knows how to calculate that I’d greatly appreciate it.)

Total number of 13 card hands = 52C13 = 635,013,559,600

Those that have 11 clubs and two others = 13C11 * 39C2 = 78 * 741 = 57798
(that is equivalent to half a drop of water in a swimming pool, or some similar analogy)

So the probability is (roughly speaking) 60 thousand / 635 billion
= 60 in 635 million = about 1 in 11,000,000.

Don’t you pass 3 cards in hearts ?

If it’s 10 clubs instead of 11, that ‘improves’ it.
13C10 * 39C3 = 286 * 9139 = 2613754
Now it’s 2.6 million out of 635 billion or 2.6 out 635,000
or merely 1 in 245000 (very roughly).
(or 4 in 1,000,000 … even rougher).

Still not something I would put any money on or hold my breath waiting for.

The chances that the right guy has the other 2 or 3 clubs are also minuscule,
and then the chances he would pass them are who knows what.

The 635 billion is just for one of the hands.
The number of combinations of 4 hands is much much bigger,
since you multiply the 635 billion by the number of hands for the next person,
which is 8,122,425,444 and then the number of hands for the third player which is
10,400,600.
So you have 635 billion * 8 billion * 10 million = … close enough to infinity for my purposes.

All in all, I’d say this is not something to stay up nights worrying about.
There are two chances this might occur, “slim and none”.

Card Games for Charity Anti-Meta 1st Place!!!!

Scrabble Slam Cards

$1.50

Parker Brother’s Scrabble Slam CardsThis is the fast-paced word game where anything can happen. Scrabble Slam is a high-speed four letter word game. Race against each other to change the existing word and get rid of your cards. Game could become fame and fame could become fate, you never know where it will go with Scrabble Slam. Play this game with your family and friends.Product Dimensions: 0.79 …

Big Screen Solitaire – White

$18.02

Put away that old deck of cards — the Big Screen is back. Now classic electronic card games are better than ever with a larger screen, easy-to-move cards, an undo button and an auto-backlight. Play Klondike or Vegas Solitaire and, for an extra challenge, turn on the electronic timer to race against the clock. Will Big Screen Solitaire bring you piles of stress or stacks of success? There’s only o…