Infinite card game
Aquarius
people.
Cards are dealt evenly between the two, so that each has twenty-six
cards. In turn, they then commence turning over the top card of their
(unseen) hand onto a central pile. If the card turned over is a face
card (2,3,4,5,6,7,8,9,10), play passes to the other player to turn
over a card. If it is a court card (J,Q,K,A), then the other player
has to turn a specific number of cards over, one by one, until the
card limit is reached or that player turns up a court card. The limit
for a jack is 1, for a queen 2, for a king 3, and for an ace 4. If the
player turns up a court card before this card limit, the first player
has to then turn cards up to the limit or until a court card is hit.
If the player fails to turn a court card before hitting the limit,
then he/she collects the central pile and adds it to the bottom of
his/her hand. Suits are irrelevant.
So an example game (showing a turn as "player: card value turned")
might go:
P1: 6
P2: 10
P1: 3
P2: K (P2 turns a court card; P1 now has 3 cards in which to turn up
a court card or else will have to pick up the central pile)
P1: 5
P1: 5
P1: Q (P1 gets a court card inside the card limit of 3; P2 now has 2
cards in which to turn up a court card)
P2: 2
P2: J (P2 gets a court card; P1 now has 1 card (because the card
turned up was a jack) in which to turn up a court card)
P1: 7 (P1 fails)
and player 1 picks up the central pile. Play then begins again.
The objective of the game is to get rid of all your cards.
Obviously, there is no skill in this game, all plays are automatic
and dictated, so the initial deal is the only thing that has an effect
on the outcome.
So far, this is not a puzzle :-)
The puzzle, question, call it what you will, is this:
Is there an initial deal (or many initial deals) such that the game
will continue forever?
Aquarius
--
http://www.kryogenix.albatross.co.uk/
"Gibberish is unintelligible sounds. Even Aq, on a
bad day, does better than that." -- Zubrette, afe
Carl G.
Aquarius wrote in message <379f8e4f...@news.albatross.co.uk>...
A question about the rules:
After a player picks up the central pile, does he or the other player play
next?
Note: I believe that the terms "face cards" and "court cards" both refer to
the jacks, queens and kings (also, "cavalier" or "coat cards"). The cards
with ranks 2 through 10 can be referred to as "spot cards", and the ace
through 10 as "non-face cards". I believe that there is also a specific
term for the face cards when they include the aces (aces, jack, queens, and
kings), but I can't recall it now (non-spot cards?).
Carl G.
Loomis Philanthrope
> The objective of the game is to get rid of all your cards.
>
I have always played the object to be to gain all the cards. When a player
fails to produce a face card or ace in the alotted time, the other player
picks up the cards, increasing his stack.
> Obviously, there is no skill in this game, all plays are automatic
> and dictated, so the initial deal is the only thing that has an effect
> on the outcome.
I also play that when two of the same card is played back to back, each
player has the chance to slap the pile and pick it up for himself. The
faster slapper has the advantage, so that would make it a somewhat skilled
game nixing the puzzle. For the sake of the puzzle, I suppose we should
leave this part out.
> So far, this is not a puzzle :-)
>
> The puzzle, question, call it what you will, is this:
>
> Is there an initial deal (or many initial deals) such that the game
> will continue forever?
My guess. Sure there are. In fact, it seems to me hard to win the game.
If you don't have face cards, it will be hard to keep from losing and you
aren't winning until you have very little face cards. So just an intuitive
guess says there are plenty of deals that would cause infinite play.
Loomis
Glenn
: The card game of "Strip Jack Naked" is normally played with two
:people.
We used to call this game "War."
: Cards are dealt evenly between the two, so that each has twenty-six
: cards. In turn, they then commence turning over the top card of their
: (unseen) hand onto a central pile. If the card turned over is a face
:card (2,3,4,5,6,7,8,9,10), play passes to the other player to turn
:over a card. If it is a court card (J,Q,K,A), then the other player
:has to turn a specific number of cards over, one by one, until the
:card limit is reached or that player turns up a court card. The limit
:for a jack is 1, for a queen 2, for a king 3, and for an ace 4. If the
:player turns up a court card before this card limit, the first player
:has to then turn cards up to the limit or until a court card is hit.
:If the player fails to turn a court card before hitting the limit,
:then he/she collects the central pile and adds it to the bottom of
:his/her hand. Suits are irrelevant.
:[example deleted]
: The objective of the game is to get rid of all your cards.
: Obviously, there is no skill in this game, all plays are automatic
:and dictated, so the initial deal is the only thing that has an effect
:on the outcome.
: The puzzle, question, call it what you will, is this:
: Is there an initial deal (or many initial deals) such that the game
:will continue forever?
I suspect there is.
I'll assume that the player who wins a pile, is the next person to play
(you didn't specify who plays next).
Look at the simpler version played with the 4 tens and 2 jacks.
Suppose the initial deal is
(1)
Player 1: J 10 10 (leftmost card is on top)
Player 2: 10 J 10
Player 1 goes first
P1: J
P2: 10
P1 picks up pile and puts it on the bottom. We now have,
(2)
Player 1: 10 10 J 10
Player 2: J 10
P1: 10
P2: J
P1: 10
P2 picks up pile and adds it to the bottom. We now have,
(3)
Player 1: J 10
Player 2: 10 10 J 10 (Player 1 and 2 have swapped hands from position (2)!)
After the next pile is won, we will reach position (2) again and the game
will forever repeat through the cycle.
In this example both players initially have an odd number of cards.
Cycles like this are still possible when both players have an even
number of cards. An example is the following initial deal (player 1
goes first)
Player 1: Q x x x x x
Player 2: x x x Q x x
x is any non-A,K,Q,J.
I'm not inclined to try to find a cycle of plays using all 52 cards
(it sound too painstaking and tedious). Perhaps there is a more
elegant way to show the existence of a cycle.
Gerry Quinn
>aqua...@kryogenix.albatross.co.uk (Aquarius) writes:
>
> : The card game of "Strip Jack Naked" is normally played with two
> :people.
>
>We used to call this game "War."
We called it "Beggar My Neighbour".
- Gerry Quinn
brian tivol
> The card game of "Strip Jack Naked" is normally played with two
> people.
> Is there an initial deal (or many initial deals) such that the
> game will continue forever?
There was an essay called "Beggar My Neighbor" (another name for the
game) in the Unsolved Problems section of the February 1999 issue of
the American Mathematical Monthly, a publication of the Mathematical
Association of America.
Marc M. Paulhus was the author. The online summary for that article
doesn't list an email address for Paulhus, whereas most other authors
have one.
I honestly can't remember if the unanswered question was "Is there a
game that doesn't stop?" or "What are the odds of getting a
non-terminating game?" The author ran some exhaustive tests of
smaller decks with two of each face card and an even number of other,
filler cards-- I think he got up to decks with twenty cards.
When I unpack in a month or so, I should be able to remember some more
details for you. <smiley>
--brian
Aquarius
>A question about the rules:
>
>After a player picks up the central pile, does he or the other player play
>next?
The player who has just picked up the central pile plays next.
However, I've seen people play the other way (i.e., the player who has
*not* just picked up the pile plays next), so solutions for both
variants would be nice ;-)
>Note: I believe that the terms "face cards" and "court cards" both refer to
>the jacks, queens and kings (also, "cavalier" or "coat cards").
Interesting; I'd always learnt it the other way......Oh well....
Aquarius
--
No sooner met, but they looked; no sooner looked, but
they loved; no sooner loved, but they sighed; no sooner
sighed, but they asked one another the reason
-- Shakespeare
Aquarius
>I'm not inclined to try to find a cycle of plays using all 52 cards
>(it sound too painstaking and tedious). Perhaps there is a more
>elegant way to show the existence of a cycle.
>
deal (or given initial deals) that would result in an endless game.
Creating said deals by working them out from first principles is, as
you say, painstaking and tedious indeed, so I don't want to do it.
Aq.
Rich Grise
>
> Carl G. spoo'd forth the following:
...
> >Note: I believe that the terms "face cards" and "court cards" both refer to
> >the jacks, queens and kings (also, "cavalier" or "coat cards").
>
> Interesting; I'd always learnt it the other way......Oh well....
>
> Aquarius
Probably one difference is that in the US, we don't have any
official royalty. But I've always heard the Jacks, Queens, and
Kings referred to as the "Face Cards," presumably because they
have some sort of human-looking face. In poker, when they want
to include the Aces, they explicitly say, "Aces and Faces."
I've also heard the Jacks referred to as "Knaves," but that
would be a little confusing, as it would go: ... 10, K, Q, K, A.
Cheers!
Rich
Chas Adrion
years ago. The games became very violent with hard slapping for the pots
and melee's when slap winners were in dispute.
One additional rule, any passers-by with no cards or players who were busted
down to no cards could sit in and try to slap their way into the game.
The name of the game was 'slap jack'.
Its a great game to keep brats entertained if you get stuck babysitting.
>I have always played the object to be to gain all the cards. When a player
>fails to produce a face card or ace in the alotted time, the other player
>picks up the cards, increasing his stack.
>
>> Obviously, there is no skill in this game, all plays are automatic
>> and dictated, so the initial deal is the only thing that has an effect
>> on the outcome.
>
NoCats
>
> We used to play this version of the game when I was in high school many
> years ago. The games became very violent with hard slapping for the pots
> and melee's when slap winners were in dispute.
> One additional rule, any passers-by with no cards or players who were busted
> down to no cards could sit in and try to slap their way into the game.
> The name of the game was 'slap jack'.
> Its a great game to keep brats entertained if you get stuck babysitting.
>
:)
Rich
Mark Brader
> > > people.
> >
>
> We called it "Beggar My Neighbour".
So did we. My wife never played it, but knows a *different* completely
mechanical card game as "War".
--
Mark Brader, Toronto \ "It is one thing to praise discipline, and another
msbr...@interlog.com \ to submit to it." -- Miguel de Cervantes, 1613
My text in this article is in the public domain.
Rich Grise
face card
face card noun
Games.
A king, queen, or jack of a deck of playing cards. Also called picture
card.
The American Heritage® Dictionary of the English Language, Third Edition
copyright © 1992 by Houghton Mifflin Company. Electronic version
licensed from INSO Corporation. All rights reserved.
:)
Rich
Lynn Johannesen wrote:
>
> Carl G. <cgi...@mindspring.com> wrote:
> : Note: I believe that the terms "face cards" and "court cards" both refer to
> : the jacks, queens and kings (also, "cavalier" or "coat cards"). The cards
> : with ranks 2 through 10 can be referred to as "spot cards", and the ace
> : through 10 as "non-face cards". I believe that there is also a specific
> : term for the face cards when they include the aces (aces, jack, queens, and
> : kings), but I can't recall it now (non-spot cards?).
>
> Perhaps you are thinking of "hono[u]r", but this also includes 10s.
> The Official Encyclopedia of Bridge (published by the ACBL, the
> sponsor of organized bridge throughout North America) has these
> definitions, which as you see are not entirely consistent:
>
> FACE CARDS: The cards which have a representation of a human figure,
> called originally coat cards, later court cards. [Examples showing
> only K, Q, J.]
>
> COAT CARDS: The original term in English for the three cards
> of each suit (etc.) [K,Q,J]... the term has been superseded by
> a corruption, "court cards".
>
> COURT CARDS: The K,Q,J of each suit are represented by coated
> figures rather than pips, [hence] "coat card". This term was
> corrupted to court card and extended to include the ace...
>
> HONOR: A, K, Q, J or 10.
>
> In practice, however, bridge players frequently do not consider
> the 10 as an honor, depending on context. Presumably the Encyclopedia
> authors disapprove. Failing that, there seems to be no word
> meaning A,K,Q,J only.
theodore hwa
["Beggar My Neighbor" article by Marc M. Paulhus in Feb 1999 issue of the
American Mathematical Monthly, "Unsolved Problems" section]
:
: I honestly can't remember if the unanswered question was "Is there a
: game that doesn't stop?" or "What are the odds of getting a
: non-terminating game?" The author ran some exhaustive tests of
: smaller decks with two of each face card and an even number of other,
: filler cards-- I think he got up to decks with twenty cards.
The unanswered question (well, one of them) was whether there was a game
with the usual 52-card deck that didn't stop.
Ted
Aquarius
Which is just what I'd like to know, along with the possibly harder
question of what the deal for that game is...
Aquarius -- or a method for working it out
Wei-Hwa Huang
>In practice, however, bridge players frequently do not consider
>the 10 as an honor, depending on context. Presumably the Encyclopedia
>authors disapprove. Failing that, there seems to be no word
>meaning A,K,Q,J only.
Informally, "point cards" will generally be understood by most players.
I'm sure Napoleon players must have a name for them ...
--
Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/
---------------------------------------------------------------------------
It's not sarcasm. It's reductio ad absurdum.
Mauro Fiorentini
Glenn wrote:
> : Is there an initial deal (or many initial deals) such that the game
> :will continue forever?
>
> I suspect there is.
> I'll assume that the player who wins a pile, is the next person to play
> (you didn't specify who plays next).
> Look at the simpler version played with the 4 tens and 2 jacks.
> Suppose the initial deal is
>
> Player 1: J 10 10 (leftmost card is on top)
> Player 2: 10 J 10
>
> Player 1: Q x x x x x
> Player 2: x x x Q x x
Two nice examples, which show a problem: to get an infinite game of such a
simple sort,
you need a large number of "idle" cards (those 'x'): mote than twice the number
of cards which
face cards can pick up. There aren't enough idle cards in 52 cards deck.
To construct an example a propose a different approach:
try to split a single suit into two sets, S1 and S2, such that when the pattern
S1 X1 vs S2 X2 is played, the pattern X1 S3 vs X2 S4 is obtained and when
S3 X1 vs S4 X2 is played, the pattern X1 S1 vs X2 S2 (or X1 S2 vs X2 S1) is
obtained.
(X1 and X2 represent any sequence of cards)
If this is possible, the full deck can be separated into two parts as follows:
S1 S2 S1 S2 to one player, S2 S1 S2 S1 to the other, using the four suits.
Checking all the patterns of a single suit means checking at most 13! * 12 =
74724249600
patterns: a number well into today's computer technology capabilities.
If the search fails, it does not imply that an endless game does not exist, but
makes it
very unlikely.
Best regards
Mauro Fiorentini