Cripple Mr Onion, v3.0
                       ----------------------

                  Reconstructed by Andrew C. Millard

               from "Witches Abroad" by Terry Pratchett.

             Thanks to Terry Tao concerning the modifiers.


This description of Cripple Mr Onion is in six parts:

       i   Introduction,
       ii  The Hands,
       iii The Non-Gambling Game,
       iv  The Gambling Game,
       v   The Modifiers,
       vi  Final Points.

i Introduction:

Cripple Mr Onion requires two standard decks of playing cards, preferably
one having the English or French suits clubs, spades, hearts and diamonds,
and the second having the Spanish or Italian suits swords, staves, cups
and coins - for the purpose of forming flushes, these are taken to be
paired in their respective order given above:

       clubs     is paired with   swords,
       spades    is paired with   staves,
       hearts    is paired with     cups,
       diamonds  is paired with    coins.

If a Spanish or Italian suit cannot be obtained, two English or French
decks can be used adequately for most purposes; see the modifiers for
further comments on this.

The game also requires at least two players, but not more than seven [this
isn't to do with the number eight for a specific reason, but a result of
the fact that there aren't enough cards for more than seven players], with
a ready supply of small coinage or tokens when gambling takes place, and
the players arranged as evenly as possible around the table on which the
game is played. A container able to hold cards should be placed centrally
on the table - this is to be the discard pot - along with another
container for coins or tokens if gambling is to take place: this is the
Pot.

ii The Hands:

Cripple Mr Onion revolves around forming groups of cards which either sum
exactly to twenty-one (an onion) or come close to this total without
exceeding it; in the usual fashion, a picture card (P) is worth ten, an
ace (A) is worth one or eleven, and other cards are worth their face
value: a ten (T) is worth ten, a nine is worth nine, and so on. Since
groups of cards which sum exactly to twenty-one can be formed in various
ways, they are ranked in a particular order according to their
composition, along with a few other groups which do not give twenty-one in
total but which are of some interest; these special hands, described
below, are worth more than any other valid combinations of cards and
usually dominate the play.

There are thirteen categories of winning hands and in increasing order of
worth are:

   1 Bagel: this is a combination of two cards which totals exactly
		twenty; it is, therefore, one of TT, TP, PP or 9A.

   2 two-card onion: this is a combination of two cards which totals
		exactly twenty-one; it is, therefore, either TA or PA.

   3 Broken Flush: this is a group of at least three cards, summing to at
		least sixteen (but not more than twenty-one) with all of
		the cards except for one in the same suit-pair.

   4 three-card onion: this is a group of three cards which totals
		twenty-one exactly; examples are ATT, 56T, and 579.

   5 Flush: this is a group of at least three cards, summing to at least
		sixteen (but not more than twenty-one) with all of the
		cards in the same suit-pair.

   6 four-card onion: ... four cards which total twenty-one; for example,
		A55T, 2469, and 3378.

   7 Broken Royal: this is a special case of a three-card onion where the
		three cards are specifically 678 (of any suit-pairs).

   8 five-card onion: ... five cards ... e.g. A235T, 23466, and 33348.

   9 Royal: this is another special three-card onion being 777.

  10 six-card onion: ... six cards ... e.g. A2233T and A23456.

 (11 Wild Royal: this is a combination that may only be played when eights
		are wild - see the modifiers for details - since it
		consists of three wild eights.)

  12 seven-card onion: ... seven cards ... e.g. A223445.

  13 Onion: an Onion (capitalised letter 'o') is a two card combination of
		a picture card and an ace; HOWEVER, PA on its own is just a
		two-card onion (place two above), since to occupy this
		exalted position, the group must consist of two Onions,
		PAPA or Double Onion, or three Onions, PAPAPA or 3[PA] or
		Triple Onion, or four Onions, 4[PA] or Lesser Onion, or
		even five Onions, 5[PA] or Great Onion. The Onions
		themselves are arranged according to their worth, with
		Double Onion the lowest and Great Onion the best.

Notice that the maximum number of cards making up an onion is seven (there
is no eight-card onion) and that for PA to be of any real value, the
player must hold at least two picture cards and two aces. Also, if a
player should be unlucky enough to receive multiple bagels, the qualifiers
"double", "triple", "lesser" and "great" (with small initials) are used.

Since each player is ultimately in posession of ten cards, a number of
groups, most of them usually winning hands, can be formed; the objective
of any individual player is therefore to form the ten cards into the best
possible set of groups, with each of the ten cards taking part in only one
of the groups. For example, representing clubs and swords by 'c', spades
and staves by 's', hearts and cups by 'h' and diamonds and coins by 'd',
the hand:

          3c 3s 4s Js Ah 7h Qh Ad 4d 6d

is best split into: Double Onion - JsAhQhAd
                    five-card onion - 3c3s4s4d7h
                    a six - 6d

whilst the hand:

          9c 4s Qs Ks 4h Jh Ad 7d Td Kd

is best split into: four-card onion - Ad4s7d9c
                    double bagel - QsKsJhTd
                    a fourteen - 4hKd.

From this list of winning hands, it follows that some cards are
intrinsically more valuable than others: tens, for example, are only
useful in bagels and small-card onions whereas twos and threes are
necessary for constructing many-card onions; aces and picture cards are
obviously of great value. However, a player's strategy in selecting cards
for replacement (see the game descriptions and certain of the modifiers)
should also be influenced by the number of players, and whether eights are
wild or not, since these factors influence the relative likelihood of each
hand winning the round.

iii The Non-Gambling Game:

At the beginning of each round, one player is identified as the Dealer,
with the player to the Dealer's left as the Elder and the player to the
Dealer's right as the Younger - this sets the order of precedence in being
dealt cards and in winning in the event of a tie as Dealer, Elder, other
players in order and, lastly, Younger. In the event that the Dealership
changes, these identifiers move to be based around the new Dealer. The
round opens when the Dealer shuffles the pack of all 104 cards and the
Younger cuts the pack.

All the players are dealt five cards in this order: the Dealer receives
two cards and deals all the other players, in order from Elder to Younger,
three cards; the Dealer then receives three cards and deals the other
players two [this is done to speed up the dealing, which isn't exactly the
most interesting part of the game]. Then, in turn, from Elder to Younger,
each player discards up to four cards into the discard pot and announces
the number of discards to the Dealer who replaces them from the top of the
pack; the Dealer then discards and replaces, also announcing the number
thrown away. It is important to note that up to this point all cards have
been dealt face down, each player is only aware of their own cards and, by
way of the draw, ought to have a better hand than was originally dealt.

The second set of five cards each is now dealt in the following way: the
Dealer receives five cards face down on the table, and then, in turn from
Elder to Younger, each other player is dealt five cards face up on the
table. Cards dealt face up on the table must remain that way, although the
owner of those cards may rearrange them there if desired.

Now the final part of the round, Showdown, takes place. Beginning from the
Elder, the highest card grouping is declared and displayed on the table;
if the player to the left of the Elder cannot equal, beat or play some
modifier that affects the Elder's cards, that player's cards are all
placed face up on the table, in their groupings if the player wishes, and
that player is out of the round; the comparison of the next leftward
player's cards with the Elder's then takes place. If the Elder's cards are
equalled, then the next card grouping must be considered. If the Elder's
cards are beaten, then the Elder has the opportunity to play a modifier or
rearrange the card grouping in an attempt to obtain a better arrangement;
once the Elder's cards are undoubtedly beaten, however, the Elder is out
of the round and the comparison of the currently leading player's cards
with the next leftward player's takes place. By this process of
comparison, consideration of lower groupings, rearrangement of card groups
and playing of modifiers, and knocking out of players, the holder of the
best set of cards, between the Elder and the Younger, is found. Finally,
the Dealer's cards are compared with the only player left in, and the
process of finding the better cards is repeated; the player who holds the
better cards has then won the game. Note that in the event of either a
complete tie between two players' cards or an impasse due to circular use
of modifiers, the player of greater seniority wins - often, this means
that the Dealer wins. Once all the players but one have been knocked out,
leaving the winner holding the best cards, the round is over, the cards
and discards are collected up and the winner becomes the Dealer for the
next round.

iv. The Gambling Game.

There are two types of betting that are used in the gambling version of
Cripple Mr Onion and these will be described before the details of how
they fit into the game are given.

The first type is "matching the Dealer's stake". First, the Dealer chooses
a number of coins or tokens to be the stake, on the basis of the cards
known to the Dealer, and, naming the amount, places it in the Pot; if the
Dealer wishes, the amount may be zero. Then, when called upon by the
Dealer to do so, each player must either match the stake, placing an equal
amount in the Pot, or fold, placing all cards in the discard pot and
losing any claim to the Pot in that round; of course, if the stake is
zero, all remaining players can stay in for free.

The second type is "raising the Dealer". When called upon by the Dealer,
each player may choose to make an extra bet against the Dealer, according
to cards that are known to that player. If the player chooses to raise,
the chosen number of coins or tokens are placed on the player's cards and
the amount is named. Finally, when all the players who have not yet folded
have done this, the Dealer must place an amount equal to the total value
of raises into the Pot - and all the individual raises then go into the
Pot as well - or lose the Dealership: often this means that the Dealer
must fold.

Each round begins in the same way as for the non-gambling game, except
that now, before the first deal takes place, every player places a
previously agreed amount, the Stake, into the Pot as the ante. Then after
every player has discarded and received replacements, the first round of
betting takes place.

The Dealer selects a stake, as described above, and then, from the Elder
to the Younger, asks each player first to match that stake and then to
raise it; if the Dealer cannot match the total value of the raises, then
the Dealer folds. This matching and raising occurs twice. The Dealer then
selects a stake for the third time and again asks each player, in order,
to match it; this time, however, the players are not asked to raise.

The second set of five cards for each remaining player is then dealt as
follows: as before, the Dealer receives five cards face down, but now each
player has the option of buying from one to all of the five cards face
down, at the price of an amount equal to the Stake per card, instead of
receiving them all face up. Cards may be bought one at a time, if desired,
and once the player has finished buying cards, the Dealer deals the
remainder from the five to that player face up on the table in front of
the player. As each player receives the full complement of ten cards, an
extra bet may be made, in the same manner as raising the Dealer, and then,
once every remaining player has ten cards, the Dealer must consider all
the extra bets.

If the Dealer matches the total extra bets made, the game continues with
the second round of betting described below; however, if the Dealer does
not wish to match the extra bets, then the Dealership changes *without*
the Dealer folding - this is the only time when this can take place. The
Dealer gives the Dealership to the Elder who, to become the new Dealer,
must match the total extra bets, the Elder's own extra bet going into the
Pot if the Dealership is accepted; of course, if the Elder does not
accept, the Dealership is passed left again until one of the other players
accepts it, or until it has gone full circle with no-one wanting it - in
that case, everyone folds, the Pot becomes the ante for the next round,
the old Dealer remains as Dealer, and the next round starts afresh.

Once the extra bets have been matched, be it by the original Dealer, the
Elder or one of the other players, the second round of betting takes
place. This consists of two stages of matching and raising as in the first
round of betting, but now not followed by a third stage of matching only.

Finally, Showdown takes place, exactly as in the non-gambling game, but
now, of course, the winner claims the contents of the Pot as the prize for
winning.

In the event that the Dealer folds, the Dealership is auctioned as
follows: from the Elder to the Younger, the players who are still in are
asked by the old Dealer if they wish to be the new Dealer - if the player
wishes to be the new Dealer, that player must advance an amount equal to
the Stake. If another player, when asked, also wishes to be Dealer, then
that player must match the existing bid and advance another amount equal
to the Stake. This process continues around and around the table, with
each prospective Dealer making sure that the most recent player's bid is
at least an amount equal to the Stake higher that the last bid, until all
the players except for one have declined to advance any more, having
placed their own total bid in the Pot as they declined, and the single
player left becomes the new Dealer, placing the winning bid in the pot. If
nobody wishes to be the new Dealer, all the players fold, the Pot becomes
the ante for the next round, the old Dealer stays as Dealer and another
round beings anew.

v The Modifiers:

The modifiers have usually been created for one of two reasons, either to
make the game a little more interesting and a little more uncertain, or to
decrease the chances of winning with a specific hand. It is not necessary
to use any of them, apart from numbers zero, which gives the game its
name, and one, which makes many-card onions and then Onions more probable,
and in a game, say, between four hardened professionals, even the Null
Eights Rules would probably not be used. The employment of the modifiers,
therefore, is left to the discretion of the players, but some
possibilities for using the modifiers beyond number zero are as follows:

          just modifer #1;
          modifiers numbers 1 to 3;
          bring in the modifiers as the game progresses, one in every or
		every other round;
          let the Dealer, for each round, declare which modifiers are in
		force in that round;
          play all the modifiers from the beginning.

A number of the modifiers use specific cards to represent mythological and
not-so mythological Discworld characters, and, if two decks of cards with
the same suits are used, confusion may arise as to which of the two, say,
queen of spades is to represent the Lady. A solution, if not particularly
satisfactory, to this is to mark one of the two cards with a symbol, in
this case, for example, the letter L, on the face side so that the marked
card becomes the relevant one for the modifier and the other becomes an
ordinary card.

The modifiers are all, some to a greater extent than others, based on
Discworld life, mythology and beliefs and have been assumed to have
evolved, with the game, over many centuries; none of the modifiers are
arbitrary in their action or purpose, but a detailed knowledge of the
Discworld is not necessary to use them. Finally, the ordering of the
modifiers in the list below is, apart from the Crippling Rules in position
zero, largely accidental and is not a guide to their usefulness or
effectiveness.

Modifier #0: Crippling Rules.
      i. A nine-card running flush may be used to cripple a Great Onion
and win the game.
      ii. A ten-card running flush outcripples a nine-card running flush
in crippling a Great Onion and may also cripple a Lesser Onion.
[Once a Great Onion or Lesser Onion have been crippled, the usual process
of Showdown stops, and the player with the crippling hand wins
immediately.]

Modifier #1: Null Eights Rules.
      i. During a round in which eights are not wild (see ii), an eight
may be used as if it had value zero in order to trump up an onion. In the
event of a tie between two onions with equal numbers of cards, the onion
with the fewer null eights wins.
      ii. In the round following a round in which a null eight has been
played, eights are wild, acting as any regular card. The wild Royal, three
wild eights, may then be played. In the next round, eights return to their
original role.
[To "trump up an onion" means to make a four-card onion into a five-card
onion by the addition of one null eight, or to make a three-card onion
into a seven-card onion with four. Note, again, that there are no onions
beyond seven-card and that wild eights cannot be used as either null
eights or as any of the special cards giving rise to later modifiers.]

Modifier #2: Wild Crippling Rule.
      In a round in which eights are wild, to successfully cripple the
relevant Onion, the running flush must have at most the same number of
wild cards as the Onion being crippled.

Modifier #3: Octavo Rule.
      When eights are wild, the card group consisting of eight eights can
be considered as a Lesser Onion, but beats other Lesser Onions and may not
be crippled like a Lesser Onion of any other composition, but may be
crippled like a Great Onion.

Modifier #4: The Lady's Rules.
      i. If eights are not wild, the queen of spades may be declared,
before or during Showdown, and replaced by the player's choice of one of
the next two cards from the deck, the chosen card taking up the place of
the queen; the other card goes to the discard pot. This move may not be
rescinded.
      ii. When eights are wild, the queen of spades devalues one ace, for
every other player, that would otherwise be played as having value eleven,
to value one only. This does not affect any aces in a Great Onion, but may
affect cards, in any grouping, which, by being wild or by other means,
would otherwise be played with value eleven.
[To "declare" means to put the card on the table face up and point it out
to the other players; here, of course, the queen may no longer be used in
forming card groupings since a replacement card has been received, but
should be left near the player on the table rather than in the discard
pot.]

Modifier #5: Fate's Rules.
      i. If the queen of spades has been declared and replaced, the king
of cups may also be declared and replaced in a like manner, in the process
making all aces held by the player who used the queen of spades have value
zero.
      ii. If eights are wild, the king of cups may be declared so that
eights immediately cease to be wild; a different player who has the queen
of spades, whether visible, played or not, may then make his own eights
wild again. The king of cups may not be revoked once declared, and a
single player may not use the king of cups and then the queen of spades in
this way.
["Zeroed" cards are of no use in the game, and cannot be used like null
eights to trump up an onion.]

Modifier #6: Great A'Tuin's Rule.
      Declaring the queen of coins allows the player to reduce the value
of one of the player's cards by eight points and to increase the value of
a different card by eight points. The two affected cards must still have
value between one and eleven inclusive.
[A two that is shifted up to value ten may be considered a picture card, a
three shifted up to eleven as an ace of value eleven.]

Modifier #7: The Elephants' Rule.
      Any four cards, each being either a nine or a ten, or an eight when
eights are wild, that are declared with the queen of coins in one player's
hand, allow that player to shift as many points as are needed to to
generate a Double Onion. This Double Onion may be beaten by any other
Double Onion. Any nines or tens in the player's hand that are not involved
in the shift may be considered as ones, not aces, and twos respectively.
[Since the five cards involved here have only been declared, and not
exchanged as well, they are, of course, still playable as cards in groups.
Remember that a ten may not take the role of a picture card in an Onion -
a shifted nine, eight etc. is needed. With two nines, two tens and the
queen of coins, a possible shift is: add one each to the nines and tens -
hence the Double Onion - and take four from the queen of coins to be a
six.]

Modifier #8: The Sender of Eight's Rules.
      i. When eights are not wild, a visible jack of diamonds makes any
aces belonging to a player who uses any eights become zeroed (see #5i).
      ii. When eights are wild, a visible jack of diamonds zeroes all aces
and disallows eights from taking on value one or eleven.

Modifier #9: Death's Rules.
      i. When eights are not wild, a visible king of swords makes one
picture card in every player's hand that has two or more picture cards
have no part in forming a Double Onion.
      ii. When eights are wild, a visible king of swords makes one picture
card in every player's hand that has two or more picture cards have no
part in forming either a Double Onion or a Triple Onion.
[The "killed" picture card can still take part in groups other than the
specified Onions.]

Modifier #10: The Archchancellor's Rules.
      i. Any player who plays the jack of staves may not also play an
eight as having value eight.
      ii. If the jack of staves is declared at any time during the game,
the king of swords must also be declared if held by another player; if the
king of swords is declared, then all the other players must also declare
one previously undisclosed card each. If the king of swords is not held by
another player, the the jack of staves becomes wild for the rest of the
round.

Modifier #11: The Fool's Rule.
        If, at any time before Showdown, the jack of clubs is declared,
then, for the rest of the round, bagels change places with Onions in the
order of winning card groupings. 
[That is: the two-card onion and the single bagel change places; the
Double, Triple and Lesser Onions are exchanged with the double, triple and
lesser bagels respectively; the great bagel becomes only beaten by, but
may also be crippled like, the Great Onion which remains at the top of the
list. This makes bagels worth something, other than a tie-breaker. The
jack of clubs, of course, can still take part in bagels, and any other
card grouping.]

vi Final Points:

Cripple Mr Onion was first mentioned in "Wyrd Sisters" and has, since
then, been seen in a number of places; the most notable of these, to date,
is the section in "Witches Abroad" on the riverboat, and it is from this
section that the game has been reconstructed. Loosely speaking, it is a
cross between pontoon (or blackjack) and poker, played with a deck of
cards having eight suits, although, as is to be expected, the nature of
the Discworld has given Cripple Mr Onion features found in no other game. 

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Andrew C. Millard
Physics Department,
Princeton University.

e-mail: millard@pupgg.princeton.edu