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A suite of tools for generation and analysis of bridge deals

Project description


endplay is a Python library providing a variety of different tools for generating, analysing, solving and scoring bridge deals. It is a collection of different tools based on Bo Haglund's famous dds library, Hans van Staveren's dealer program and other personal projects which have been cobbled together into a compatible interface using a common type system based on the encodings defined in the dds library.

If you find this useful and would like to contribute, or found it totally buggy and broken and want to fix it, then I am very open to contributions.

Table of Contents

Building and installing

From PyPI

Binary Python wheels are built and distributed on PyPI for the following Python versions:

Architecture Windows Linux MacOS
x86 N/A N/A 3.7-3.11
x64 3.7-3.11 3.7-3.11 3.7-3.11

On these systems python3 -m pip install endplay will install these pre-built wheels, otherwise it will attempt to install from the source distribution which requires a C++ compiler on your system. Note that endplay requires Python 3.7+.

The version of the library available on PyPI may be older than the current status of the repo, this is to ensure stability of these builds. For access to the latest bug fixes and preview features, you can install directly from the GitHub repo with python3 -m pip install +git:

From source

endplay uses setuptools to manage its build and can be installed with pip.

# Clone repo and submodules
git clone --recursive
cd endplay
python3 -m pip install .

If you want to build the binary wheels for your system, you can use the build package. This will create an isolated environment when collecting packages so you do not need to perform this in a virtual environment.

# Only build is required to start the build, other packages
# are automatically fetched
python3 -m pip install build
python3 -m build # generates dist/endplay-<VERSIONSUFFIX>.whl

For development

If you are trying to develop for the library, then it is recommended to do all your testing in a virtual environment:

python3 -m pip install virtualenv
virtualenv venv
source venv/bin/activate # on windows, `cmd venv\scripts\activate`
python -m pip install . # installs into the created venv

You can then modify some files, and when you want to debug simply rerun python -m pip install . and the old build will be overwritten. This also has the advantage of being able to reuse the cache from the previous install (including the CMake cache) which speeds up build time.

If you are not planning on modifying the underlying C library, its packaging logic or the config file, then you can avoid having to reinstall each time by making an in-source build and symlinking this into your site packages. The simplest way to do this is to run the following from the root directory:

mkdir build && cd build
cmake -DCMAKE_INSTALL_PREFIX=../src ..
cmake --build . --target install
cd ../src
pwd > "$(python -m site --user-site)/endplay.pth"

The last command will work on POSIX systems, on Windows you can get the site packages directory by running python -m site --user-site and creating a file endplay.pth there with a single line containing the absolute path to <ENDPLAY_ROOT>/src.

The .gitignore is set up to ignore the files CMake installs so no extra care needs to be taken when staging and committing your changes to git.

Building the documentation

The documentation is semi-auto generated with sphinx. To build it, ensure that endplay is installed and then cd into the root directory and then run

cd docs
make html # or latex, or whatever output format you want

The documentation will be built in the build directory.

Running the test suite

The test suite is implemented with the unittest library and can be run from the root directory with

python3 -m pytest

Overview of submodules

endplay is divided into six main components, each of which can interoperate with each other:

  • endplay.types is the basis for the whole library, providing the classes which are used by all the other modules for encapsulating the key objects in bridge. The 'master' class is Deal, whose state consists of the four hands in the deal, the cards played to the current trick, a trump suit and the player to lead to the current trick. All the methods one would expect to be defined on this are provided - accessing the hands, playing/unplaying cards from the current trick, importing and exporting from PBN format etc. From this class there is a hierarchy of types Deal -> Hand -> SuitHolding -> Rank which allows introspection of the deal at any level wanted. Many other types, such as containers for holding results from double dummy analysis and storing contracts, are also provided here.

  • provides functions for generating bridge hands. The main function is generate_deals which can accept a list of constraints (either functions which accept a Deal object and return True/False, or strings written in dealer syntax) and generates a specified number of deals which satisfy the constraints. The dealer module can also be run as a main module with python3 -m (or simply endplay-dealer) which works very similarly to the Hans van Staveren dealer program, but with some different output options and extra functionality.

  • endplay.evaluate is the simplest component, consisting of a variety of functions which evaluate various properties of bridge hands, such as calculating high card points, shape, losers, controls and other algorithms for estimating the quality of a hand.

  • is a high-level wrapper around Bo Haglund's dds library which takes care of converting between the different types and encodings it uses internally and providing sensible defaults for things such as the number of threads it uses. A lower level wrapper endplay._dds, which is little more than the basic ctypes declarations, is also provided and is used internally by the dds functions when making library calls.

  • endplay.parsers provides tools for parsing common file types which are used as inputs and outputs for bridge software, this includes PBN and Dealer. These produce document tree representation of the input files and are used internally for many things, but can also be traversed manually to create programs which interact with other bridge software easily.

  • endplay.interact provides the CommandObject class which keeps an undo stack whenever its state is modified, making it easier to interact with the deal. The main purpose of the module is to provide a tool to create interactive deal programs, such as the main module (python3 -m endplay.interact or endplay-interact) which provides a a set of frontends analysing bridge deals.


Inspecting deals

The Deal object is the class which is most frequently used in endplay. A deal can be constructed most simply by specifying it as a PBN string:

>>> from endplay.types import Deal
>>> d = Deal("N:974.AJ3.63.AK963 K83.K9752.7.8752 AQJ5.T864.KJ94.4 T62.Q.AQT852.QJT")

The PBN string starts with a letter representing the first hand and a colon, and then each of the four hands separated by a space, where each hand consists of the cards in spades, hearts, diamonds and clubs respectively separated by a dot. The __str__ method of the deal returns the deal as a PBN string, but a pprint method is provided to view the deal as a hand diagram:

>>> print(d)
N:974.AJ3.63.AK963 K83.K9752.7.8752 AQJ5.T864.KJ94.4 T62.Q.AQT852.QJT
>>> d.pprint()
T62                         K83
Q                           K9752
AQT852                      7
QJT                         8752

The four hands can be viewed by using the north, east, south and west properties, by using the __getitem__ operator or by iterating over the deal to loop over all four hands:

>>> d.north
>>> from endplay.types import Player
>>> w = d[Player.west]
>>> w.pprint()
>>> for p, h in d:
...   print(h)

Note that iterating over the deal returns (Player, Hand) tuples. If your terminal doesn't handle the Unicode suit symbols, then you can tell endplay to use the letters SHDC instead:

>>> from endplay import config
>>> config.use_unicode = False
>>> w.pprint()
S T62
D AQT852

If there is a particular section of code which you would like to turn off unicode suit symbols for, for example if you are trying to export to export to a certain file format or would just like a particular piece of output to be formatted in plaintext, then you can use the suppress_unicode context manager:

>>> config.use_unicode = True
>>> from endplay.config import suppress_unicode
>>> print(Denom.spades.abbr)

>>> with suppress_unicode():
...   print(Denom.spades.abbr)
>>> print(Denom.spades.abbr)

The Hand object which is returned is bound to the data inside the deal, so any operations you perform on the hand will update the deal too; to get a copy of the hand which doesn't affect the deal object you should use the copy method. Deal also overloads the __setitem__ function and accepts a Hand object which is copied into the deal, or a PBN string which sets the cards in the hand to the specified cards:

>>> from endplay.types import Hand
>>> d = Deal()
>>> h = Hand("AQ..T964.QJ975")
>>> d.west = h
>>> d.west = "AQ..T964.QJ975" # equivalent

Modifying the contents of the hand can be done using the add, extend and remove methods. add and remove return True if the operation was successful: attempting to remove a card which isn't in a hand, or adding a card which is already there causes it to return False.

>>> h = Hand()
>>> h.add("SQ")
>>> print(h)
>>> h.extend(["SQ", "HA", "CT"])
>>> h.remove("D2")

extend returns the number of cards which were added to the hand. As well as specifying cards by strings, the Card class which stores a Rank and Denom object can also be used:

>>> from endplay.types import Card, Rank, Denom
>>> c = Card(suit=Denom.hearts, rank=Rank.R9)
>>> c in h # or "H9" in h
>>> len(h)
>>> print(", ".join(str(c) for c in h))
Q, A, T

Card objects are immutable, but should not be tested for equality using identity (i.e. use == not is). The individual suit holdings in the hand can be examined by using the spades, hearts, diamonds and clubs properties or using the __getitem__ operator. This returns a SuitHolding object which, like accessing hands of a deal, returns an object which is bound to the data in the hand. Many of the methods defined in Hand are also defined in SuitHolding, but use the Rank class instead of the Card class:

>>> s = h.spades
>>> s.add(Rank.R2)
>>> print(h)
>>> Rank.RQ in s
>>> for rank in s:
...   print(rank)

Holdings in a hand can be specified using the __setitem__ operator too:

>>> = "9752"

Moving back to the Deal object itself, as well as the four hands it also contains some other information such as the trump suit, player on lead and cards played to the current trick. Many functions in the endplay library will ignore these values, but the double dummy solving algorithms in particular may rely on these to provide accurate results. The trump suit and player on lead can be set by setting the trump and first properties respectively:

>>> d = Deal("65..2. .A.AK. .J.97. 8..83.")
>>> d.trump = Denom.hearts
>>> d.first = Player.south # not so fun, must concede all tricks to E
>>> d.first = Player.north # helicopter coup successful

Tricks can be played by using the play method, and picked up using the unplay method. By default, endplay attempts to take the card to be played from the hand who is currently on lead and will raise an error if they do not hold it.

>>>"S6") # north tries a coup-en-passant
>>> d.pprint()
8                 ^6       ---
---                         A
83                          AK
---                         ---
>>> d.unplay() # East picks back up the DA
>>>"HA") # try ruffing instead...
>>> d.pprint()
---                         ---
---                         ---
83                          AK
---                         ---
>>> d.first
<Player.east: 1>

Notice how after the final card to the trick is played, the trick is cleared and d.first is assigned the winner of the trick. By passing fromHand=False to play, you can cause a card to be added to the current trick without attempting to remove it from anybody's hand:

>>>"HA") # can't play the HA again
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "endplay\types\", line 124, in play
    raise RuntimeError("Trying to play card not in hand")
RuntimeError: Trying to play card not in hand
>>>"HA", fromHand=False) # let's hope N isn't paying too much attention

Similarly, unplay can be passed toHand=False to not move the picked-up card back into somebody's hand. The contents of the current trick can be examined by looking at the curtrick property which returns a list of cards played to the current trick, however this is a read-only object and attempting to modify it will not alter the Deal object.

Enumerated types

endplay exposes five enumerated types: Denom, Penalty, Player, Rank and Vul. These all have a fairly consistent interface to make handling them as convenient as possible:

  • They have a static find method which allows them to be constructed from a string, e.g. Denom.find("hearts"), Penalty.find("x") or Vul.find("ew"). There are often multiple ways of expressing these objects as strings (suit-symbols vs letters, luv vs none for vulnerability etc.) and the find method does its best to convert whatever string you give it into a value. This raises a ValueError if the conversion fails
  • As well as the name property inherited from Enum which returns a lowercase string, they also have an abbr property which return a one or two character abbreviation for the object. This is used by e.g. the Card class to construct a string representation of the card (the __str__ method consists of the single line return f"{self.suit.abbr}{self.rank.abbr}")

All enumerations can have their members iterated over using e.g. for x in Player , however many also provide functions which allow iterating over the elements in a different order or over a subset of the elements (e.g. Denom.suits(), Denom.bidorder()). A few other unique methods for the enumerated types include

  • Denom.is_major()/Denom.is_minor()/Denom.is_suit()
  • Player.lho/Player.partner/Player.rho. Rotating a player n positions left or right can be done with and Player.prev(n)
  • Vul.from_board(n) for determining vulnerability from board number.
  • Rank has a sister-class AlternateRank which is used internally by some double dummy routines, but should not be used outside of this context.

A full list of the methods can be found in the API reference of the documentation.

The interact module

One of my main motivations for building up this library is that sometimes I just want a quick way to see how a hand would play in a particular contract, or step through a deal card by card checking to see if a particular play would work. Using an interactive Python environment this is relatively easy, but in the end I developed a separate module called interact which implements a variety of frontends for interacting with deals. they can be run by executing python3 -m endplay.interact, and a specific frontend can be selected by using the -x FRONTEND flag:

  • -x cmd The default frontend, a simple REPL inside your terminal
  • -x curses A curses frontend which runs inside the terminal
  • -x html An HTML frontend which opens inside your web browser, with the python program acting as a local server.

Both the cmd and curses frontends require you to enter shell-like commands such as shuffle, deal 'PBNSTRING' or play SA. You can type help to get a list of all available commands, or help CMDNAME to get a specific help message about a command. The html interface allows you to click on cards and buttons to interact with it, which under the hood it turns into these commands which it sends back to the server.

The interactive interface keeps account of all the actions which have taken place, allowing you to type commands such as undo and redo to go back and forth through the state (or rewind and fastforward to go to either end of the history).

Generating hands

The can be used to generate deals satisfying some constraints. The most basic usage is as follows:

>>> from import generate_deal
>>> generate_deal()
Deal('N:Q6.A872.KT3.J974 KT7.53.A42.AKQ85 AJ9853.KQ.J87.63 42.JT964.Q965.T2')

Constraints can be provided as functions which take a Deal object and return True or False based on some condition. The functions provided in the endplay.evaluate module are useful for specifying these. In the following example, we generate a list of 10 deals where north might open 2NT:

>>> from endplay.evaluate import hcp, is_balanced
>>> def north_2nt(deal):
...   return 20 <= hcp(deal.north) <= 22 and is_balanced(deal.north)
>>> d = generate_deal(north_2nt)
>>> d.pprint()
AK                          J7652
862                         T9
K75                         JT3
A8754                       962

Instead of defining the named function north_2nt, we can of course also just provide an anonymous lambda to do the same thing. generate_deal can be passed an arbitrary number of constraints which must all be satisfied, so the above is equivalent to:

>>> d = generate_deal(lambda deal: 20 <= hcp(deal.north) <= 22, lambda deal: is_balanced(deal.north))

Internally, generate_deal generates random deals and checks whether they satisfy the constraints until it finds one which does which it then returns. If many conditions are specified, or you wish to generate freak deals, then the number of deals which need to be generated might be very large. generate_deal will throw an exception if it generates enough deals that it doesn't think it will find a matching deal (defaulting to 1,000,000). This can be altered by providing the max_attempts parameter; if it is set to -1 then it will never throw this exception.

generate_deal also accepts string constraints which contain expressions using the dealer syntax which it will parse and evaluate on the deal, making the above condition for a north 2NT opening equivalent to the following:

>>> d = generate_deal("hcp(north) >= 20 && hcp(north) <= 22 && shape(north, any 4333 + any 4432 + any 5332)")

This is ok for experimenting, but there is a large overhead involved with parsing and evaluating the string as this is currently all implemented in non-optimised Python, so if you are looking to do stats over many thousands of hands it is recommended to create a function instead.

If you need to generate more than one deal then the generator function generate_deals is supplied. It accepts the exact same parameters as generate_deal with an extra produce parameter which defaults to 40. The deals are yielded, so if you want to collect them into a list then this must be done manually with list(generate_deals()) , however iterating over the lists as they are generated can be done with the natural for deal in generate_deals(): construct.

The main module

The dealer module can also be run as a program by executing python3 -m Without any arguments this will generate and print 40 random deals. The main usage of this script is to emulate the behaviour of the dealer program and so if it is passed a dealer script file then it will interpret and execute it, although the format of the output will not correspond 1:1 with original program. Dealer scripts allow simple as well as more advanced functions to be performed. A simple example of a dealer script is the following stayman.dl which produces hands where west opens a strong notrump and east has a Stayman hand and prints the two hands, which is useful for practicing partnership bidding.

produce 2 // Number of hands we want to output
west1n =
	hcp(west) >= 15 &&
	hcp(west) <= 17 &&
	shape(west, any 4333 + any 4432 + any 5332)
eastStayman =
	hcp(east) >= 10 &&
	(hearts(east) == 4 || spades(east) == 4) &&
	hearts(east) < 5 && spades(east) < 5
condition west1n && eastStayman
action printew

Running python3 -m -s 510 stayman.dl outputs (with some whitespace trimmed)

AQ5                         KT76
Q54                         AKT8
AQ62                        JT
Q97                         T65

AJ                          96
J43                         AQ72
AJT7                        Q65
AT97                        K843

The -s parameter specifies a seed for the random number generator allowing reproducible results. Another use for the dealer module is to gather statistics about different hand types. The following script named oops_2nt.dl generates hands where north opens 2NT and finds south without any honours, and calculates the average number of tricks north can make double dummy playing the contract:

produce 30 // producing more will make the statistics more accurate
north2n =
    hcp(north) >= 20 &&
    hcp(north) <= 22 &&
    shape(north, any 4333 + any 4432 + any 5332)
disappointingSouth = hcp(south) == 0
condition north2n && disappointingSouth
action average tricks(north, notrumps)

Running this on my machine takes a few minutes, even with only 30 hands, as the hand type is quite rare. In order to get some progress updates you can pass the -m flag which will display a progress bar as the hands are generated. To speed up generation of these sorts of hands, one of the swapping options can be passed which perform rotations on each shuffle: -2 swaps the EW hands, and -3 produces all permutations of the east, south and west hands; by default the -0 switch (no swapping) is used. As the shuffle is a relatively expensive operation this can improve performance, however it is not fully compatible with predealt hands. A (not particularly scientific) comparison of the three swapping algorithms is outlined here using the stayman.dl file using the seed -s 1234 and the number of hands to produce increased to 1000:

Swapping method Flag stayman.dl runtime Predeal compatibility
No swapping -0 53s N✅ E✅ S✅ W✅
2-way swapping (E, W) -2 46s (~13% faster) N✅ E❌ S✅ W❌
3-way swapping (E, S, W) -3 33s (~38% faster) N✅ E❌ S❌ W❌

Of course, had we set up stayman.dl to produce bidding patterns for north and south, 2-way swapping would be significantly worse as swapping the east west hands does not change the value of the predicate.

Evaluating hands

When constructing constraints for use with the generate_deal/generate_deals functions, or performing statistics over deals, various metrics for evaluating the quality of various aspects of a hand are useful. endplay comes with a variety of functions for evaluating hands in the endplay.evaluate submodule. A full list of the functions contained in this submodule can be found in the API documentation; the list here is merely representative of the sorts of things which can be done.

Assigning point values to hands

By far the most well known and widely applied metric for calculating the quality of a hand is the traditional 'high card points' scale where we assign points to each of the face cards: 4 for an ace, 3 for a king, 2 for a queen and 1 for a jack. The hcp function can be used to evaluate a hand or suit holding using this metric:

>>> from endplay.types import Hand
>>> from endplay.evaluate import hcp
>>> hand = Hand("AQ963.J64.852.K2")
>>> hcp(hand)
>>> hcp(hand.hearts)

Although the 4321 metric is the most widely applied, it is sometimes preferable to use a different scale. One such scale is the Bergen scale which assigns 4.5/3/1.5/0.75/0.25 to the top 5 cards. This scale is built into endplay as bergen_hcp_scale and the hcp can be told to use it by passing it as the second parameter:

>>> from endplay.evaluate import bergen_hcp_scale
>>> hcp(hand, bergen_hcp_scale)

If you want to use your own custom scale, then you can pass a list of numbers containing the point values of the cards in the order A, K, Q, J, ..., 3, 2. If the list has less than 13 values, then it is assumed to be continued with zeroes:

>>> custom_hcp_scale = [6,4,2,1] # A=6, K=4, Q=2, J=1, all other cards worth no points
>>> hcp(hand, custom_hcp_scale)

Another quality of the hand which is often described in terms of points is the distribution. A common system is to assign 3 points for a void, 2 points for a singleton and a single point for a doubleton. This is the standard behaviour of the dist_points function:

>>> from endplay.evaluate import dist_points
>>> hand2 = Hand("AK.JT98765..Q963")
>>> dist_points(hand2)
>>> dist_points(

As with the high card points scale, there are many different ways of counting points and so the dist_points function accepts a scale parameter which defines the counting method. endplay comes with five different scales built into the evalute module:

  • shortage_nofit_dist_scale: The standard 3/2/1 scale
  • shortage_fit_dist_scale: A 5/3/1 scale, often applied to a hand once a trump fit has been found
  • length_dist_scale: Assigns a point for every extra card in a suit longer than 4, e.g. a five card suit is worth 1 point and a seven card suit is worth 3.
  • mixed_nofit_dist_scale: A combination of shortage_nofit_dist_scale and length_dist_scale
  • mixed_fit_dist_scale: A combination of shortage_fit_dist_scale and length_dist_scale

Custom scales can be passed as lists where the nth element (zero-indexed) is the number of points awarded to a suit of length n, and as with the hcp function the list is assumed to be padded with zeroes if later elements are omitted. As an example, the following scale just counts the number of tripletons in a hand:

>>> tripletons = [0, 0, 0, 1]
>>> dist_points(hand, tripletons)
>>> dist_points(hand2, tripletons)

If a trump suit is found, then it usually the case that shortage points are not included in the calculation of distribution points. To account for this, dist_points also takes an exclude parameter with a list of suits to exclude from the calculation. Note that this is ignored if the object is a SuitHolding instead of a Hand:

>>> dist_points(hand2, exclude=[Denom.spades])
>>> dist_points(, exclude=[])

High card points and distribution points are often combined into a scale known as 'total points'. In its most basic form, this is simply the sum of the two metrics:

>>> from endplay.evaluate import total_points
>>> total_points(hand2) # = hcp(hand2) + dist_points(hand2) = 10 + 4

An optional trump parameter can be provided with a suit which is added to the exclude list of dist_points:

>>> total_points(hand2, trump=Denom.spades)

Unprotected honours, i.e. honours which will drop if the opponents play higher honours from the top, are often discounted from the total points calculation. This can be enabled by setting the protect_honours flag:

>>> total_points(hand) # 10 HCP and 1 doubleton
>>> total_points(hand, protect_honours=True) #Jxx drops and the point is removed

A more advanced method of calculating the overall strength of a hand is the Kaplan Four Cs method which is implemented in the cccc algorithm:

>>> from endplay.evaluate import cccc
>>> cccc(hand)
>>> cccc(hand2)

Evaluating shape

The shape of a hand can be evaluated using the shape and exact_shape functions; the former returns the shape ordered from longest to shortest whilst the latter always returns the shape in the order spades, hearts, diamonds and clubs:

>>> from endplay.types import Hand
>>> from endplay.evaluate import shape, exact_shape
>>> h = Hand("AK92.A3.Q9.AK762")
>>> shape(h)
[5, 4, 2, 2]
>>> exact_shape(h)
[4, 2, 2, 5]

Various predicate functions are provided to query more generally the 'class' of the hand shape:

>>> from endplay.evaluate import is_balanced, is_semibalanced, is_single_suited, is_two_suited
>>> is_balanced(h) # 4333, 4432 or 5332
>>> is_semibalanced(h) # balanced or 5422
>>> is_single_suited(h) # 6 or more cards in one suit
>>> is_two_suited(h) # 10 cards in two suits

There are more variants on these and optional parameters to fine tune their definitions, which can be found in the API documentation.

Double dummy analysis

A particularly important feature of endplay is the ability to call routines from the C++ dds library. The library is built and distributed with endplay so it is not necessary to have a copy of the library built on your machine.

The double-dummy solving algorithms are split across four components:

  • contains algorithms for analysing play sequences, calculating the maximum number of tricks which can be made after each card is played
  • has the functions for calculating double-dummy tables, showing the maximum number of tricks that each player could make in each contract
  • provides par contract calculation algorithms
  • provides functions for calculating the maximum number of tricks each card in a player's hand can make

NB: out of laziness, I will often refer to 'maximum number of tricks' instead of 'double-dummy maximum number of tricks', i.e. the number of tricks that can be made assuming everybody at the table has perfect knowledge of where all the cards are and makes optimal plays at each opportunity.

Most algorithms come in two variants, one which calculates a result for a single deal and a second which accepts multiple deals. The multiple deal variant is trivial to use if you understand how the single-deal versions work, so will not be covered here, but if you need to do calculations for multiple deals it is always better to use versions as they use multithreading and can reuse internal data structures.


The analyse module consists of two pairs of functions: analyse_play/analyse_all_plays and analyse_start/analyse_all_starts.

The analysis functions are useful when you have the play history of a deal and want to see how optimal each card played was. Take the following four card ending:

>>> from endplay.types import Deal, Player
>>> d = Deal("AJ.6.A. KQ..K8. 4.A.Q4. 7..T.Q5", first=Player.south)
>>> d.pprint()
7                           KQ
---                         ---
T                           K8
Q5                          ---

The optimal play here is of course to unblock the ace of diamonds and then return to hand with a heart which squeezes east; the play history for this would be something like (depending on which losing option east goes for):

>>> from import analyse_play
>>> history = [
...    "D4", "DT", "DA", "D8",
...    "H6", "DK", "HA", "S7",
...    "DQ", "C5", "SJ", "SQ",
...    "S4", "CQ", "SA", "SK"]

As everyone has played optimally (not that EW get much of a chance to make a mistake) running analyse_play will show that at each point in the play history EW can make no tricks:

>>> h_analysis = analyse_play(d, history)
>>> print(", ".join(str(n) for n in h_analysis))
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Despite being on the surface being nothing more than a computationally expensive way of printing a load of zeroes, it is worth noting two interesting things here:

  1. The number of tricks is displayed from the perspective of the player to the right of player on lead. This is because it attempts to show declarers trick count, and in a full deal the declarer is to the right of the person on lead. In this case, as we have a four card ending with declarer on lead we can pass declarer_is_first=True to perform the swap and print 4, 4, 4, ...
  2. There are 16 cards in the play history, but only 13 cards in the output. Two things are going on here: a) the number of tricks before any card is played is appended to the front and b) as the last four cards are all forced and no-one can alter the outcome of the contract at this stage these are not calculated by the algorithm. Therefore the number of cards returned in this instance is 16 (cards in play history) + 1 (starting tricks) - 4 (remove final trick) = 13.

We all know that partner will never find this line though, so lets see what the function does when we play bridge ping-pong:

>>> history2 = [
...    "HA", "C5", "H6", "SK",
...    "S4",  "S7", "SJ", "SQ"]
>>> h2_analysis = analyse_play(d, history2, declarer_is_first=True)
>>> print(", ".join(str(n) for n in h2_analysis))
4, 3, 3, 3, 4, 4, 4, 3, 3

We could find all the suboptimal plays by checking whether the number of tricks goes up or down after each card is played:

>>> from itertools import pairwise # Python 3.10 upwards only
>>> for card, tricks in zip(history2, pairwise(h2_analysis)):
...     if tricks[0] != tricks[1]:
...         print(Card(card))

Cashing the ace at the start breaks up the squeeze, but when east incorrectly tosses a spade playing to the ace will drop the queen, however this leads to south finessing into east's now stiff queen.

Because the analyse_play function calculates the maximum tricks before any card is played, calling it with an empty play history is actually one of the most efficient ways of calculating the double dummy result of a deal. This is all analyse_start is - a wrapper for analyse_play with an empty play history.

DD Tables

The ddtable module consists of two functions, calc_dd_table and its multiple-deal variant calc_all_tables. The slight naming inconsistency is in order to keep the naming convention consistent with the original DDS library.

This is one of the simplest and most powerful functions in the dds module. Let's cast our minds back to 1975 with this famous deal and remember just how thin the 7♣ contract really is:

>>> from endplay.types import Deal, Player, Denom
>>> from import calc_dd_table
>>> d = Deal("QJ8.AJ965.K82.AQ 43.QT87.QT64.754 AKT9..A97.J98632 7652.K432.J53.KT")
>>> table = calc_dd_table(d)
>>> table.pprint()
  N 13 10  9 13 13
  S 13 10  9 13 13
  E  0  2  4  0  0
  W  0  2  4  0  0

Individual results are accessible through the overloaded __getitem__ operator:

>>> assert(table[Denom.clubs, Player.south] == 13) # Filthy, but the assert passes

If, like me, you can never remember whether the table is indexed by strain or seat first, then luckily the operator is agnostic to which order you pass them:

>>> assert(table[Player.south, Denom.clubs] == 13)

The multiple-deal variant calc_all_tables accepts an extra argument not available to calc_dd_table with a list of strains to be excluded from the calculation, if e.g. you want to calculate how a series of deals would play in notrumps and don't want to waste time calculating the table for the other strains. In this case, the results for all other strains will be set to 0. The exclude parameter can be any iterable, so [Denom.notrumps, Denom.hearts]would produce results for clubs, diamonds and spades, or in the example below we use Denom.suits() as a shorthand for excluding all the suits:

>>> from import calc_all_tables
>>> table, *_ = calc_all_tables([d], exclude=Denom.suits())
>>> table.pprint()
  N  0  0  0  0 13
  S  0  0  0  0 13
  E  0  0  0  0  0
  W  0  0  0  0  0

(NB: If you don't understand how table, *_ = works then don't worry, it is just a quick way to store the first element of the returned list into table and the other elements, in this case an empty list as we only requested one table, into the variable _ which we will throw away.)

Par contract calculation and scoring contracts

The module contains only one function, par, which calculates the optimum contract on a deal, i.e. the lowest contract over which the opponents cannot bid any making contract and which sacrificing is too expensive. The par contracts are always returned as a list, as there are often multiple contracts which score the same (commonly the same contract played by either partner). As well as the deal (or double dummy table, as this is the only relevant information about the deal required) there are two more pieces of information which come into play:

  1. The vulnerability, as this affects the score
  2. The dealer, as there are occasions where i.e. both sides can make 1NT, and so the par contract depends on who gets to bid it first

Here are some examples of how the par function can be used:

>>> from endplay.types import Deal, Vul, Player
>>> from import par
>>> d = Deal("N:AKQJ8..AT8632.43 T742.Q9543.J.QT8 63.AJT8.97.J7652 95.K762.KQ54.AK9")
>>> for contract in par(d, Vul.none, Player.north):
...     print(contract)
>>> for contract in par(d, Vul.ew, Player.north):
...     print(contract)

Notice that when EW become vulnerable, the level of the par contracts goes down as their possible sacrifice in hearts becomes too expensive. Note that if you have previously calculated the double dummy table for a board, then it is much more efficient to pass this instead of the Deal object:

>>> from import calc_dd_table
>>> table = calc_dd_table(d)
>>> par(table, Vul.ew, Player.north) # saves `par` having to recalculate the DD table

The score associated with the par contracts is a property of the list-type object which holds the list of contracts, as it is of course constant across all the contracts. In the following high-stakes deal, NS can sacrifice in seven clubs over EW's heart slam:

>>> d = Deal("N:J976..762.KQJ982 K5.JT9843.AK93.A AT42.765.J84.T54 Q83.AKQ2.QT5.763")
>>> parlist = par(d, Vul.ew, Player.north)
>>> parlist.score

The Contract class also has a score method which calculates the score of a contract based on a given vulnerability:

>>> for contract in parlist:
...     print(contract.score(Vul.ew))

You can calculate the score of an arbitrary contract by constructing a Contract object and scoring it:

>>> from endplay.types import Contract
>>> c = Contract("4HNx=") # construct from a string
>>> c.score(Vul.none)
>>> from endplay import Denom, Penalty
>>> c = Contract( # construct from values
... level = 4,
... denom = Denom.hearts,
... declarer = Player.north,
... penalty = Penalty.doubled,
... result = 0 # number of over/undertricks
>>> c.score(Vul.ns)
>>> c.result = -5
>>> c.score(Vul.ns)

Bids and auctions: an aside

While on the topic of contracts, it is worth mentioning the Bid class which represents a call in an auction. Bid objects are very weird, as they fulfill a double purpose of being able to represent penalty actions, i.e. "Pass", "Double" and "Redoule", as well as contract actions which name a strain and a level. These are represented by the PenaltyBid and ContractBid classes respectively, which derive from Bid but define different member variables - PenaltyBid.penalty vs ContractBid.denom and ContractBid.level. You can construct these directly using their __init__ functions:

from endplay.types import PenaltyBid, ContractBid, Penalty, Denom
>>> oneclub = ContractBid(1, Denom.clubs)
>>> double = PenaltyBid(Penalty.double)

or by using the Bid constructor to supply the name of the bid as a string:

>>> twohearts = Bid("2H")
>>> double = Bid("double") # Bid("x") also works

Notice however that the type you get is actually always one of PenaltyBid or ContractBid - the Bid constructor will always automatically downcast the class instance to the appropriate type:

>>> type(twohearts)
<class ''>
>>> type(pass_)
<class ''>

All bid class constructors also accept optional boolean alertable and string announcement parameters, of which none, either or both can be defined to allow for the case where e.g. the point range of a notrump bid is announced but not alertable:

>>> unusual2nt = Bid("2H", announcement="Weak")
>>> forcing_pass = Bid("Pass", alertable=True, announcement="Forcing for one round")

The alertable and announcement attributes can be assigned and altered after construction of the Bid object, but the other properties are immutable.

An auction is simply a list of bid objects:

>>> auction = [
...   oneclub,     forcing_pass, two_hearts, double,
...   Bid("Pass"), Bid("Pass"),  Bid("pass") ]

To calculate a contract from a given auction, you can use the Contract.from_auction method and provide the name of the first player to bid:

>>> from endplay.types import Player, Contract
>>> Contract.from_auction(auction, Player.west)

Any iterable of Bid objects satisfying the Reversible interface can be passed as an auction.

Solving for a player's hand

The final module,, provides the solve_board/solve_all_boards function pair which returns the number of tricks each card in a player's hand can yield. Let's go back to a nice four card ending:

>>> d = Deal("Q2..6.A 5.632.. A..A.Q8 K4...K9", first=Player.south)
>>> d.pprint()
K4                          5
---                         632
---                         ---
K9                          ---

Can you work out how to pull off this squeeze? We can see what the optimal play is using solve_board:

>>> from endplay import solve_board
>>> for card, tricks in solve_board(d):
...     print(card, tricks)
A 4
A 3
8 3
Q 3

We can then see west's options after south plays the ♦A by playing this to the trick:

>>> d.pprint()
K4                          5
---                         632
---                         ---
K9                vA       ---
>>> for card, tricks in solve_board(d):
...     print(card, tricks)
4 0
9 0
K 0
K 0

Oops, out of luck! Notice how as opposed to the analyse family of functions, solve_board always returns the number of tricks the person playing the card can make.

Parsing to and from bridge file formats (PBN, LIN, JSON)

While not the primary aim of the library, endplay does support experimental parsing and writing of PBN and LIN file formats. These interfaces are in the endplay.parsers submodule, and aim to provide an interface consistent with that of the standard library parsing libraries. Each of the parsing packages endplay.parsers.pbn, endplay.parsers.lin and endplay.parsers.json provide four functions:

  • load: Parse a file object into a list of Board objects
  • loads: Parse a string into a list of Board objects
  • dump: Write a list of Board objects to a file object
  • dumps Write a list of Board objects to a string

Internally, each module provides *Encoder and *Decoder classes which do the heavy lifting. These can be used directly, but their interface may be unstable so cannot be recommended.

The libraries store file information in lists of endplay.types.Board objects, which wrap a Deal as well as other information which is usually provided by these file formats. The full list of defined members can be found in the API reference as this is one of the bulkiest classes in endplay, in order to deal with the wealth of information that these file formats can store. We will present here a lighter introduction to the class by reading a PBN file and examining the result. We being by opening the sample PBN file in the examples directory and putting the first board into the variable boardA:

>>> import endplay.parsers.pbn as pbn
>>> with open("examples/pbn_files/sample.pbn") as f:
...   boards = pbn.load(f)
>>> boardA = boards[0]

From here we can explore a lot of the basic information about the deal using the tools which we have already learned:

  • The deal
KJ85                        76432
AQT853                      4
9                           KQ
K4                          QJT72
  • The auction
>>> from import pprint_auction
>>> pprint_auction(,, include_announcements=True)
N    E    S    W
P    P    1   P
1NT  2*  3   4
5   P    P    5*
X    P    P    P

2*: Spades & minor
  • The play history
>>> from import analyse_play
>>> analyse_play(, boards[0].play)
<SolvedPlay object; data=(8, 9, 9, 9, 9, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8)>
  • Meta-information about the board. As this can store just about anything you might want it can get a bit messy, so although I have tried to keep it as basic as possible don't worry if the code samples below go in one ear and out the other
dict_keys(['Event', 'Site', 'Date', 'West', 'North', 'East', 'South', 'Dealer', 'Scoring', 'Score', 'Table', 'HomeTeam', 'VisitTeam', 'ScoreIMP', 'DoubleDummyTricks', 'OptimumResultTable', 'OptimumScore', 'Competition'])
>>> # Dot access is case-insensitive
>>>["Site"] # Subscript access is case-sensitive

PBN tags ending in Table (but not equal to Table - that key is for the table number the board was played at) are tabular data, and entries in the dictionary which end in Table are treated differently; instead of having string values they are dictionaries with keys for the column headings and the rows:

>>> from pprint import pprint
>>> pprint(
{'headers': ['Declarer',
             {'alignment': 'R',
              'minwidth': '2',
              'name': 'Denomination',
              'ordering': None},
             {'alignment': 'R',
              'minwidth': '2',
              'name': 'Result',
              'ordering': None}],
 'rows': [['N', 'NT', '7'],
          ['N', 'S', '4'],
          ['N', 'H', '6'],
          ['N', 'D', '11'],
          ['N', 'C', '5'],
          ['W', 'NT', '5'],
          ['W', 'S', '8'],
          ['W', 'H', '6'],
          ['W', 'D', '2'],
          ['W', 'C', '7']]}

The headers key is a list of the column names; they can either be strings or dictionaries specifying how the columns should be displayed (see the API reference for more information). The rows key is a 2D list representing the rows of the table.

In sample.pbn, the second board contains some fields with value "#" indicating that they should be copied over from the previous board, these are automatically resolved:

>>> boardB = boards[1]
>>> assert ==

On the second board, the hand was passed out. The Board object is populated with an empty play history and a Contract object representing the pass:

>>> boardB.contract

Using the endplay.parsers.lin module, we can export these boards to LIN in order to use them on BBO:

>>> import endplay.parsers.lin as lin
>>> l = lin.dumps(boards)
>>> print(l)
pn|JOHN SMITH,ARTHUR SOMEBODY,JORDAN PRESENTLY,EDWARD PEABODY|st||md|3S9TAH2D234JC3689A,S23467H4DQKC27TJQ,SQH679JKD5678TAC5,|rh||ah|Board 17|sv|o|mb|p|mb|p|mb|1H|mb|p|mb|1N|mb|2H|an| Spades & minor|mb|3D|mb|4S|mb|5D|mb|p|mb|p|mb|5S|an| !S|mb|d|mb|p|mb|p|mb|p|pg||pc|H2|pc|H4|pc|HK|pc|HA|pg||pc|D9|pc|D2|pc|DQ|pc|DA|pg||pc|C5|pc|C4|pc|CA|pc|C2|pg||pc|C9|pc|C7|pc|SQ|pc|CK|pg||pc|H6|pc|H8|pc|S9|pc|CT|pg||pc|C8|pc|CJ|pc|D5|pc|H3|pg||pc|S2|pc|D6|pc|SK|pc|SA|pg||pc|ST|pc|S3|pc|D7|pc|SJ|pg||mc|8|
pn|LOUISE FORWEES,JEAN JEANY,MARTINE ESPEREDO,BRENDA CALLOUGHWAY|st||md|1S29JAH478D6TJC3QA,S3467H3TQD23C69JK,S8TKH69AD59AC2457,|rh||ah|Board 11|sv|o|mb|p|mb|p|mb|p|mb|p|pg||

Suit symbols are automatically escaped using the !S, !H etc... names used by BBO. Of course, far less information is stored in a LIN file than a PBN file and so many of the fields in the info dictionary of the Board are lost during the conversion. We can of course also load a LIN file and dump it into a PBN file, any keys which the PBN file expects which aren't provided by the LIN file can either be specified by appending to the dictionary, or else they will be given the default value of ? as specified by the PBN standard.

Finally, for compatibility with projects which make use of other langauges or which need an easily parsable serialisation format, the endplay.parsers.json module provides the ability to parse to and from a JSON format defined by this schema. Note that this is not an officially recognised schema but has been developed for the specific purpose of providing a JSON format which translates naturally to PBN and, in particular, the data types which endplay uses.

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