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FINESSE

John Henry Smith

: 'E SCHOOL93940

United StatesNaval Postgraduate School

THESIS

FINESSE

by

John Henry Smith

June 1970

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Finesse

by

John Henry SmithLieutenant Colonel, United States Marine Corps

B.S., United States Naval Academy, 1953

Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN COMPUTER SCIENCE

from the

NAVAL POSTGRADUATE SCHOOLJune 1970

ISTGRADUATE SCHOOL\ CALIF. 93940

ABSTRACT

Finesse is a program written to investigate the role of a general-

ization scheme in computer learning. The finessing play in the game

of bridge is developed as an example in which the computer starts with

a few basic bridge rules and improves its play through self-analysis

of successive plays of the same hands. After deciding that an optimum

play has been found for a particular hand, Finesse makes the generaliza

tion that all hands with approximately the same distribution should be

played in the same way.

TABLE OF CONTENTS

I. INTRODUCTION 5

II. BACKGROUND 7

III. RATIONALE --- 9

IV. PROGRAM EXAMPLES 13

V. MEMORY STRUCTURE 17

VI. PROGRAM DESCRIPTION 22

VII. CONCLUSIONS 29

APPENDIX A 31

COMPUTER PROGRAM 36

LIST OF REFERENCES 65

INITIAL DISTRIBUTION LIST 66

FORM DD 1473 --- 67

u

I. INTRODUCTION

This paper describes an interactive bridge -playing program,

Finesse, designed to solve finessing problems in no-trump hands.

The program is written is PL/1 in two versions, one for batch proces-

sing, the other to be played on-line. The object of the thesis is to

investigate computer learning using Finesse as the vehicle. This was

done by writing a program which produces its own set of finessing

rules; rules which continue to build and improve as the program plays

more and more hands. As new and different card combinations are

encountered, the program amends the rules stored in memory either

by adding to the knowledge contained, or when that knowledge proves

faulty, deleting from memory those rules which no longer apply.

Finesse was designed with the idea that it should play in as human-

istic a way as possible. A beginner in any game starts by learning a

few basic rules, then builds on these as his degree of expertise increases.

New rules are generally learned as new situations are encountered.

This is the approach taken in Finesse . A few simple rules were built

into the program so that Finesse would have a basis for making an

initial play for any given hand. These rules were designed to insure

that players follow suit whenever possible and that certain rules of dis-

tribution are followed in the initial play of a hand. For instance, if

declarer's hands contain eleven or more cards of the same suit, there

would be little requirement to finesse for the King. Another example

of this is the popular "eight ever, nine never" rule by which beginners

learn to finesse for a missing Queen if they hold eight or less cards,

but to play for the Queen to fall if nine cards are held. Such heuristics

are refined and amended as the analysis of play directs.

Before any programming could be done, certain basic decisions had

to be made concerning the scope of the thesis and the direction that its

development would follow. It quickly became obvious that time would

not permit the writing of a program to play all aspects of the game and,

more important, that such a program would not be required to study

the stated problem of computer learning. For the finessing problem,

the playing of one suit with the intent of winning the greatest number of

tricks has enough of the same strategic and tactical problems found in

playing the entire hand, that it is a worthy vehicle for the purpose of

this thesis. In short, finessing can be considered bridge in miniature.

Certain restrictions were placed on the type of hands to be played

in Finesse , thus reducing programming problems without detracting

from the thesis objective. For example, with the use of no-trump hands

only, the problem of counting and keeping track of trump cards was

eliminated. Also, certain information that would normally be available

and useful, such as the bidding sequence, is unknown in Finesse . Omit-

ting this type of information provides a more generalized line of play

than might otherwise be found.

II. BACKGROUND

Several authors have published papers on bridge programs, some

of which consider the play of all aspects of the game. Until 1969, how-

ever, no reference could be found to show that any real efforts had been

made toward generalizing on the results of completed plays and estab-

lishing a line of play for similar hands that follow.

The earliest three papers on bridge-playing programs were pub-

lished in 1962. Two of these were the result of individual thesis work

at Massachusetts Institute of Technology, by E. R. Berlekamp and

Gay Carley (Refs. 1 and 2). The third, by Thomas A. Throop (Ref. 3),

is a short description of a program to conduct bidding for one round.

The programs written by Berlekamp and Carley were more ambitious

and deserve a closer look.

Carley's thesis describes a full-length bridge program written in

assembly language for the IBM 7090 computer. The program bids,

decides upon a strategy for the hand, and plays a fair game of bridge,

largely through programmed heruistics. The program is flexible in

the sense that it contains a number of subroutines which could be easily

changed by the author. But these changes were not controlled by the

program as the result of any self-analysis of previous plays, and this

should be the object of a generalization process.

In the case of Berlekamp's paper, a generalization process is in-

cluded. Here the author has constructed a program to solve the specific

bridge problem of finding the winning play in seven no-trump hands in

double-dummy bridge. The final solution for a particular hand was

reached by first playing it in accordance with a set of heuristics built

into the program. Then the same hand was re-examined with a different

defensive play. If the original line of play was again successful, a new

defensive strategy would be tried until either all strategies had been

played, or a particular defense proved better than the previous plays.

If this latter event occurred, a new offensive play would be tried and

the play and test procedure would be repeated. In this manner, the play

of a particular hand would improve until the optimum play had been found.

Thus, this program generalizes only on the line of play to be followed

with one specific hand when all tricks must be taken.

Riley and Throop (Ref. 4) presented their paper in 1969. It describes

what appears to be the first bridge program to attack the problem of

generalization, including generalizing in finessing. Riley and Throop's

approach to the finessing problem was to handle it through pattern analysis,

with each finessing hand falling into one of eight patterns. This method

differs from the method used in Finesse , which makes generalizations

according to previous plays and stores them in decision trees. New and

better plays are found, primarily through a trial and error process,

much as they were in Berlekamp's program. The inferences drawn and

rules developed are not made for one specific hand, but for any hand in

which certain key cards are missing.

III. RATIONALE

In Finesse , the declarer's hands (North/South) are played by the

computer, while a human opponent plays the East/West cards. The

program learns to play the cards in much the same manner as a human

player does. It starts with the knowledge that there are certain basic

rules which must be followed:

1. All players must follow suit whenever possible.

2. If a player cannot follow suit, a card in another suit, preferably

a loser, must be played.

3. When specific numbers and denominations of cards are held by

the declarer and his partner, they should be played in a prearranged

manner to win the most tricks. For example, if nine or more cards

are held by declarer and the Queen is the only missing honor, the prob-

ability of it falling if the Ace and King are played out is greater than 50%.

This play would be dictated if no further information were known con-

cerning the opponents' distribution. With fewer than nine cards, the

probability of the drop falls below the 50% level and a finessing play is

required. Similar rules require Finesse to play for the drop of the King

when more than ten cards are held and for the drop of either the Jack

or Ten when more than six cards are held.

4. No suit with fewer than seven cards in declarer's hands has

been considered as a finessing suit in this program. This is not because

such finesses cannot be made, but because suits in which declarer has

fewer cards than his opponents are not normally identified as advantageous

for early development in the play of a No-Trump hand. These suits are

usually held in reserve for transportation purposes, stoppers in short

suits, and for sure tricks when needed either to make the contract or

avert a serious loss.

5. For a similar reason, no suit distributions with more than two

missing honors have been considered. Had such consideration been

given, a small extension of the program would have been required to

determine the initial strategy for playing such suits, but the actual play

of the hand would be similar.

6. If the suit to be played falls into the category of a finessing suit,

then the missing honor(s) is singled out and designated as the card(s) to

be located. The idea of identifying the cards declarer is missing, rather

than those he has, was decided upon to cut down on the number of possible

card holdings which could arise.

If a suit is identified as one to be played for a finesse, the next lower

card to the missing honor, or a card of equivalent value, is selected as

the finessing card and the initial finesse is made. The program will

determine whether North or South must be the leader in order to finesse

properly and will use transportation cards to position itself in the right

hand if necessary. If the finesse fails and the missing honor takes the

trick, Finesse will assume that there are no more key cards left in the

suit to be concerned with. When the declarer has the lead again, the pro-

gram will play out all remaining cards, anticipating the capture of all

10

unplayed tricks.

If the finesse is successful and the missing card does not appear,

Finesse will assume that it has located the missing honor. It proceeds

to make as many finessing plays as are required and/or possible through

the opponent holding the missing card. When this card appears, Finesse

will infer that all remaining cards should be played out. If at any point

in this play an opponent wins a trick, the declarer's strategy does not

change. Upon regaining the lead, he continues to draw the remaining

cards.

As each trick is played, a tally is kept of the number of tricks won

by declarer, and the identity of all winning opponent cards is stored in

memory. When all cards in the suit have been played, an analysis is

made of the number of tricks won by declarer as opposed to the maxi-

mum number he could have won. If, for example, declarer's cards

were split 4-3, he could have won at most four tricks. If he were also

missing the Ace, he could have won only three. In this case, if he

actually won three, Finesse infers that the hand was played correctly

and the play terminates, indicating that the optimum play had occurred.

If this cannot be determined, then the suit must be played again, using

a different strategy, and the results of the two plays will be compared.

The strategy to be followed in the second play is determined by

the highest ranking card that won a trick for the opponents. This be-

comes the new card for which the program finesses. After it appears,

the finesse is made for the original missing honor. The remaining

11

cards are then drawn as before, the tricks are tallied, and another

comparison is made. If fewer tricks were made on the second play, the

play is discarded and the original play is assumed to be the best. Other-

wise, the new play is stored and will be used again the next time that

combination of missing cards is encountered. This process of searching

for a better play can be continued until the play analysis shows that

there are no more alternatives, or that the last play is inferior to its

predecessor. In this way the "optimum" play is left in memory until

the same situation is encountered again and a better play developed.

12

IV. PROGRAM EXAMPLES

To see how Finesse works, let us study the plays of two different

hands. The first has a suit distribution as shown below:

North

K J 5 2

West East

10 8 4 3 Q 7

South

A 9 6

Finesse first analyzes the hand and determines if at least seven

cards are held in the North/South hands. If so, it looks for the highest

ranking missing honor. In this hand the Queen is recognized as this key

missing card. Since the declarer only holds seven cards, a finesse is

required. North, having been predetermined to be the leader, leads

the Jack to finesse for the Queen. East, as played by the human player,

covers an honor with an honor. South rises with his Ace to take the

trick and West plays low. The program decides that North/South is

the winner and signals that they have one trick. Since the trick was

taken by South, the lead shifts to that hand.

Since the key card has been played, Finesse plays the remaining

cards in descending order. The six is led by South to North's King,

with West playing low and East giving up the seven. North then leads

13

his low card, the two, back to the nine, the highest card left in declarer's

hand. When East shows out, West wins the last two tricks with the ten

and eight. The values of these two cards are stored, as is declarer's

final trick count of two.

Finesse then determines that the ten was the highest ranking of the

opponents' cards to take a trick and designates the ten and the Queen

as key cards. The hand is played again with the finesse for the lower

of these two key cards, the ten, being tried first. Once again North is

the initial leader. This time North leads his two. When East plays low,

North attempts a finesse with the nine. When West's ten wins again, it

is stored in memory and the play continues.

Since the ten has been played, the Queen again becomes the critical

card and the Jack is led. At this stage the play follows the original

hand with the Queen falling to South' s Ace and West playing low. The

remaining cards are played out with South leading the six to the King,

West playing the four, and East showing out. Again, declarer wins only

two tricks as West's eight takes the last trick. Analysis of the hand

shows no reduction in thv number of tricks won over the previous play.

Finesse , applying an heuristic, assumes that the second play, attempting

a deeper finesse, is a superior play to the first.

The evaluation after this second play shows that the eight is the new

key card and adds it to memory. With North leading again, his two is

covered by the seven and South' s nine loses to the ten. Then the five

is led and South's Ace takes East's Queen with West playing low.

14

South' s last card, the six, is then led and West plays the four which is

taken by the Jack as East shows out. North's last card, the King, is

then led and West's eight falls to it, winning three tricks for declarer.

Analysis of the play shows that one more trick was taken. Since no

new key cards were discovered, Finesse infers that the optimum play

has been found. The analysis is concluded, all key cards are left in

the decision tree, and play terminates.

In a second example, the suit distribution is as shown:

North

10 8 3

West East

J 9 5 K 7 4

South

A Q 6 2

With North in the lead, the initial play of the suit is as follows:

Play #1: King recognized to be missing.

Leader Lead Opponent 1 Leader's Partner Opponent 2 Trick Count

North 3 4 Q 5 1

North* 10 K A 9 1

South 2 J 8 7

South 6 out out out 1

3

*Lead changed hands through transportation cards to take advantage of

the successful finesse.

15

Play #2: King, Jack recognized to be key cards .

Leader Lead Opponent 1 Leader's Partner Opponent 2 Trick Count

North 10 K A 5 1

North-- 8 4 2 9

North 3 7 Q J 1

South 6 out out out 1

3

**Lead changed hands to take the only finesse left.

Play #3: King, Jack, 9 recognized to be key cards.

North 8 4 2 9

North 10 K A 5 1

South Q J 3 7 1

South 6 out out out 1

3

Three tricks were made in each play. After the final play, when no

new key cards were found, play of the hand terminated. The results of

the third attempt were stored as the program inferred that the deepest

finesse is the best play.

16

V. MEMORY STRUCTURE

Finesse uses tree structures for storage of key cards and their

associated finessing cards. Three different types of cells are used,

and examples of each are shown in Figures 1 and 2.

The MCARDTREE cell is used only as a header cell for each decision

tree. Each of these, along with its associated FPLAY cell, is initialized

in the early stages of the program. The header cell contains the value

of the highest missing honor in declarer's hands while the FPLAY cell

holds the value of the finessing card to be used. The other fields of the

header are pointers. M6 connects the header cell to its FPLAY cell

and M1-M4 are initialized as null pointers. As the trees grow, these

latter four pointers are used to connect the header cell to its descendents.

The cells to be joined are those declared as N3 cells having a field

holding the value of a key card and three pointer fields.

Four separate decision trees are used in Finesse ; one for each of

the top four honors. No Ten Tree is used, for unless the opponents'

distribution is highly unusual (either 5-1 or 6-0), the ten will fall to

successive plays of the other honors. If the unusual distribution should

occur, Finesse will recognize it and play the hand accordingly without

further recourse to a decision tree.

Since the header cell holds the value of the highest ranking honor

missing from declarer's hands, any cards subsequently added to the tree

must have a lower rank. The decision as to which pointer should be

17

CDK\ MCARDTREE CELLGDI \ (HEADER)

CD'

FPLAY CELL

M6KllNU

Ml M2 M3 M4

QUEEN EM

FIGURE 1

HEADER CELL

CD3-

FPLAY CELL

CD

FIGURE 2

18

used to join these two cells together is made by comparing the value of

the two cards concerned. If the card to be added is an honor and has a

value of one greater than that of the card in the header cell, pointer Ml

is used to connect the cells. If two greater, M2 is used, and so forth.

If the card is not an honor, it is automatically pointed to by Ml. Clearly

then, only the Ace Tree will use all four pointers.

Like the header cell, each N3 cell has an FPLAY cell associated

with it and containing the value of the card to be used in finessing.

Pointer PL connects these cells. The other two pointer fields of this

cell are BP and M7. BP is a back pointer used in moving up the tree

when changes in tree position are made, while M7 points to the next

lower N3 cell in the tree. The final pointer to be mentioned, the EM

field of the FPLAY cell, is also a back pointer connecting the previous

FPLAY cell in the tree. To better understand the tree construction, let

us follow through with the addition of one level to the header cell, using

one of the hands played earlier as an example.

North

10 8 3

West East

J 9 5 K 7 4

South

A Q 6 2

Pointer CD was set to the header cell originally and CDl was then

set equal to it. A new N3 cell is allocated and a determination is made

as to which of the M1-M4 pointers should be used. In this instance, with

19

the King in the header cell and the Jack the next key card missing,

pointer M2 is chosen and set to the N3 cell (Figure 2). Level one

pointers are set as shown and CD is moved to the N3 cell. BP is set

to point the way back up the tree and a new FPLAY cell is allocated.

All level two pointers are set, with M7 having a null value, and the

construction is complete.

Subsequent levels are added in a similar manner with the setting

of the M7 pointer to the new N3 cell rather than one of the M1-M4

pointers. CD continues to be used as the first pointer to be moved as

each new cell is allocated and the other moving pointers follow it.

Pointers CDl and CD3 remain at the header cell level.

A level of cells may be moved easily up or down the tree by recon-

necting the appropriate M7, BP and EM pointers, and rearranging the

movable pointers so that CD, CD2, CD4 and CD5 always point to the

lowest and next to lowest level cells. Figure 3 shows the decision tree

after the final play has been completed.

20

CDKCD1\

CD3>

/ M6QUEEN EMKING

Ml M2 M3 M4

\5 /

• CD4Y

/JACK PL

10EM

i

BP M7Jf

CE>2 /\ CJ>\

9

IDL

8EM

BP M7

FIGURE 3

21

VI. PROGRAM DESCRIPTION

Finesse begins each new play of a suit by determining whether

initialization of the decision trees is necessary. If initialization is re-

quired, the header cells and their associated FPLAY cells are construc-

ted. Otherwise, this part of the program is bypassed so that the hands

to be played may be read in. Figure 4, a Macro Flow Chart, shows

how the play of a hand flows through the program.

Each player's cards are represented in an array consisting of

thirteen bits, with a one indicating the presence of a card in the hand.

The cards are represented in inverse order, with the Ace occupying the

first array position, the King the second, and the two the thirteenth.

Thus the highest ranking cards have the lowest array numbers. This

simplifies the many searches required to locate the high cards of arrays

HAND1 and HAND2. For input/output purposes, however, the card

values are inverted and represented more normally with the Ace having

a value of 14, King 13, Queen 12, Jack 11 and ten through two the values

of 10-2.

All four hands of the suit to be played are read into the program.

Either North (NH) or South (SH) is declared to be the initial leader

(LEADER) in ( e play. The array HAND1 is set equal to the leader's

hand, HAND2 equal to his partner's, and OHANDl and OHAND2 set equal

to the correct East/West hands. These arrays are then used as the

playing hands and the North, South, East and West arrays are stored,

22

YES

FINISH3

NO

NO

YES

Initialize

trees

FINESSE

~t~

YES

NO

PLAY

Add key-

card to

. tree

e

FIGURE 4

23

to be used only to recreate these playing hands when required. The

number of cards held by declarer is determined and the number of mis-

sing honors is counted. A determination is made as to whether a finesse

is required or the cards should be played consecutively. This decision

is made on the basis of what honor is missing, how many cards in the

suit are held by declarer, and the probability of a finesse being the play

most likely to capture the missing card. Here, heuristics such as the

"eight ever, nine never" rule, come into play in directing the play of the

cards to one of two major sections of the program, Procedures PLAY

or FINESSE.

The procedure PLAY is designed to play the cards, starting with

the highest ranking card in declarer's hands, without regard to any

missing key cards. PLAY is called whenever the initial program

analysis determines that the probability of the key cards falling to this

sort of strategy exceeds the probability of falling to a finesse. It is also

called from Procedure FINESSE whenever all key cards have been played

by the opposition.

PLAY accomplishes its mission by continually searching the de-

clarer's hands to locate the highest ranking card in the suit, or an

equivalent card (the Queen is equal to the Ace if the Ace, King, Queen

are held by partners). The correct lead is made by determining whether

the high card, or its equivalent, can be led directly, and which hand

declarer wishes to be in upon completion of the play.

The strategy decided upon will play the cards in a manner requiring

the fewest transportation plays per suit. For example, Finesse determines

24

which hand has the most cards and, whenever possible, that hand is given

the lead before his partner becomes void in the suit.

When all cards have been played from the North/South hands, the

program calls BETPLAY to analyze the completed play of the suit.

Before looking at this portion of the program, a thorough study should

be made of the Procedure FINESSE which is the heart of the finessing

play. Upon entering FINESSE, the program determines the highest

ranking honor missing from the declarer's hands and goes to the ap-

propriate decision tree to find the correct card to play.

The first time a finessing hand is played, the tree will be only one

level deep and will contain just the header cell and its associated FPLAY

cell containing the value of the card to be played. In this case the tree

traversal is limited to going to the FPLAY cell to find the finessing

card. The card is then located in the North/South hands. Should it be

missing, an adjustment is made in the designation of the card to be

played so that the next lower ranking card held by declarer becomes the

new finessing card. Both of the declarer hands are inspected for dis-

tribution of cards to be used in finessing and a decision is made as to

how the finesse should be attempted. For example, if the King is mis-

sing and the other honors are distributed as shown in either of the hands

below, the finesse can be made in only one way, although the exact play

of the cards \ ill be different.

North Leader NA

NA 10

S

Q J 10

S

Q J

25

In either case, the finesse must be made through the Ace as it is recog-

nized as the only card of a higher rank than the King, and transportation

cards must be used to get to the South hand for finessing purposes.

Then, assuming that the Queen is successfully finessed, the program

infers that the King is located in West's hand and that it must use trans-

portation cards to return to the South hand. Successive finesses will be

attempted until the missing honor appears, declarer runs out of finessing

cards, or loses his transportation capability.

It should be noted here that the assumption has been made that

sufficient transportation cards will be available to allow the play of a

suit to proceed as envisioned by Finesse . The routine TRANSPO is

called whenever such transportation is required. It changes the lead

from one hand to another and prints out the statement "Lead Changes

Hands".

Whenever the missing honor appears, and when there is only one

level to the decision tree, the program infers that there are no more

key cards to worry about and goes to the PLAY block for completion of

the suit play. If the tree level is greater than one, however, there is

more than one missing card to be finessed, and control reverts to the

beginning of FINESSE for another iteration.

As each complete play of four cards is made, a count is made of

the key cards played by the opponents. When this count equals the num-

ber of key cards to be found, all required finesses have been taken. The

routine PLAY is entered and, if there are any cards left, they are played

26

as required by that section of the program. When all declarer's cards

have been played, Procedure BETPLAY, the initial part of the analysis

of the hand, is called.

BETPLAY determines the maximum number of tricks that might be

taken by declarer by counting the cards in each declarer hand and

assuming that the maximum tricks possible equals the number of cards

in the longer hand. If that number of tricks wa.s actually made, BETPLAY

will infer that the optimum play has been made, make a statement to

that effect and terminate the play of that hand. If a lesser number of

tricks was taken and it appears as if a better play might have been

made, the analysis of the play continues. Simple rules are applied to

determine whether it is possible to take more tricks than were made in

the previous play. For example, if North has four cards and South

three, then four tricks are the most that can be won. If the Ace is

missing, or if the King is not held by declarer and is not fines sable be-

cause it sits behind the Ace, then only three tricks can be made. If

the previous play took those three tricks, the inference will be drawn

that the best possible play has been made, and the play of the hand will

terminate. Otherwise, the routine BPLAY will be called. This is the

portion of the program in which decision trees are built and manipulated.

BPLAY immediately checks the value of all opponents' cards, with

the exception of the Ace, that won tricks. The value of the highest rank-

ing card in this category is then checked to see if it has already been

used as a key card. If so, the next such card in the array is located and

checked until a new key card is discovered. When the new key card is

27

found, the next lower ranking card is assigned as its finessing card

and a new level added to the tree.

As each new key card is identified and added to the tree, Procedure

CHUP is used to compare its value with the value of the card immediately

above it. If the last card added is found to be of a higher rank than its

predecessor, the tree positions of the two cards are interchanged, and

this procedure is repeated until all cards occupy their proper place in

the tree, with the higher ranking cards at the top.

If no new key cards are found, the program infers that there are no

other important cards to finesse and that the optimum play has been

made. The message "All Key Cards Have Been Tested" is printed out

and the program looks for another hand to play.

The play and replay of a suit may also terminate when the newest

play proves to be bad. Finesse determines this by comparing the number

of tricks won with the number taken by the previous play. If the last

play takes the same number, or more tricks than the preceding play,

the program assumes the method of play to be good and leaves the infor-

mation stored in the tree. If fewer tricks are taken, the line of play is

considered bad and that play is removed from the decision tree. The

last play remaining in the tree is considered the optimum play.

28

VII. CONCLUSIONS

The program Finesse does learn. It develops a line of play by

successively finessing for newly discovered key cards, as long as each

new play does at least as well as the previous play. Then, when the

apparent best play is found, it is stored in a decision tree in memory

for future use. The next time the same situation is presented for a

solution, the hand is played in the same way. In a subsequent play of

what appears to be an identical hand, the opponents' card distribution

may cause the pre-planned play to take fewer tricks than anticipated.

If so, Finesse will erase the previous play and try to find a better one.

Thus Finesse is learning to finesse in much the same way that a human

player would. It starts by learning a few basic bridge rules and adds

to these through experience.

The rules developed could be improved upon by expanding Finesse

to include more information and give the declarer a better idea of what

adversities may face him. Information which might be provided includes

the bidding sequence and a listing of cards already played from other

suits (to show declarer something about the distribution of the entire

hand). With such information added, the probability of finding the op-

timum play in a specific situation would increase. But this increase in

information will require an equivalent increase in the size and complexity

of the decision trees. If they become too detailed, the plays will become

too specific, and the result may be specialization rather than generalization.

29

As it is, Finesse provides a good general method of play for any suit of

seven cards or more. For example, any hand with the King, Jack, 9

missing will be played in the same general way, rather than in the two

or three more specialized ways it might have been played if additional

information were known. Special rules for each specific situation

should not have to be developed. However, some additional information,

particularly in the area of knowledge of the bid, would be helpful in

determining which opponent to finesse through. Such an improvement

should help significantly to close the gap between what Finesse does now

and what it would have to do as a part of a complete bridge playing program.

By storing in the decision trees only information concerning the

missing key cards, rather than those held by the declarer, the size of

the decision trees was reduced, saving storage requirements and data

manipulation time. This principle of working with the complement of

required information may prove a valuable technique which can be used

in other programming problems.

30

APPENDIX A

This section provides a chronological listing of major Begin Blocks

and Procedures found in Finesse with a brief description of their purposes

and means of accomplishment.

PSTART; This block is the entry point to Finesse. After each complete

play of a suit, control of the program returns to PSTART for a deter-

mination of whether another hand will be played or the program will

terminate. Subsequent action is decided by the setting of variable

QUEST to a value of zero, one or two.

READIN : The purpose of this block is to provide an entry point to all

program input.

LOWCARD1, LOWCARD2 : These two routines find the lowest ranking

cards in HAND1 and HAND2 respectively by searching the HANDl and

HAND2 arrays backwards for the first bit equal to 1. Upon termination,

they return the values of variables LCARDl and LCARD2 to the calling

section of the program.

CHHAND : This is the routine called to change the lead from one de-

clarer hand to the other when the trick has been won by a card from

HAND2, When this happens, HANDl and HAND2 exchange card values

as do OHAND1 and OHAND2 and the lead then changes to the hand now

called HANDl.

TWIN : Twin is designed to count the number of tricks won by the

declarer hands. The variable TRICKCT returns the new trick count

31

value. If the trick has been won by either the East or West hand,

TWIN calls Procedure OWIN.

OWIN: OWIN identifies and stores key cards in the array OHCARD.

If East's nine wins a trick, for example, the bit OHCARD (6), the array

position for the nine card, is set to one. OWIN then returns control to

TWIN.

FOLCH: Folch is a routine called whenever the FOLLOW card is to

be played. It checks the present value of FOLLOW and, by looking at

the card that has been played from hand OHANDl, determines whether

a change must be made in the FOLLOW value.

The play of the FOLLOW card has been pre-programmed for one of

these two standard plays:

1. If the LEAD card is other than the lowest card in the HANDl

hand, that is, it is either the highest card in the hand or a selected

finessing card, HAND2 is programmed to play its lowest card unless

the analysis by FOLCH dictates a different play. This will occur when

the OHANDl card is higher ranking than the card led. Then, if HAND2

can beat the opponents' play, FOLCH will change the FOLLOW value

to play the card from HAND2 immediately higher than that played by the

first opponent.

2. If LCARDl is to be led from HANDl, HAND2 is programmed to

play either its highest card or a designated finessing card. This will be

done unless FOLCH determines that OHANDl has played a card higher

in value than the programmed FOLLOW card. If so, a higher card will

32

be played if available. If such a card is not held, LCARD2 is played.

OPLAYl, OPLAY2: These two routines are called when the play of a

card is required by the East/West hands. OPLAYl tells opponent one to

input the value of a card from his hand, and OPLAY2 does the same for

OHAND2. The cards played are removed from the opponents' hands.

ONEHMISS: If only one honor is determined to be missing from the com-

bined declarer hands, this procedure applies a set of simple rules to

decide whether control should pass to the PLAY or to the FINESSE

sections of the program.

PLAY: That section of Finesse which plays the declarer's cards in

numerical order. It is called when there is no requirement to finesse

for key cards. A detailed description of this program block and its in-

ternal blocks and procedures has been included in the Program Description

section.

FINESSE : This is the section of the program which determines the

cards to be used for finessing purposes and how the finesses will be

made. A detailed description of FINESSE and its internal procedures

and blocks has been included in the Program Description section.

TRANS PO : This section of coding is called whenever the program de-

termines that the lead is located in the wrong hand and that a play using

transportation cards is required to get the lead in the correct hand.

TRANSPO does this through an artificial play of the cards designed to

require CHHAND to change the cards held by all four players. The state-

ment "LEAD CHANGES HANDS" is printed out.

33

BETPLAY : BETPLAY is a procedure designed to recreate the original

hands for all four players, to count the number of cards in each of de-

clarer's hands, and determine the maximum number of tricks which

might possibly be made. If required, it also directs control of the play

to MISS1 or MISS2.

MISSl, MISS2 : By checking the suit distribution against a few distribu-

tional rules, a quick determination may be made within these program

blocks concerning the maximum number of tricks that can be made.

See the Program Description for a more detailed account of these pro-

gram sections.

BPLAY: This procedure looks for new key cards by searching the array

OHCARD. If one is found, BPLAY adds it and its associated finessing

card to the decision tree and switches the program back to the FINESSE

procedure so that a new line of play may be tried. BPLAY also removes

plays from the decision trees when the analysis of a play shows that it

takes fewer tricks than its predecessor. See the Program Description

section for a more detailed discussion of BPLAY.

CHUP : CHUP is a procedure which is called after each new level has

been added to the decision tree. CHUP will rearrange the tree levels

if a lower level cell is found to contain a higher ranking card than its

immediate predecessor in the tree.

FINISH: FINISH is a begin block used as an exit from Finesse . When

there are no more hands to be played and the value of two has been en-

tered for the variable QUEST, program control passes to FINISH, the

34

message "Finish" is printed, and the program terminates.

LOPUT, FOPUT : These two procedures take the array values of the

LEAD and FOLLOW cards respectively and convert them to their actual

card values ranging from fourteen for the Ace to two for the two. The

conversion is made by searching the VTREE cells for the correct array

value, then substituting for it the value found in the associated DESIG

cell.

INI, IN2: These procedures are the opposite of LOPUT and FOPUT.

Their purpose is to take the OHl and OH2 input (the cards played by

opponents 1 and 2) and convert these card values to array numbers.

35

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64

LIST OF REFERENCES

L, Berlekamp, E. R. , "Program for Double-Dummy Bridge Problems-A New Strategy for Mechanical Game Playing", Journal of the

Association for Computing Machinery, v. 10, p. 357-364, July 1963.

Z, Carley, G. L. , A Program to Play Contract Bridge , M. S. Thesis,

Massachusetts Institute of Technology, June 1962.

3, Throop, T. A. , "The Univac Plays Bridge", COMPUTERS ANDAUTOMATION , v. XI, p. 3B-5B, March 1962.

4. Riley, W. , and Throop, T. A. , An Interactive Bridge Playing

Program , paper presented at National Gaming Council Symposium,1969.

65

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2

Cameron Station

Alexandria, Virginia 22314

2. Library, Code 0212 2

Naval Postgraduate SchoolMonterey, California 93940

3. LTJG Robert Bolles, USNR 1

Department of Mathematics (Code 53)

Naval Postgraduate SchoolMonterey, California 93940

4. LTCOL John H. Smith, USMC 1

8 Biddle LaneMonterey, California 93940

66

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA -R&D/Security clas silication of title, body of abstract and ind' xinfi annotation must be entered when the overall report is classified)

I ORIGINATING ACTIVITY ( Corpora te author)

Naval Postgraduate School

Monterey, California 93940

2«. REPORT SECURITY CLASSIFICATION

Unclassified26. GROUP

3 REPORT TITLE

Finesse

4. DESCRIPTIVE NOTES (Type of report and.inclusive dates)

Master's Thesis; June 19705. AUTHORISI (First name, middle initial, last name)

John Henry Smith

6. REPORT DATE

June 19708a. CONTRACT OR GRANT NO.

b. PROJEC T NO

la. TOTAL NO. OF PAGES

67

lb. NO. OF RE FS

49a. ORIGINATOR'S REPORT NUMBER(S)

9b. OTHER REPORT NO(S) (Any other numbers that may be assigned(his report)

10. DISTRIBUTION STATEMENTThis document has been approved for public release and

sale; its distribution is unlimited.

11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Naval Postgraduate School

Monterey, California 93940

13. ABSTR AC T

Finesse is a program written to investigate the role of a generalization

scheme in computer learning. The finessing play in the game of bridge is

developed as an example in which the computer starts with a few basic bridge

rules and improves its play through self-analysis of successive plays of the

same hands. After deciding that an optimum play has been found for a particular

hand, Finesse makes the generalization that all hands with approximately the

same distribution should be played in the same way.

DD .'i?..1473S/N 0101 -807-681 1

(PAGE 1)UNCLASSIFIED

67 Security ClassificationA-31406

UNCLASSIFIEDSecurity Classification

key wo RDS

inesse

)\rh

'

Annie- playing

ificial intelligence

D,T;..1473 <back,

I 0101-607-682) 68UNCLASSIFIEDSecurity Classification A-31 409

^>30CT73

l n21970

iir no

SmithFinesse.

2 NO 1

/ 7 2

^ OCT 732 10 2 921970

ThesisS594 Smithc.l Finesse.

3 2768 002 0094