Games in RLCard

Blackjack

Blackjack is a globally popular banking game known as Twenty-One. The objective is to beat the dealer by reaching a higher score than the dealer without exceeding 21. In the toolkit, we implement a simple version of Blackjack. In each round, the player only has two options: “hit” which will take a card, and ‘stand’ which end the turn. The player will “bust” if his hands exceed 21 points. After the player completes his hands (chooses “stand” and has not busted), the dealer then reals his hidden card and “hit” until obtaining at least 17 points.

State Representation of Blackjack

In this toy environment, we encode the state as an array [player_score, dealer_score] where player_score is the score currently obtained by the player, and the dealer_score is derived from the card that faces up from the dealer.

Action Encoding of Blackjack

There are two actions in the simple Blackjack. They are encoded as follows:

Action ID

Action

0

hit

1

stand

Payoff of Blackjack

The player may receive a reward -1 (lose), 0 (tie), or 1 (win) in the end of the game.

Leduc Hold’em

Leduc Hold’em is a smaller version of Limit Texas Hold’em (first introduced in Bayes’ Bluff: Opponent Modeling in Poker). The deck consists only two pairs of King, Queen and Jack, six cards in total. Each game is fixed with two players, two rounds, two-bet maximum and raise amounts of 2 and 4 in the first and second round. In the first round, each player puts 1 unit in the pot and is dealt one card, then starts betting. In the second round, one public card is revealed first, then the players bet again. Finally, the player whose hand has the same rank as the public card is the winner. If neither, then the one with higher rank wins. Other rules such as ‘fold’ can refer to Limit Texas hold’em.

State Representation of Leduc Hold’em

The state is encoded as a vector of length 36. The first 3 elements correspond to hand card. The next 3 elements correspond to public card. The last 30 elements correspond the chips of the current player and the opponent (the chips could be in range 0~14) The correspondence between the index and the card is as below.

Index

Meaning

0~2

J ~ K in hand

3~5

J ~ K as public card

6~20

0 ~ 14 chips for the current player

21~35

0 ~ 14 chips for the opponent

Action Encoding of Leduc Hold’em

The action encoding is the same as Limit Hold’em game.

Payoff of Leduc Hold’em

The payoff is calculated similarly with Limit Hold’em game.

Limit Texas Hold’em

Texas Hold’em is a popular betting game. Each player is dealt two face-down cards, called hole cards. Then 5 community cards are dealt in three stages (the flop, the turn and the river). Each player seeks the five best cards among the hole cards and community cards. There are 4 betting rounds. During each round each player can choose “call”, “check”, “raise”, or “fold”.

In fixed limit Texas Hold’em. Each player can only choose a fixed amount of raise. And in each round the number of raises is limited to 4.

State Representation of Limit Texas Hold’em

The state is encoded as a vector of length 72. The first 52 elements represent cards, where each element corresponds to one card. The hand is represented as the two hole cards plus the observed community cards so far. The last 20 elements are the betting history. The correspondence between the index and the card is as below.

Index

Meaning

0~12

Spade A ~ Spade K

13~25

Heart A ~ Heart K

26~38

Diamond A ~ Diamond K

39~51

Club A ~ Club K

52~56

Raise number in round 1

37~61

Raise number in round 2

62~66

Raise number in round 3

67~71

Raise number in round 4

Action Encoding of Limit Texas Hold’em

There 4 actions in Limit Texas Hold’em. They are encoded as below.

Action ID

Action

0

Call

1

Raise

2

Fold

3

Check

Payoff of Limit Texas Hold’em

The stardard unit used in the leterature is milli big blinds per hand (mbb/h). In the toolkit, the reward is calculated based on big blinds per hand. For example, a reward of 0.5 (-0.5) means that the player wins (loses) 0.5 times of the amount of big blind.

Dou Dizhu

Doudizhu is one of the most popular Chinese card games with hundreds of millions of players. It is played by three people with one pack of 54 cards including a red joker and a black joker. After bidding, one player would be the “landlord” who can get an extra three cards, and the other two would be “peasants” who work together to fight against the landlord. In each round of the game, the starting player must play a card or a combination, and the other two players can decide whether to follow or “pass.” A round is finished if two consecutive players choose “pass.” The player who played the cards with the highest rank will be the first to play in the next round. The objective of the game is to be the first player to get rid of all the cards in hand. For detailed rules, please refer to Wikipedia or Baike.

In the toolkit, we implement a standard version of Doudizhu. In the bidding phase, we heuristically designate one of the players as the “landlord.” Specifically, we count the number of key cards or combinations (high-rank cards and bombs), and the player with the most powerful hand is chosen as “lanlord.”

State Representation of Dou Dizhu

At each decision point of the game, the corresponding player will be able to observe the current state (or information set in imperfect information game). The state consists of all the information that the player can observe from his view. We encode the information into a readable Python dictionary. The following table shows the structure of the state:

Key

Description

Example value

deck

A string of one pack of 54 cards with Black Joker and Red Joker. Each character means a card. For conciseness, we use ‘T’ for ‘10’.

3333444455556666777788889999TTTTJJJJQQQQKKKKAAAA2222BR

seen_cards

Three face-down cards distributed to the landlord after bidding. Then these cards will be made public to all players.

TQA

landlord

An integer of landlord’s id

0

self

An integer of current player’s id

2

initial_hand

All cards current player initially owned when a game starts. It will not change with playing cards.

3456677799TJQKAAB

trace

A list of tuples which records every actions in one game. The first entry of the tuple is player’s id, the second is corresponding player’s action.

[(0, ‘8222’), (1, ‘pass’), (2, ‘pass’), (0 ‘6KKK’), (1, ‘pass’), (2, ‘pass’), (0, ‘8’), (1, ‘Q’)]

played_cards

As the game progresses, the cards which have been played by the three players and sorted from low to high.

[‘6’, ‘8’, ‘8’, ‘Q’, ‘K’, ‘K’, ‘K’, ‘2’, ‘2’, ‘2’]

others_hand

The union of the other two player’s current hand

333444555678899TTTJJJQQAA2R

current_hand

The current hand of current player

3456677799TJQKAAB

actions

The legal actions the current player could do

[‘pass’, ‘K’, ‘A’, ‘B’]

State Encoding of Dou Dizhu

In Dou Dizhu environment, we encode the state into 6 feature planes. The size of each plane is 5*15. Each entry of a plane can be either 1 or 0. The 5 rows represent 0, 1, 2, 3, 4 corresonding cards, respectively. The 15 columns start from “3” to “RJ” (Black Jack). For example, if we have a “3”, then the entry (1, 0) would be 1, and the rest of column 0 would be 0. If we have a pair of “4”, then the entry (2, 1) would be 1, and the rest of column 1 would be 0. Note that the current encoding method is just an example to show how the feature can be encoded. Users are encouraged to encode the state for their own purposes by modifying extract_state function in `rlcard/envs/doudizhu.py`__. The example encoded planes are as below:

Plane

Feature

0

the current hand

1

the union of the other two players’ hand

2-4

the recent three actions

5

the union of all played cards

Action Abstraction of Dou Dizhu

The size of the action space of Dou Dizhu is 33676. This number is too large for learning algorithms. Thus, we make abstractions to the original action space and obtain 309 actions. We note that some recent studies also use similar abstraction techniques. The main idea of the abstraction is to make the kicker fuzzy and only focus on the major part of the combination. For example, “33345” is abstracted as “333 **”. When the predicted action of the agent is not legal, the agent will choose “pass.”. Thus, the current environment is simple, since once the agent learns how to play legal actions, it can beat random agents. Users can also encode the actions for their own purposes (such as increasing the difficulty of the environment) by modifying decode_action function in rlcard/envs/doudizhu.py. Users are also encouraged to include rule-based agents as opponents. The abstractions in the environment are as below. The detailed mapping of action and its ID is in rlcard/games/doudizhu/jsondata/action_space.json:

Type

Number of Actions

Number of Actions after Abstraction

Action ID

Solo

15

15

0-14

pair

13

13

15-27

Trio

13

13

28-40

Trio with single

182

13

41-53

Trio with pair

156

13

54-66

Chain of solo

36

36

67-102

Chain of pair

52

52

103-154

Chain of trio

45

45

155-199

Plane with solo

24721

38

200-237

Plane with pair

6552

30

238-267

Quad with solo

1339

13

268-280

Quad with pair

1014

13

281-293

Bomb

13

13

294-306

Rocket

1

1

307

Pass

1

1

308

Total

33676

309

Payoff

If the landlord first get rid of all the cards in his hand, he will win and receive a reward 1. The two peasants will lose and receive a reward 0. Similarly, if one of the peasant first get rid of all the cards in hand, both peasants will win and receive a reward 1. The landlord will lose and receive a reward 0.

Simple Dou Dizhu

Simple Dou Dizhu is a smaller version of Dou Dizhu. The deck only consists of 6 ranks from ‘8’ to ‘A’ (8, 9, T, J, Q, K, A), there are four cards with different suits in each rank. What’s more, unlike landlord in Dou Dizhu, the landlord in Simple Dou Dizhu only has one more card than the peasants. The rules of this game is the same as the rules of Dou Dizhu. Just because each player gets fewer cards, they end the game faster.

State Representation of Simple Dou Dizhu

This is almost the smae as the state representation of Dou Dizhu, but the number of the ‘deck’ has reduced from 54 to 28, and the number of the ‘seen cards’ reduced from 3 to 1. The following table shows the structure of the state:

Key

Description

Example value

deck

A string of one pack of 28 cards without Black Joker and Red Joker. Each character means a card. For conciseness, we use ‘T’ for ‘10’.

88889999TTTTJJJJQQQQKKKKAAAA

seen_cards

One face-down card distributed to the landlord after bidding. Then the card will be made public to all players.

K

landlord

An integer of landlord’s id

0

self

An integer of current player’s id

1

initial_hand

All cards current player initially owned when a game starts. It will not change with playing cards.

8TTJJQQKA

trace

A list of tuples which records every actions in one game. The first entry of the tuple is player’s id, the second is corresponding player’s action.

[(0, ‘8’), (1, ‘A’), (2, ‘pass’), (0, ‘pass’)]

played_cards

As the game progresses, the cards which have been played by the three players and sorted from low to high.

[‘8’, ‘A’]

others_hand

The union of the other two player’s current hand

889999TTJJQQKKKAAA

current_hand

The current hand of current player

8TTJJQQK

actions

The legal actions the current player could do

[‘J’, ‘TTJJQQ’, ‘TT’, ‘Q’, ‘T’, ‘K’, ‘QQ’, ‘8’, ‘JJ’]

State Encoding of Simple Dou Dizhu

The state encoding is the same as Dou Dizhu game.

Action Encoding of Simple Dou Dizhu

The action encoding is the same as Dou Dizhu game. Because of the reduction of deck, the actions encoded have also reduced from 309 to 131.

Payoff of Simple Dou Dizhu

The payoff is the same as Dou Dizhu game.

Mahjong

Mahjong is a tile-based game developed in China, and has spread

throughout the world since 20th century. It is commonly played by 4 players. The game is played with a set of 136 tiles. In turn players draw and discard tiles until | The goal of the game is to complete the leagal hand using the 14th drawn tile to form 4 sets and a pair. We revised the game into a simple version that all of the winning set are equal, and player will win as long as she complete forming 4 sets and a pair. Please refer the detail on Wikipedia or Baike.

State Representation of Mahjong

The state representation of Mahjong is encoded as 6 feature planes, where each plane has 34 X 4 dimensions. For each plane, the column of the plane indicates the number of the cards in the given cards set, and the row of the plane represents each kind of cards (Please refer to the action space table). The information that has been encoded can be refered as follows:

Plane

Feature

0

the cards in current player’s hand

1

the played cards on the table

2-5

the public piles of each players

Action Space of Mahjong

There are 38 actions in Mahjong.

Action ID

Action

0 ~ 8

Bamboo-1 ~ Bamboo-9

9 ~ 17

Characters-1 ~ Character-9

18 ~ 26

Dots-1 ~ Dots-9

27

Dragons-green

28

Dragons-red

29

Dragons-white

30

Winds-east

31

Winds-west

32

Winds-north

33

Winds-south

34

Pong

35

Chow

36

Gong

37

Stand

Payoff of Mahjong

The reward is calculated by the terminal state of the game, where winning player is awarded as 1, losing players are punished as -1. And if no one win the game, then all players’ reward will be 0.

No-limit Texas Hold’em

No-limit Texas Hold’em has similar rule with Limit Texas Hold’em. But unlike in Limit Texas Hold’em game in which each player can only choose a fixed amount of raise and the number of raises is limited. In No-limit Texas Hold’em, The player may raise with at least the same amount as previous raised amount in the same round (or the minimum raise amount set before the game if none has raised), and up to the player’s remaining stack. The number of raises is also unlimited.

State Representation of No-Limit Texas Hold’em

The state representation is similar to Limit Hold’em game. The state is represented as 52 cards and 2 elements of the chips of the players as below:

Index

Meaning

0~12

Spade A ~ Spade K

13~25

Heart A ~ Heart K

26~38

Diamond A ~ Diamond K

39~51

Club A ~ Club K

52

Chips of player 1

53

Chips of player 2

Action Encoding of No-Limit Texas Hold’em

There are 6 actions in No-limit Texas Hold’em. They are encoded as below.

*Note: Starting from Action ID 3, the action means the amount player should put in the pot when chooses ‘Raise’. The action ID from 3 to 5 corresponds to the bet amount from half amount of the pot, full amount of the pot to all in.

Action ID

Action

0

Fold

1

Check

2

Call

3

Raise Half Pot

4

Raise Full Pot

5

All In

Payoff of No-Limit Texas Hold’em

The reward is calculated based on big blinds per hand. For example, a reward of 0.5 (-0.5) means that the player wins (loses) 0.5 times of the amount of big blind.

UNO

Uno is an American shedding-type card game that is played with a specially deck.The game is for 2-10 players. Every player starts with seven cards, and they are dealt face down. The rest of the cards are placed in a Draw Pile face down. Next to the pile a space should be designated for a Discard Pile. The top card should be placed in the Discard Pile, and the game begins. The first player is normally the player to the left of the dealer and gameplay usually follows a clockwise direction. Every player views his/her cards and tries to match the card in the Discard pile. Players have to match either by the number, color, or the symbol/action. If the player has no matches, they must draw a card. If that card can be played, play it. Otherwise, keep the card. The objective of the game is to be the first player to get rid of all the cards in hand. For detailed rules, please refer to Wikipedia or Uno Rules. And in our toolkit, the number of players is 2.

State Representation of Uno

In state representation, each card is represented as a string of color and trait(number, symbol/action). ‘r’, ‘b’, ‘y’, ‘g’ represent red, blue, yellow and green respectively. And at each decision point of the game, the corresponding player will be able to observe the current state (or information set in imperfect information game). The state consists of all the information that the player can observe from his view. We encode the information into a readable Python dictionary. The following table shows the structure of the state:

Key

Description

Example value

hand

A list of the player’s current hand.

[‘g-wild’, ‘b-0’, ‘g-draw_2’, ‘y-skip’, ‘r-draw_2’, ‘y-3’, ‘y-wild’]

target

The top card in the Discard pile

‘g-wild’

played_cards

As the game progresses, the cards which have been played by the players

[‘g-3’, ‘g-wild’]

others_hand

The union of the other player’s current hand

[‘b-0’, ‘g-draw_2’, ‘y-skip’, ‘r-draw_2’, ‘y-3’, ‘r-wild’]

State Encoding of Uno

In Uno environment, we encode the state into 7 feature planes. The size of each plane is 4*15. Row number 4 means four colors. Column number 15 means 10 number cards from 0 to 9 and 5 special cards—“Wild”, “Wild Draw Four”, “Skip”, “Draw Two”, and “Reverse”. Each entry of a plane can be either 1 or 0. Note that the current encoding method is just an example to show how the feature can be encoded. Users are encouraged to encode the state for their own purposes by modifying extract_state function in `rlcard/envs/uno.py`__. The example encoded planes are as below:

Plane

Feature

0-2

hand

3

target

4-6

others’ hand

We use 3 planes to represnt players’ hand. Specifically, planes 0-2 represent 0 card, 1 card, 2 cards, respectively. Planes 4-6 are the same.

Action Encoding of Uno

There are 61 actions in Uno. They are encoded as below. The detailed mapping of action and its ID is in rlcard/games/uno/jsondata/action_space.json:

Action ID

Action

0~9

Red number cards from 0 to 9

10~12

Red action cards: skip, reverse, draw 2

13

Red wild card

14

Red wild and draw 4 card

15~24

green number cards from 0 to 9

25~27

green action cards: skip, reverse, draw 2

28

green wild card

29

green wild and draw 4 card

30~39

blue number cards from 0 to 9

40~42

blue action cards: skip, reverse, draw 2

43

blue wild card

44

blue wild and draw 4 card

45~54

yellow number cards from 0 to 9

55~57

yellow action cards: skip, reverse, draw 2

58

yellow wild card

59

yellow wild and draw 4 card

60

draw

Payoff of Uno

Each player will receive a reward -1 (lose) or 1 (win) in the end of the game.

Gin Rummy

Gin Rummy is a popular two person card game using a regular 52 card deck (ace being low). The dealer deals 11 cards to his opponent and 10 cards to himself. Each player tries to form melds of 3+ cards of the same rank or 3+ cards of the same suit in sequence. If the deadwood count of the non-melded cards is 10 or less, the player can knock. If all cards can be melded, the player can gin. Please refer the detail on Wikipedia.

If a player knocks or gins, the hand ends, each player put down their melds, and their scores are determined. If a player knocks, the opponent can layoff some of his deadwood cards if they extend melds of the knocker. The score is the difference between the two deadwood counts of the players. If the score is positive, the player going out receives it. Otherwise, if the score is zero or negative, the opponent has undercut the player going out and receives the value of the score plus a 25 point undercut bonus.

The non-dealer discards first (or knocks or gins if he can). If the player has not knocked or ginned, the next player can pick up the discard or draw a card from the face down stockpile. He can knock or gin and the hand ends. Otherwise, he must discard and the next player continues in the same fashion. If the stockpile is reduced to two cards only, then the hand is declared dead and no points are scored.

State Representation of Gin Rummy

The state representation of Gin Rummy is encoded as 5 feature planes, where each plane is of dimension 52. For each plane, the column of the plane indicates the presence of the card (ordered from AS to KC). The information that has been encoded can be referred as follows:

Plane

Feature

0

the cards in current player’s hand

1

the top card of the discard pile

2

the dead cards: cards in discard pile (excluding the top card)

3

opponent known cards: cards picked up from discard pile, but not discarded

4

the unknown cards: cards in stockpile or in opponent hand (but not known)

Action Space of Gin Rummy

There are 110 actions in Gin Rummy.

Action ID

Action

0

score_player_0_action

1

score_player_1_action

2

draw_card_action

3

pick_up_discard_action

4

declare_dead_hand_action

5

gin_action

6 - 57

discard_action

58 - 109

knock_action

Payoff of Gin Rummy

The reward is calculated by the terminal state of the game. Note that the reward is different from that of the standard game. A player who gins is awarded 1 point. A player who knocks is awarded 0.2 points. The losing player is punished by the negative of their deadwood count divided by 100.

If the hand is declared dead, both players are punished by the negative of their deadwood count divided by 100.

Settings

The following options can be set.

Option

Default value

dealer_for_round

DealerForRound.Random

stockpile_dead_card_count

2

going_out_deadwood_count

10

max_drawn_card_count

52

is_allowed_knock

True

is_allowed_gin

True

is_allowed_pick_up_discard

True

is_allowed_to_discard_picked_up_card

False

is_always_knock

False

is_south_never_knocks

False

Variations

One can create variations that are easier to train by changing the options and specifying different scoring methods.