Full Report for Connect 4 by Howard Wexler,Ned Strongin

Rules

Representative game (in the sense of being of mean length). Wherever you see the 'representative game' referred to in later sections, this is it!

Play

Each turn, place a piece in an empty square so that it is supported below.

Goal

Make a line of 4 to win.

Miscellaneous

General comments:

Requires accurate responses to threats.

Play: Combinatorial

Family: Line games

Mechanism(s): Pattern

Components: Board

Level: Beginner,Standard

BGG Stats

BGG Entry	Connect 4
BGG Rating	4.88267
#Voters	7144
SD	1.55033
BGG Weight	1.2039
#Voters	510
Year	1974

BGG Ratings and Comments

User	Rating	Comment
atkinsst	N/A	Gifted to Mark
drcsaba	9
kyogensho	10
sannekitareal	10
alkaiser	6	[Children's Game] My kids can play this over and over. They love it. The game drives me insane though. It's pretty much one step above tic-tac-toe for me. But they love it so I'll play it with them.
sebaz	10
Arctic Jack	6	A better game than it is probably given credit for by most. A great platform for budding young abstractees too. I bought this book to deeper understand Connect 4. The Complete Book of CONNECT 4: History, Strategy, Puzzles by James D. Allen A good abstract, well worth it's cheap price. I wish a larger grid was also commercially available.
wejejeei	10
Ammarg	4	variation of tic tac toe
GaffaUK	9
alanykl	3	How to play? Just the same as the name: Connect Four.
Apathy	4	This game is basically tic tac toe, but it'll always be fun for me. I'm not sold on the new ways to play the new version of Connect 4. The pop out game is not fun at all, and I mainly just prefer the classic game.
Arcturian	5	A childhood classic that's still fun to play on occasion.
josephc4	9.5
adularia25	2	Of all the variants of tic-tac-toe, this one seems like it should be so much more... and yet it disappoints like the rest. Either you crush your opponent because they don't see what you are doing, or you lose because you lost track of how many they had in a row. Either way, I despise playing this and would rather play tic-tac-toe (at least it ends faster.)
Altugas	5	A nice classic, with more strategy than it may seem.
Agataka	7	Very addictive game, a bit like harder version of tic tac toe :) It's so simple, yet so fun to win and so frustrating to lose.
Cheryllion	9	Here, diagonally! Pretty sneaky, Sis!
alexanderbanning	5	ABSTRACT, CHILDREN'S Recommended with 2 players. 10 mins.
anemaat	10
Admiral Fisher	4	A good one for kids and adults can play it and get a modicum of enjoyment from it. We have a wooden set called "4 in a row"
asta	3	AT MUM AND DAD'S I have a travel version. Fun for children.
guerecon	10
AnyMouse	N/A	I adore connect four. I don't care that it's "solvable" as I don't play with anyone who's studied the dissertation.
adamolanna	5	Vaghi ricordi di alcune partite giocate prima del 1985, mi piaceva molto, lo trovavo strategico e difficile.
aca83	10	Jugadores: 2 Tengo varios
ArtB	3	down from 4 likely won't play this again although could be convinced played many times before I began recording plays
Abso	2	Suffers from the same fate as Tic-tac-toe. Fun at start but eventually turns out into a draw or a loss by just counting the remaining turns and who happens to drop the final piece.
Arctocebus	N/A	2020 Edition
acekim	5	Not too bad for playing with small children just learning logic and how to block ones opponent. Much superior to Candyland...
dune2009	10
pilialohawaiian	10
a2greg	6	Classic. Nuff said.
AmericanEagle	N/A	Travel
IWilloughbyTroy17	9	you have to get four pieces in a row going diagonal, vertical, or horizontal. There are games that have no winners too.
Anakin1981	2	A simple game for kids.
atlcribber	5	For those not ready for pente, there is connect four.
airship51	N/A	Captain's Mistress - wood w/glass marbles.
Ajax	6	Classic game. Adds a little more strategy to tic-tac-toe. My daughter enjoys it, and I don't hate it.
alextvalencic	6	Children's Game
nojjon	10
mogreece	9
alethic	4	One of those kids games that kids don't actually seem to enjoy a lot, but game theorists do.
grammarxcore	10
deTobn	9
Artax	5	Gyerekorunk ismert jateka.
Asociacion_El_Duende	N/A	Año 1996
rg258	9
AnttiT	3.3	As a child, I played this quite a lot. It can be entertaining, but will become repetitive if you play too long.
ryannameth	10
hervalix1	10
phattso	10
jancourtois	10
ataniker	N/A	-
Olley Mauley Mim	10	Great game to play with KIDS. I have to rate it higher based on that fact. ANYONE can play. And if any KID proposed a game of Connect Four, I'd play it. :-)
Asmoridin	3.5	Again, probably loved this as a kid. Growing to being an adult, it's just too simple for me to want to play again. Played it again as an adult... still pretty simple, but can be fun on occasion =).
Mladenl	10
AndyHowell	7	There's a pretty fun bar in Arlington that has a giant Connect 4 set. I had so much fun playing it (with a bunch of other type-A overly competitive military officers) that I've got to raise my rating. I'm always up for a game of Connect 4. Also, my two year-old is starting to play a little.
amishburrito	5	A great game from my youth. I used to play this every day in elementary school with friends while the rest of the class had recess outside. Very simplistic for an advanced gamer though.
kabutopszn	10
arhtu	7	McDonald's edition. ;)
Dalkuldar	9
Whipfire	10
alextrov	N/A	Travel version
CodeAndReload	10
adam_ethTroy	7	Fun to play with someone in your free time using strategy as well as manipulation, but can get boring after a while
amwiles	1	Not a game. All plays are recorded from Yucata.de.
astroglide	5	i shouldn't care about games being solved unless i can actually do it myself. a master would no doubt blow me away at this game. fairly fun, easy to teach abstract with quick playing time. i'm sure i'll play it with my kids when i have some.
AGargTroy22	6	The title of the game is Connect Four. The game has a very simple concept and is easy to play. It is fun playing a quick game that does not require much critical thinking. I like that the player cannot keep a strategy the whole game. The player has to keep making spontaneous moves.
adstille	6	Great game that I kept for decades but it eventually became boring.
The Bus	9
JJEblam	10
CoraLeenaMarie	10
binraix	9	Classic game. I played this one in kindergarten and still love it. Very simple and still hard one if you have a good opponent! Recommend to math geeks out there!
Arnott	5	Basic, but still fun.
alexmate	6	Fairly fun game.
ajewo	N/A	Classic, abstract game that works especially well with kids. Similar games: * Qwirkle
AnnC	5.5	04+ or 06+, 2 player, 10 mins.
Aeneas	N/A	Pre.owned italian version "Forza 4"
Amirabutwo	N/A	Home.
UTSquishy	10
alcatraz13	5	Fast and superlight!
disthymia	10
aaronseeber	4	I had a lot of fun with this one as a kid, which gains it a point. Might not quite be my thing these days.
JHeughtroy20	10	Connect 4 is a very fun strategy game that i enjoy playing. I like the concept on having to predict your oppenents next move.
matt_sbd	9
123SimPY	N/A	rode kruis editie
mrgrimm11	10
Alberto_Mena	4	It was a "must have" when it came out, more than 40 years ago.
bzzybee75	10
Ashavan	3	Intro: Kua Klassen
H1landr	9
ellsworth77	9.5
Erichmond04	9
fstock96	10
AbigailEMG	N/A	Home.
areeves	5	Always a fun game to play with kids and adults.
agiese	N/A	Storage - Box 12
Anganatyr	5	In swedish it´s called "Fyra i rad".
anazagarus	4	A simple game, that if both players play optimally will be decided by who plays first. Playing with mixed-age pairings is tough, because the superior player will win always and easily.
amatyarakshasa	8	A fantastic game to play with children!
Alannamairead	3	I wouldn't care if I never ever played this again in all my life
adamscott	5	Meh. Thrift Store find. Donated to my classroom, where it has been played hundreds (no exaggeration) of times.
Sone	10
MGT_PL	9
aitan_3	4	Hearts edition
1 Family Meeple	5	It's a classic.
LoganDGarcia	10	So I'm biased because it's the game my fiancee and I played a lot when we were in college. But its a great game. Play several times win or lose always fun.
stewartcc	9
Aussie550	6	I play this with my 3 yr old...which usually involves putting tokens in as quickly as possible one after the other and shouting "I win!" when you mak a row of four...sooner or later I'm sure he'll get the idea and then it's hex and counter brainwashing time! Still playing. Now the boy is five we have progressed to the proper rules.
sirollerblader	10
missstarsineyes	10	red pieces spray painted pink
simppapee	9
ZucriyAmsuna	9
Armbar	N/A	Why am I so bad at this?
Kraai	10
FabulousAcidTrip	10
alfonzos	N/A	Something to play with kids who are too sophisticated for Tic Tac Toe but not ready for Go Moku.
arbitrarychoice	4	Classic children's pure strategy game. Not much to it after you figure out the main strategies.
Auntbeast	N/A	$1.98 Bought it because it was the German version. YAY! I have a German game! (never played, game still with packing intact
DIenciutroy24	10	Connect 4 is the best game to play on long car rides or while waiting for dinner to finish. Always great to have around.
amodman	2	One of the few universal abstracts that's actually more or less "solved." I mean, it was a fun idea when I was a kid and it is a neat use of components. But yeah, not really much of a real game.
Apparos Achaparos	3	For kids mostly. Grownups should find it very shallow and lacking.
antoinedebruxelles	6	Puissance 4 Fond memories, like to trash my kids from time to time :)
cass_xoxo16	10	This is a good game beacuse it's easy and fun!
wheeljack601	10
2ndinBeautyContest	5	Quick with some strategy. Satisfying way to get the pieces out at the end of the game.
Anthares	6	A very good classic. Great for kids and adult too.
Alleman85	6	Briek
AFragnoliTroy20	7	Simple and fun strategy game. This game is geared towards younger age groups.
Lightbringer12	9
amast	N/A	Vier hintereinander, Schmidt Spiele
gecykkah	9	I love playing this one with kids. You can often get a good laugh out of them by making really bone-head obvious fours-in-a-row vertically or across the bottom horizontally. Kids are usually up for playing silly variants, like dropping two at a time instead of one.
alfredo lorente	5.5	A classic abstract that seems simpler than it is. After all, gravity is a harsh mistress, and you need to play with her as much as you play against your opponent. It may not be a "Gamer's classic," but there are many more much worse choices in the toy departments of the Walmart's of the world.
max_ra	10	This game is mostly undervalued. It is really strategical. You have to force your opponent to take the row you wnat him to take. You have to creat double-traps to win the game.
JenaTu	10
zander226	10	Connect 4 will always be a classic and its always fun to play
Paisen20	10
Area51	2	Busy 4 is my favorite Band.
acaldeira99	N/A	2 Players
PapaPizza	10
simpkins	9
boardgamegeek0	9
anujalamahewa	10
sao123	9
Don E	9
Archi	N/A	1985 FX Schmidt
heidibee	10
aaarg_ink	9	151105 Good memories for days gone by. Such a perfect tactile experience. 111130 something hypnotic about...I could play again and again. I'm certain its been solved, but is it easily solved? I'm not sure...I guess I should look it up sometime. Later.
cangarooo	10
happy_2728	10	A classic game for kids.
1000rpm	7	Great fun in the pub or garden (with a giant set). Also great for kids - taking turns, strategy, visualisation, etc.
afrey15	2	Parents
AndersonCouncil	4	It's a simple game and fun but not one I'd take along to a game night with me. It's good for playing with small children though as it's so easy to learn.
nomsai	10
Tijmenn	10
zeruf	9
pathagobi	9	Okay this is one of THE classics!!! I just love this game... all you have to do is get 4 in a row (any direction) and you say "connect 4!!!" This game for me is a timeless classic that is so much fun!!!
Anemelos	2	A simple abstract game. Its a game for kids.
Alex the Pretty Good	5	A good combo of strategy and deduction. Starts to get predictable after a few games with the same opponent though.
Aarontu	5	A simple, if slightly juvenile, abstract game.
mafiul	10	Best 2 player game (No luck, only brain)
Doctor2Hearts	10
alemfi	1	Unlike tic-tac-toe, the decision space is a bit too big to quickly teach them that a game can be "solved".
jinnetics	9
Andy Mesa	6	It's glorified tic-tac-toe but I still enjoy it.
guitarhouse	10
Algernon88	5	Quite good a game, after all. Just not something you would ask to play, more like you won't refuse to play it if someone else wants to.
anisai	9
Iron Knight	10
Asociacion Noctis	N/A	?
Lnamcc	10
msommer	10
mleyva515	10
tuujohns	10
govmarley	10
superrussellman	10
Pumprnikldono	9
effdee	10
scottcoody	10
kaksdee	10
joshadkins	9
Ace Pumpkin	5	Game Folio/Fun-on-the-Run/travel edition
adebisi	3	You're just repeating the same patterns over and over and wishing that your opponent will not see them
internetotaku	10
ashrael	5	Fun with kids
The Eraser	10
arnest_r	5	Feels solved (yes, I know it IS solved), playing it feels almost like Tic Tac Toe
airjudden	4	This is really a kid's game, but it's one of the more enjoyable ones that I play with them. It has enough "oomph" that a couple of adults could squeeze in a quick game without being bored, and it's fast enough that it won't bore you for a long time (unlike Monopoly).
annily	10
ABCafe	N/A	B5
piticutzi	9
BrandenTheFirst	10	Connect Four has been a staple board game for me since my youth and I can say it's easily one of the first games I'd truly enjoyed when it comes to true strategy. Realistically, It's about a step above tic-tac-toe but it's also just different enough to keep that simple formula entertaining and fresh. I'd recommend this game to anyone just getting into board games as it's a good way to start expanding your thought process for more complex games. That being said- Connect Four has an optimal strategy but is one of the best in terms of beginning board games and will always hold a special place in my heart due to experiences with my family and friends.
AndrePOR	6	Classic (Before 2000)
radagast319	9
chateauzou	10

Kolomogorov Complexity Analysis

Size (bytes)	13757
Reference Size	10293
Ratio	1.34

Ai Ai calculates the size of the implementation, and compares it to the Ai Ai implementation of the simplest possible game (which just fills the board). Note that this estimate may include some graphics and heuristics code as well as the game logic. See the wikipedia entry for more details.

Playout Complexity Estimate

Playouts per second	1237470.61 (0.81µs/playout)
Reference Size	564111.24 (1.77µs/playout)
Ratio (low is good)	0.46

Tavener complexity: the heat generated by playing every possible instance of a game with a perfectly efficient programme. Since this is not possible to calculate, Ai Ai calculates the number of random playouts per second and compares it to the fastest non-trivial Ai Ai game (Connect 4). This ratio gives a practical indication of how complex the game is. Combine this with the computational state space, and you can get an idea of how strong the default (MCTS-based) AI will be.

State Space Complexity

% new positions/bucket

State Space Complexity	15321966
State Space Complexity (log 10)	7.19
Confidence	31.05	0: totally unreliable, 100: perfect
Samples	1285006

State space complexity (where present) is an estimate of the number of distinct game tree reachable through actual play. Over a series of random games, Ai Ai checks each position to see if it is new, or a repeat of a previous position and keeps a total for each game. As the number of games increase, the quantity of new positions seen per game decreases. These games are then partitioned into a number of buckets, and if certain conditions are met, Ai Ai treats the number in each bucket as the start of a strictly decreasing geometric sequence and sums it to estimate the total state space. The accuracy is calculated as 1-[end bucket count]/[starting bucklet count]

Playout/Search Speed

Label	Its/s	SD	Nodes/s	SD	Game length	SD
Random playout	3,333,748	49,419	71,050,418	1,053,263	21	7
search.UCT	1,672,680	79,418			35	4

Random: 10 second warmup for the hotspot compiler. 100 trials of 1000ms each.

Other: 100 playouts, means calculated over the first 5 moves only to avoid distortion due to speedup at end of game.

Mirroring Strategies

Rotation (Half turn) lost each game as expected.
Reflection (X axis) lost each game as expected.
Reflection (Y axis) lost each game as expected.
Copy last move lost each game as expected.

Mirroring strategies attempt to copy the previous move. On first move, they will attempt to play in the centre. If neither of these are possible, they will pick a random move. Each entry represents a different form of copying; direct copy, reflection in either the X or Y axis, half-turn rotation.

Win % By Player (Bias)

1: White win %	57.90±3.08	Includes draws = 50%
2: Black win %	42.10±3.02	Includes draws = 50%
Draw %	12.00	Percentage of games where all players draw.
Decisive %	88.00	Percentage of games with a single winner.
Samples	1000	Quantity of logged games played

Note: that win/loss statistics may vary depending on thinking time (horizon effect, etc.), bad heuristics, bugs, and other factors, so should be taken with a pinch of salt. (Given perfect play, any game of pure skill will always end in the same result.)

Note: Ai Ai differentiates between states where all players draw or win or lose; this is mostly to support cooperative games.

UCT Skill Chains

Match	AI	Strong Wins	Draws	Strong Losses	#Games	Strong Score	p1 Win%	Draw%	p2 Win%	Game Length
0	Random
2	UCT (its=3)	629	4	276	909	0.6635 <= 0.6942 <= 0.7233	51.93	0.44	47.63	20.05
7	UCT (its=19)	630	1	99	730	0.8369 <= 0.8637 <= 0.8867	53.15	0.14	46.71	16.12
8	UCT (its=52)	629	3	213	845	0.7157 <= 0.7462 <= 0.7743	58.46	0.36	41.18	16.81
9	UCT (its=141)	624	13	159	796	0.7625 <= 0.7921 <= 0.8188	55.78	1.63	42.59	20.25
10	UCT (its=382)	619	23	220	862	0.7009 <= 0.7314 <= 0.7600	50.35	2.67	46.98	26.88
11	UCT (its=1039)	617	27	247	891	0.6769 <= 0.7076 <= 0.7366	48.71	3.03	48.26	30.45
12	UCT (its=2824)	617	27	223	867	0.6966 <= 0.7272 <= 0.7558	51.79	3.11	45.10	31.53
13	UCT (its=7676)	617	27	239	883	0.6834 <= 0.7140 <= 0.7429	59.91	3.06	37.03	31.62
14	UCT (its=20867)	609	43	253	905	0.6660 <= 0.6967 <= 0.7258	63.65	4.75	31.60	32.31
15	UCT (its=56722)	611	40	201	852	0.7101 <= 0.7406 <= 0.7689	47.42	4.69	47.89	34.19
16	UCT (its=154185)	614	34	278	926	0.6507 <= 0.6814 <= 0.7106	23.97	3.67	72.35	35.19
17	UCT (its=154185)	481	41	478	1000	0.4706 <= 0.5015 <= 0.5324	12.00	4.10	83.90	34.87

Search for levels ended. Close to theoretical value: player 2 wins.

Level of Play: Strong beats Weak 60% of the time (lower bound with 95% confidence).

Draw%, p1 win% and game length may give some indication of trends as AI strength increases.

1st Player Win Ratios by Playing Strength

This chart shows the win(green)/draw(black)/loss(red) percentages, as UCT play strength increases. Note that for most games, the top playing strength show here will be distinctly below human standard.

Complexity

Game length	33.97
Branching factor	5.91
Complexity	10^24.70	Based on game length and branching factor
Samples	1000	Quantity of logged games played

Computational complexity (where present) is an estimate of the game tree reachable through actual play. For each game in turn, Ai Ai marks the positions reached in a hashtable, then counts the number of new moves added to the table. Once all moves are applied, it treats this sequence as a geometric progression and calculates the sum as n-> infinity.

Move Classification

Board Size	42	Quantity of distinct board cells
Distinct actions	42	Quantity of distinct moves (e.g. "e4") regardless of position in game tree
Good moves	29	A good move is selected by the AI more than the average
Bad moves	13	A bad move is selected by the AI less than the average
Response distance	2.36	Mean distance between move and response; a low value relative to the board size may mean a game is tactical rather than strategic.
Samples	1000	Quantity of logged games played

Board Coverage

A mean of 80.88% of board locations were used per game.

Colour and size show the frequency of visits.

Game Length

Game length frequencies.

Mean	33.97
Mode	[42]
Median	37.5

Change in Material Per Turn

Mean change in material/round	0.94	Complete round of play (all players)

This chart is based on a single representative* playout, and gives a feel for the change in material over the course of a game. (* Representative in the sense that it is close to the mean length.)

Actions/turn

Table: branching factor per turn, based on a single representative* game. (* Representative in the sense that it is close to the mean game length.)

Action Types per Turn

This chart is based on a single representative* game, and gives a feel for the types of moves available throughout that game. (* Representative in the sense that it is close to the mean game length.)

Red: removal, Black: move, Blue: Add, Grey: pass, Purple: swap sides, Brown: other.

Trajectory

This chart shows the best move value with respect to the active player; the orange line represents the value of doing nothing (null move).

The lead changed on 2% of the game turns. Ai Ai found 4 critical turns (turns with only one good option).

Position Heatmap

This chart shows the relative temperature of all moves each turn. Colour range: black (worst), red, orange(even), yellow, white(best).

Good/Effective moves

Measure	All players	Player 1	Player 2
Mean % of effective moves	59.95	63.87	56.04
Mean no. of effective moves	3.59	3.76	3.41
Effective game space	10^16.19	10^8.30	10^7.89
Mean % of good moves	32.22	4.20	60.24
Mean no. of good moves	2.00	0.29	3.71
Good move game space	10^8.95	10^0.60	10^8.35

These figures were calculated over a single game.

An effective move is one with score 0.1 of the best move (including the best move). -1 (loss) <= score <= 1 (win)

A good move has a score > 0. Note that when there are no good moves, an multiplier of 1 is used for the game space calculation.

Quality Measures

Measure	Value	Description
Hot turns	70.59%	A hot turn is one where making a move is better than doing nothing.
Momentum	11.76%	% of turns where a player improved their score.
Correction	20.59%	% of turns where the score headed back towards equality.
Depth	5.24%	Difference in evaluation between a short and long search.
Drama	0.33%	How much the winner was behind before their final victory.
Foulup Factor	35.29%	Moves that looked better than the best move after a short search.
Surprising turns	0.00%	Turns that looked bad after a short search, but good after a long one.
Last lead change	8.82%	Distance through game when the lead changed for the last time.
Decisiveness	50.00%	Distance from the result being known to the end of the game.

These figures were calculated over a single representative* game, and based on the measures of quality described in "Automatic Generation and Evaluation of Recombination Games" (Cameron Browne, 2007). (* Representative, in the sense that it is close to the mean game length.)

Openings

Moves	Animation
d1,g1,c1,f1,c2,b1,d2
b1,g1,d1,f1,e1,c1,c2
b1,g1,g2,e1,d1,d2,d3
d1,g1,b1,f1,e1,c1,c2
a1,e1,b1,e2,d1,c1,c2
b1,e1,a1,e2,d1,c1,c2
b1,f1,a1,c1,d1,d2,c2
d1,f1,a1,c1,b1,d2,c2
a1,d1,b1,a2,d2,g1
a1,d1,b1,g1,d2,a2
b1,d1,a1,a2,d2,g1
b1,d1,a1,g1,d2,a2

Opening Heatmap

Colour shows the success ratio of this play over the first 10moves; black < red < yellow < white.

Size shows the frequency this move is played.

Unique Positions Reachable at Depth

0	1	2	3	4	5	6	7	8	9	10	11	12
1	7	56	294	1410	5611	21625	74456	252762	791184	2428956	6945828	19444845

Note: most games do not take board rotation and reflection into consideration.
Multi-part turns could be treated as the same or different depth depending on the implementation.
Counts to depth N include all moves reachable at lower depths.
Inaccuracies may also exist due to hash collisions, but Ai Ai uses 64-bit hashes so these will be a very small fraction of a percentage point.

Shortest Game(s)

648 solutions found at depth 7.

Puzzles

Puzzle	Solution
Black to win in 22 moves
Black to win in 23 moves
White to win in 19 moves
Black to win in 19 moves
Black to win in 21 moves
White to win in 17 moves
White to win in 17 moves
White to win in 21 moves
Black to win in 19 moves
Black to win in 17 moves
White to win in 17 moves
Black to win in 17 moves

Selection criteria: first move must be unique, and not forced to avoid losing. Beyond that, Puzzles will be rated by the product of [total move]/[best moves] at each step, and the best puzzles selected.