# Checkers From Zero > Learn American checkers from the first move to strong play: the rules and the 1-32 notation, why forced captures make the game, shots and exchanges, strategy and the opposition, endgames, and how a computer proved that perfect play is a draw. --- # Checkers From Zero You have played checkers. Move diagonally, jump when you can, get a king. Then someone beat you in four moves by handing you a piece, and you could not see how. Checkers looks like a children's game and plays like a puzzle box: one rule, "you must capture," turns every move into a question about what your opponent is about to be forced to do. This guide teaches you to see that. It starts with the exact rules and the 1 to 32 notation that lets you read any game ever written down, then builds up through forced-capture tactics, strategy, and endgames. It ends with a surprise: in 2007 a team proved that if both sides play perfectly, checkers is a draw. You can play every idea on this page against the site's engine at [play checkers](/games/checkers), which has a coach mode to help you along. ## Which checkers is this? "Checkers" names a family of games. This guide teaches **American checkers**, also called **English draughts**: an 8x8 board, twelve pieces each, men that move and capture only forward, kings that move one square at a time, and captures that are mandatory. It is the exact ruleset the site's playable game uses. International draughts (10x10 board, men that can capture backward, "flying" kings that glide across the board, and a rule that you must take the most pieces), Russian draughts, and Brazilian draughts differ. Everything here is about the 8x8 game. ## How to read this - **Brand new?** Read in order. Phase 1 is five minutes of rules, and every later phase assumes it. - **Know the rules, lose to shots?** Start at [Phase 2](02-forced-captures.md) and [Phase 3](03-tactics.md). - **Want to know why it is a draw?** Jump to [Phase 5](05-endgames-and-the-solved-game.md). ## The phases 1. **[The Board, the Pieces, and the Numbers](01-the-board-the-pieces-and-the-numbers.md)** - exact rules, how captures and crowning work, and the 1 to 32 notation. 2. **[Forced Captures: The Rule That Makes Checkers Tactical](02-forced-captures.md)** - why a mandatory capture lets you move your opponent's pieces for them. 3. **[Tactics: Exchanges, Shots, and Breakthroughs](03-tactics.md)** - the patterns that win material, and how to spot them before your opponent does. 4. **[Strategy: Center, King Row, Tempo, and the Move](04-strategy.md)** - what to aim for when no shot is on the board. 5. **[Endgames and the Solved Game](05-endgames-and-the-solved-game.md)** - kings against kings, trapped corners, and what "checkers is solved" really means. Computers and games are a big topic of their own: [How Computers Play Games](/guides/how-computers-play-games) explains the search ideas behind the program that solved checkers. If you like boards, [Chess From Zero](/guides/chess-from-zero) is next door. --- # The Board, the Pieces, and the Numbers Almost everyone knows checkers "roughly," and the rough version is where the arguments start. Can a king jump backward? Do you have to jump? What if you land on the last row in the middle of a multiple jump? This phase pins every rule down, then gives you the numbering that lets you write a game on a napkin and read any checkers book. ## The board and the start The board is 8x8, but only the 32 dark squares are used. Pieces never stand on a light square. Turn the board so that each player has a dark square in the near left corner. Each side starts with 12 pieces, called **men**, on the dark squares of the three rows nearest that player. The two middle rows start empty. **Black moves first**, then the players alternate. (The official rulebook calls the first mover's color Red; this guide uses Black and White, like the site's game.) ```text Black men (b) start at the top, White men (w) at the bottom. Dots are empty dark squares: b b b b b b b b b b b b . . . . . . . . w w w w w w w w w w w w ``` Black moves down the board; White moves up. "Forward" always means toward the enemy's side. ## How pieces move - A **man** moves one square diagonally forward onto an empty dark square. Never sideways, never backward. - A man that reaches the far row, the **king row**, is **crowned** and becomes a **king**. A king moves one square diagonally in any of the four directions. Crowned pieces are traditionally marked by stacking a second piece on top. Kings in this game take one step at a time. In international draughts and some other variants, a "flying king" can slide any distance along a diagonal. Not here. ## The numbers: reading and writing games Every dark square has a number from 1 to 32, counted left to right and top to bottom as the board looks with Black at the top: ```text 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 ``` Black's home row is squares 1 to 4 and White's is 29 to 32. A move is written **from-to**: `11-15` means "the piece on 11 moves to 15." Because the board is the same every game, the numbers carry all the information. Black's seven possible first moves are `9-13`, `9-14`, `10-14`, `10-15`, `11-15`, `11-16`, and `12-16`. Notice there is no single "add 4" rule, because the rows are staggered. A Black man on squares 1-4, 9-12, 17-20, or 25-28 steps to the number 4 or 5 higher; on squares 5-8, 13-16, or 21-24 it steps to the number 3 or 4 higher. A man on the edge of the board has only one of the two steps. For White, subtract instead. One more piece of vocabulary, because it matters in the endgame. The long diagonal from corner to corner (`29-25-22-18-15-11-8-4`) is called the **main road**. The other two corners of the board each hold a pair of dark squares side by side (`1` and `5`, and `28` and `32`) and are called the **double corners**. ## Jumping If an enemy piece stands on a diagonally adjacent square and the square directly behind it, on the same diagonal, is empty, your piece may **jump** over it, land on the empty square, and the enemy piece is removed. Men jump forward only. Kings jump in all four directions. A capture is written with an `x`: `14x23`. ```text . . . . . . . . . . . . . b . . . w . . . . . . . . . . . . . . Black men: 14; White men: 18 ``` Black to move. The Black man on 14 jumps the White man on 18 and lands on 23: `14x23`. ## Multiple jumps If, after landing, the same piece can jump again, it **must** keep going until no more jumps are available. You cannot stop partway and you cannot switch to a different piece mid-move. A chain is written with every landing square: `10x17x26`. ```text . . . . . . . . . b . . . w . . . . . . . w . . . . . . . . . . Black men: 10; White men: 14, 22 ``` Black to move. The man on 10 jumps the man on 14 and lands on 17, then jumps the man on 22 and lands on 26. Both White men are gone in one turn. ## Crowning ends the move When a man reaches the king row by jumping, it becomes a king, and the move **ends there**. The new king may not continue jumping until its next turn, even if another capture is lined up. ```text . . . . . . . . . . . . . . . . . . . . . b . . . w w . . . . . Black men: 22; White men: 26, 27 ``` Black to move. The man on 22 jumps 26 and lands on 31, the king row, and is crowned. Once a king, it could jump the White man on 27 (landing on 24, which is empty), but the turn is over. White gets a move first and can respond to the threat. ## When is a game over? - **A win:** your opponent has no legal move on their turn. That happens when all their pieces are captured, or when every remaining piece is blocked. A player also wins when the opponent resigns. - **A draw:** both players agree. The site's game also lets a player claim a draw when the same position (with the same side to move) has occurred three times, or when 40 moves by each side pass with no capture and no man move. The official rules have similar limits. They exist to stop endless shuffling. Notice what is missing: there is no "check" and no pass. If you have a legal move you must make one, and if the only legal moves are bad, you still must make one. That fact powers the next phase and Phase 4. Check yourself before moving on: ```quiz [ {"q": "A Black man stands on square 10 with both squares ahead of it empty. Where can it move?", "choices": ["13 or 14", "14 or 15", "6 or 7", "14 only"], "answer": 1, "explain": "Square 10 is in the row 9-12, so a Black man steps to the number 4 or 5 higher: 14 or 15. Squares 6 and 7 are behind it, and men never move backward."}, {"q": "A man jumps into the king row on its second jump of a chain, and another enemy piece is lined up for a third jump. What happens?", "choices": ["It must take the third jump too", "It is crowned and the move ends", "It stays a man until the chain finishes", "The jump is illegal and must be undone"], "answer": 1, "explain": "A man that reaches the king row by a capture is crowned there and its move ends. The new king cannot jump again until its next turn."}, {"q": "Which of these is a complete way a game can end by the rules?", "choices": ["A player runs out of legal moves", "A player gets a king first", "A player captures the first piece", "A player reaches the middle of the board"], "answer": 0, "explain": "A player who has no legal move on their turn loses, because all their pieces are gone or blocked. Getting a king or the first capture does not end the game."} ] ``` ## Recap 1. The board is 8x8, only the 32 dark squares are used, each side starts with 12 men, and Black moves first. 2. Men move and jump one square diagonally forward; kings move and jump one square in all four directions. 3. Squares are numbered 1 to 32 from Black's side, and a move is written from-to (`11-15`), a capture with an `x` (`14x23`, `10x17x26`). 4. A multiple jump must be completed, and a man that is crowned during a capture stops there. 5. You win when your opponent has no legal move. Next up, [Forced Captures: The Rule That Makes Checkers Tactical](02-forced-captures.md): the one rule that turns your opponent's moves into your weapon. --- # Forced Captures: The Rule That Makes Checkers Tactical In most board games you choose your move. In checkers, sometimes the board chooses it for you. If you can capture, you must, and a player who understands that can offer a piece on purpose, watch the opponent have no choice but to take it, and collect two pieces in return. This phase is the whole secret behind most of the games you lost as a kid. ## The rule, exactly If the player to move has at least one capture available, they **must make a capture**. A quiet move is not allowed. This holds even when the capture is terrible for you, and even when the capture only exists because your opponent moved a piece into contact. (The rulebook's phrase is that captures are compulsory "whether offered actively or passively.") Two details matter for everything that follows: - **You choose which capture.** If several captures are available, with different pieces or different routes, you may play any of them. American checkers has **no majority rule**: you are not required to take the route that removes the most pieces. International draughts does require that, so a book written for it will teach you something that is not true here. - **You must finish what you start.** A chain of jumps has to be carried through to its end (Phase 1). You cannot take one piece and decline the second. ```text . . . . b b . . w . . . . . . . w . . . w . . . . . . . . . . . Black men: 5, 6; White men: 9, 17, 21 ``` Black to move. Black has exactly two legal moves, and both are captures: `5x14` takes one man, and `6x13x22` takes two. Neither is forced over the other. Which is better depends on what the position looks like afterward, not on the count alone. ## Why this rule makes a weapon Here is the mental model. When captures exist, the list of your opponent's legal moves collapses to only those captures, and often to exactly one. If you can arrange that, you have made their next move for them. So a mandatory capture is a lever. A **sacrifice** is giving a piece up on purpose. A **shot** is a sacrifice that forces a capture and then wins more than it cost. The simplest shot is "give one, take two." ## A shot, move by move ```text b . . . b . . . . . . . w . w . . . . . . . . . . . . . . . . . Black men: 1, 5; White men: 13, 15 ``` Black to move. Material is even, two men against two. Black plays `5-9`. White now has exactly one legal move, because the man on 13 can jump the man on 9, and a capture is mandatory: ```text b . . . . . . . b . . . w . w . . . . . . . . . . . . . . . . . Black men: 1, 9; White men: 13, 15 ``` `13x6`: White's man jumped from 13 over 9 and landed on 6. White had no choice. Look at what that capture did. The White man landed on 6, directly in front of Black's man on 1, with 10 empty behind it, so Black can jump it. And from 10, the White man on 15 is next in line, with 19 empty behind it. Now Black captures: ```text . . . . . . . . . . . . . . . . . . b . . . . . . . . . . . . . Black men: 19 ``` `1x10x19`: the man on 1 jumps the man on 6 to land on 10, then jumps the man on 15 to land on 19. Black gave up one man, took two, and White has no pieces left, so Black wins. The pattern has three beats, and you can use it to find your own shots: 1. **Offer.** Move a piece where it can be captured. 2. **Force.** Check that the capture is mandatory and, ideally, the only legal move for your opponent. 3. **Reload.** The capturing piece has landed somewhere it can be jumped, or its departure has opened a path for one of your pieces, so you recapture and come out ahead. ## Two questions before every move Because the forced reply is the entire engine of the game, build the habit of asking, on every single move: 1. **"After my move, what must my opponent capture, and what does that capture open up for me?"** This is how you find shots. 2. **"After my move, can my opponent offer me a piece, and what will I be forced to do?"** This is how you stop being the victim. If you are about to move a man next to an enemy man and there is a capture waiting behind it, run the sequence in your head: their reply, your forced capture, their next capture. The habit costs two seconds a move, and it is worth more than any opening you will memorize. ## Passive forced captures You do not have to be the one who moved into contact. Say your opponent plays a quiet move that happens to put one of their men beside one of yours with an empty square behind it. On your turn you now **must** jump. That is how most shots start: the sacrificed piece is the one you are forced to take. Check yourself before moving on: ```quiz [ {"q": "You have one legal capture and several quiet moves you like better. What must you do?", "choices": ["Play any move you like", "Capture, because a capture is mandatory", "Play the quiet move, then capture next turn", "Capture only if it wins material"], "answer": 1, "explain": "If any capture is available, the player to move must capture. Quiet moves are not legal while a capture exists."}, {"q": "You can capture one piece with one man or two pieces with a different man. Under American checkers rules, what is true?", "choices": ["You must take the two", "You must take the one", "You may choose either capture", "You must take whichever is closer to your king row"], "answer": 2, "explain": "American checkers has no majority rule, so you may play any available capture. International draughts is different: it forces the capture that removes the most pieces."}, {"q": "In the shot from this phase, Black plays 5-9 with White men on 13 and 15 and a Black man on 1. Why does White have to play 13x6?", "choices": ["Because 13x6 wins a piece for White", "Because it is the only legal move and captures are mandatory", "Because White men must always move toward Black's home row", "Because Black's man on 9 would otherwise be crowned"], "answer": 1, "explain": "The man on 13 can jump the man on 9, so White must capture. That jump is White's only capture, so it is White's only legal move. The forced capture then opens 1x10x19."} ] ``` ## Recap 1. If you can capture you must, even when it hurts, and a capture offered to you counts. 2. You may choose any capture and any route; there is no majority rule in American checkers. 3. A multiple jump must be completed once started. 4. A shot is a sacrifice that forces a capture and then wins more: offer, force, reload. 5. Before every move, ask what your opponent must capture and what that capture opens up. Next up, [Tactics: Exchanges, Shots, and Breakthroughs](03-tactics.md): trading pieces on purpose, a sacrifice that earns a king, and a short checklist for finding these patterns. --- # Tactics: Exchanges, Shots, and Breakthroughs Phase 2 gave you one lever: a mandatory capture decides your opponent's move. This phase shows the three ways strong players pull it. Each one is a short forced sequence, so you can check it by counting moves, with no intuition required. ## The exchange: one for one, on purpose An **exchange** (or trade) is a forced capture followed by a forced or likely recapture, so each side loses one piece. Here is the most common one in real games, straight from the starting position: ```text 1. 11-15 (Black steps toward the middle) 22-18 (White offers a man next to it) 2. 15x22 (Black must jump) 25x18 (White jumps back; 26x17 is also legal) ``` *What just happened:* White's `22-18` put a man next to Black's `15` with 22 empty behind it, so Black had to capture. The Black man landed on 22, where White could jump it, and the counts are 11 men against 11. Why would anyone trade? The usual reasons are rules of thumb, not laws: - **When you are ahead in material, trade.** Every trade makes your extra piece a bigger share of what is left, and it removes the pieces your opponent would use for tricks. - **When you are behind, avoid trades.** You need pieces on the board for shots to exist at all. - **Trade to break a cramp.** If your men are jammed together with no safe moves, a trade opens space. You cannot refuse a capture, so the only way to avoid a trade is to not step into contact in the first place. ## The shot: give one, take more You met this in Phase 2. The shot is the most valuable tactic in checkers because it wins material outright. Finding one is a short routine: 1. List your **sacrifices**: moves that put a man where it can be jumped. 2. For each, ask: **is the capture forced, and is it the opponent's only legal move?** If they have a choice of captures, they will pick the one that hurts least. 3. Play the forced reply on the board in your head. **Where did their capturing piece end up, and what square did it leave?** 4. See if you now have a **multiple jump**. Shots are rarer in the opening and become more common in the middle of the game when pieces are in contact. They are also the main way beginners lose: the sacrifice you did not notice. ## The breakthrough: a sacrifice that earns a king Sometimes the prize is not material but a **king**. A man standing guard on your king row blocks the enemy's jump into it. If you can pull that guard away, the way is open. ```text . . . . . . . . . . . . . . . . . . . . b . b . w . . . . w . . Black men: 21, 23; White men: 25, 30 ``` Black to move. Black's man on 21 would like to jump White's man on 25, but White's man on 30 stands on the landing square. So Black plays `23-26!`. The man on 30 can jump it, and nothing else is legal for White, so `30x23` is forced: ```text . . . . . . . . . . . . . . . . . . . . b . w . w . . . . . . . Black men: 21; White men: 23, 25 ``` The guard has left its post. Now `21x30` is open, and Black's man jumps 25, lands on the king row at 30, and is crowned. Men are even, one each, but Black has a king. A fair warning: a king is a big advantage in a real game with many pieces on the board, because it moves in all four directions and attacks men from behind. But a king alone is not an automatic win. In this tiny position, an exhaustive computer search of the remaining play says the result is a draw. The breakthrough is a means, not an end. ## Kings change the arithmetic Men capture only forward. Kings capture in all four directions. That has a consequence people forget: **a man that has walked past an enemy king can be captured from behind.** ```text . . . . . . . . . . . . . W . . . b . . . . . . . . . . . . . . Black men: 18; White kings: 14 ``` White to move. The White king on 14 sits behind the Black man on 18, which has already walked past it. The king jumps backward: `14x23`. A man could not do that. Two practical rules follow. Before you advance a man past an enemy king, check the square behind the man. And when you have a king, look for men that think they are safe. ## A short checklist Run through this when a position feels tense, in this order: 1. What captures does my opponent have right now? (They must take one.) 2. For each candidate move of mine, what will they be forced to do? 3. Can I play a sacrifice that forces them and opens a multiple jump or a path to a king? 4. Does my move leave a guard square empty that a breakthrough could use? Check yourself before moving on: ```quiz [ {"q": "In the opening exchange 11-15, 22-18, 15x22, why must Black play 15x22?", "choices": ["Because Black's man on 15 is attacked", "Because a capture is available and captures are mandatory", "Because jumping always wins material", "Because White's man on 18 would capture it otherwise"], "answer": 1, "explain": "After 22-18, Black's man on 15 can jump the man on 18 into the empty square 22. A capture is available, so Black must make one."}, {"q": "In the breakthrough with Black men on 21 and 23 and White men on 25 and 30, what does Black's 23-26 accomplish?", "choices": ["It wins a man for nothing", "It forces 30x23, which pulls the guard off 30 and lets 21x30 crown", "It blocks White from moving", "It crowns the man on 23 immediately"], "answer": 1, "explain": "White's only legal move is 30x23. That empties square 30, so Black's man on 21 can jump 25 and land on 30, the king row."}, {"q": "Which statement about backward captures is true in American checkers?", "choices": ["Men and kings both capture backward", "Only kings capture backward", "Neither captures backward", "Only men capture backward"], "answer": 1, "explain": "Men capture and move forward only. Kings move and capture in all four diagonal directions."} ] ``` ## Recap 1. An exchange is a forced capture plus a recapture; trade when ahead, avoid trades when behind. 2. A shot wins material: list the sacrifices, check the forced reply, and look for the multiple jump. 3. A breakthrough sacrifices a man to pull a guard off the king row so another man can crown. 4. Kings capture backward and men do not, so check behind any man that has passed an enemy king. 5. A king is valuable but does not by itself guarantee a win. Next up, [Strategy: Center, King Row, Tempo, and the Move](04-strategy.md): what to aim for when no shot is on the board. --- # Strategy: Center, King Row, Tempo, and the Move Most moves in a checkers game are not shots. You are choosing between quiet moves, and nothing on the board tells you which one is right. This phase gives you the principles strong players use to choose. They are rules of thumb, not theorems: checkers is a draw with perfect play (Phase 5), so no principle wins by itself, but ignoring them hands your opponent the chances. ## Pieces that back each other One fact from the jumping rule drives most of checkers strategy: **a piece can only be jumped if the square directly behind it is empty.** A man with a friend standing on the far side of it is safe from that direction. So you aim to move in connected groups, where every man has a neighbor on the squares behind it, and you avoid sending a lone man forward where the square behind it is open. This also explains why shots work: they need an empty square behind a target. When you plan a move, look at the squares behind your pieces first. ## The center and the edges The four central dark squares are **14, 15, 18, and 19**. A man there has two ways forward, supports pieces on both sides, and eyes many squares. A man on the edge has only one way forward, and a piece on the edge squares (the columns holding 5, 13, 21, 29 and 4, 12, 20, 28, and the top and bottom rows) can **never be jumped**, because there is no square behind it. That makes edge pieces safe, and also passive. The working advice: put men in the center when you can support them, and use the edges for pieces you want to park. A common beginner mistake is to push everything down the sides because it feels safe, and then run out of useful moves (see tempo below). ## Guard your king row: the bridge The enemy needs to reach your king row to crown a man. Black's king row is squares 1-4. A White man gets there only by first standing on one of 5, 6, 7, or 8. The classic defense for Black is to keep men on **1 and 3**, called the **bridge**. (For White, the matching squares are **30 and 32**.) ```text b . b . . w . . . . . . . . . . . . . . . . . . . . . . . . . . Black men: 1, 3; White men: 6 ``` Black to move. A White man has stepped onto 6, hoping to slip to 2 and crown. But Black's man on 1 jumps it: `1x10`, because 10 is empty behind it. In the same way, the man on 3 covers 7 (landing on 10) and 8 (landing on 12). A White man on 5 can only step to 1, which is occupied, so it is stuck. So with the bridge in place, every approach square is covered. The defense only holds while the landing squares 10 and 12 stay empty. If an enemy man or your own man stands on them, the jumps are blocked, and the bridge leaks. This is also why you do not rush your back men out: each one you move weakens the guard, so most players move them last. ## Tempo and the move A **tempo** is one move of a man. Every man has a limited number of forward steps before it reaches the end of its journey or runs into contact. In a crowded position, the side with more safe waiting moves can sit still and let the opponent run out first. When a player has only bad moves left, being **on the move** (having to move) is a disadvantage. Checkers players talk about "the move" and "the opposition" for this fight over who must give way. Chess players call a position where any move is bad **zugzwang**, a German word meaning "compulsion to move." Here is the idea in its purest form, a position where whoever must move loses. ```text . . b . b . . . . . w . w . . . . . . . . . . . . . . . . . . . Black men: 3, 5; White men: 11, 13 ``` Black men on 3 and 5, White men on 11 and 13. Nobody has a capture. Look at what each step does: - **Black to move.** Every move loses. After `3-7`, White's man on 11 jumps it `11x2` and is crowned. Black's only remaining piece plays `5-9`, and White's man on 13 jumps `13x6`. Black has no pieces left. The other two Black first moves, `3-8` and `5-9`, lose as well. - **White to move.** The same, mirrored. After `11-7`, Black's man on 3 jumps it `3x10`. White's only piece plays `13-9`, and Black's man on 5 jumps `5x14`. White has nothing left. Whoever has to move steps into a capture, so each side wants the **other** to be on the move. We checked this by listing every move and following every forced reply to the end, so it is a real result, not a trick of the picture. Real games are messier, but the principle is the same. In a locked position, count the safe moves each side has left. If you can make a safe move and your opponent cannot, you win the standoff. This is why a player who has already moved most of their men forward is often in trouble: they have used up their waiting moves. Check yourself before moving on: ```quiz [ {"q": "A White man stands on 6 and Black has men on 1 and 3 with 10 empty. What can Black do?", "choices": ["Nothing, White man is safe", "Jump it with 1x10", "Jump it with 3x10", "Move the man on 3 to 7"], "answer": 1, "explain": "The man on 1 jumps over 6 and lands on 10 (empty). That is the bridge at work. Because the capture is mandatory, Black must jump. The man on 3 does not touch square 6."}, {"q": "Why can a piece on the edge of the board never be jumped?", "choices": ["Edge pieces are protected by a special rule", "A jump needs an empty landing square behind the piece, and past the edge there is none", "Edge pieces are always kings", "Only the center can be attacked"], "answer": 1, "explain": "To jump a piece you land directly behind it on the same diagonal. Behind an edge piece there is no square at all."}, {"q": "In the position with Black men on 3 and 5 and White men on 11 and 13, who is better off?", "choices": ["Whoever is on the move", "Whoever is not on the move", "Black always", "Neither side loses material either way"], "answer": 1, "explain": "Any move steps into a capture, so the player to move loses material. The player who is not on the move wins that standoff."} ] ``` ## Recap 1. A piece can only be jumped if the square behind it is empty, so keep pieces backing each other. 2. Prefer the center (14, 15, 18, 19); edge pieces cannot be jumped but have few moves. 3. The bridge (men on 1 and 3 for Black, 30 and 32 for White) covers every square an enemy man needs to reach before crowning, as long as the landing squares stay empty. 4. Tempo is a count of safe waiting moves; in a locked position the side that runs out first must give way. 5. Having to move can be a burden: a player whose every move steps into a capture is in zugzwang. Next up, [Endgames and the Solved Game](05-endgames-and-the-solved-game.md): kings against kings, and what happens when a computer plays checkers perfectly. --- # Endgames and the Solved Game When the board empties, checkers changes character. Tactics shrink, kings dominate, and the question stops being "who wins material?" and becomes "can anyone force a win at all?" This phase covers the king endgame you will actually meet, and then steps back to the biggest fact about the game: a team of researchers proved that, played perfectly, checkers is a draw. A note on method. The claims below about small endgames come from an exhaustive computer search written for this guide under the exact rules of the site's game: it explores every position reachable from the starting arrangement and labels each one win, loss, or draw. We cross-checked its move generator against the site's own game code on tens of thousands of positions. Treat these as checked facts, not rules of thumb. ## Kings are hard to catch A king moves in four directions, so it can slip away from almost anything. Catching one takes several kings working together, and the first thing to learn is what "caught" looks like. A king is trapped when it has **no legal move**: every neighbor square is blocked, and every jump it could make is blocked too. ```text . . . . . . . . . . . . . . . . . . . . . . B . . . B B . . . W Black kings: 23, 27, 28; White kings: 32 ``` White to move, and White has no legal move, so White loses. The lone White king on 32 sits in a double corner. Its neighbors are 27 and 28. Black's king on 28 blocks one and cannot be jumped, because beyond it is the edge of the board. Black's king on 27 blocks the other, and White cannot jump it, because the square behind it, 23, is occupied by a third Black king. Three kings, one trap. The same idea works in the other double corner, 1 and 5. ## Three kings against one: a forced win Here is the useful fact. **Three kings beat one king from every starting arrangement, as long as the three-king side is to move, and the win never takes more than 15 moves.** That is well inside the rule that lets a player claim a draw after 40 moves each without a capture or a man move, so the win is real, not only theoretical. The technique is to herd the lone king toward a double corner or the edge and then close the net, with each of your kings guarding a square your other kings need. You do not need to memorize the maneuvers. You need to know that the win exists, so you do not give up a position with three kings against one, and so you do not trade into this ending when you are the one with the lone king. ## Two kings against one: it depends Two kings are not enough to win from every arrangement. Our search found that the two-king side wins from the large majority of arrangements, and that the lone king survives with a draw from a minority of them. For example, Black kings on 1 and 2 against a White king on 15, with Black to move, is a forced win for Black, but it takes 17 moves of careful play. What decides these positions is the idea from Phase 4: who is forced to move into a worse square. A lone king that cannot be herded into a corner draws, and one that can be herded loses. If you have two kings against one in a game, play for the trap, but do not assume it works from every start. ## What "solved" means A game is **solved** when the correct result with perfect play is known. Researchers use three levels: - **Ultra-weakly solved:** the result of the starting position is known, perhaps by a clever argument, but nobody knows how to achieve it. - **Weakly solved:** the result is known, and there is a strategy that achieves it from the starting position against any opponent. - **Strongly solved:** the correct result is known for every legal position, not only the starting one. Checkers is **weakly solved**. ## The Chinook proof Jonathan Schaeffer and his colleagues at the University of Alberta wrote the checkers program **Chinook** starting in 1989. On July 19, 2007, the journal *Science* published their paper online (it appeared in the print issue of September 14, 2007) "Checkers Is Solved." The result: **with perfect play by both sides, the game is a draw.** It was an enormous computation. Checkers has about 5 x 10^20 possible positions (500 billion billion). The team combined a proof search through the opening and middlegame with databases of endgame positions, every position with 10 or fewer pieces on the board (about 39 trillion of them). Two things the result does **not** mean: - It does not mean every position is known. Weak solution is about the starting position. Chinook has not labeled all 5 x 10^20 positions. - It does not mean checkers is boring or that human games end in draws. Humans do not play perfectly, and the games you lose are lost to mistakes, most of them tactical. Everything in Phases 2 and 3 still applies. The proof method is the same family of ideas as every game-playing program: search the tree of moves, evaluate the leaves, and use stored endgame knowledge to cut the search short. [How Computers Play Games](/guides/how-computers-play-games) teaches those ideas from the ground up, and its [fifth phase](/guides/how-computers-play-games/5) covers how games get solved. ## Where to go from here Play. The site's [play checkers](/games/checkers) page gives you an engine to practice against, with a coach mode if you want help finding your legal moves. A good first goal: win a game by a shot, with the sacrifice, the forced reply, and the multiple jump all happening on the board in front of you. A good second goal: reach a three-kings-against-one ending and trap the king in a double corner. Sources for this phase: the paper J. Schaeffer et al., "Checkers Is Solved," *Science* 317 (2007), pp. 1518-1522, [doi:10.1126/science.1144079](https://doi.org/10.1126/science.1144079); the University of Alberta's [Chinook page](https://webdocs.cs.ualberta.ca/~chinook/); and the [American Checker Federation rules](https://www.usacheckers.com/rulesofcheckers.php). Check yourself before moving on: ```quiz [ {"q": "In the trap diagram, why can't White's king on 32 jump Black's king on 27?", "choices": ["Kings cannot jump kings", "The square behind 27 on that diagonal, 23, is occupied", "White's king is not allowed to move backward", "27 is a light square"], "answer": 1, "explain": "A jump needs an empty square directly beyond the piece. Square 23 holds another Black king, so there is nowhere to land."}, {"q": "Which statement about three kings against one king is true under these rules?", "choices": ["It is always a draw", "The three-king side wins from every arrangement when it is to move", "It is a win only if the lone king is in the center", "The lone king always escapes to the main road"], "answer": 1, "explain": "An exhaustive search shows the three-king side wins from every arrangement when it is on the move, in at most 15 moves."}, {"q": "What does it mean that checkers is 'weakly solved'?", "choices": ["Every possible position has been labeled win, loss, or draw", "The result with perfect play from the starting position is known, along with a strategy that achieves it", "A computer can beat every human", "Only the endgame has been studied"], "answer": 1, "explain": "Weak solution covers the starting position: perfect play leads to a draw, and there is a proof. Labeling every position would be a strong solution, which has not been done for checkers."} ] ``` ## Recap 1. A king is trapped when it has no legal move, including no legal jump; a double corner makes this possible with three kings. 2. Three kings beat one king from every arrangement when the three-king side is to move, within 15 moves. 3. Two kings against one is not automatic: it wins from many arrangements and draws from some. 4. A game is weakly solved when the result of the starting position, with a strategy to achieve it, is known. 5. Chinook (Schaeffer et al., Science, 2007) showed that checkers is a draw with perfect play, and that does not mean the games you play are drawn. You have reached the end of the checkers ladder. If you want to see how a program decides on a move, read [How Computers Play Games](/guides/how-computers-play-games).