Lessons from my games - converting winning positions

 "The hardest game to win is a won game."
- Emanuel Lasker

This quote exists for good reason. Almost every chess player has undoubtedly had those painful experiences of being completely winning, knowing that you are completely winning, but then somehow failing to actually win the game - or even worse, losing! In fact, this is a universal struggle, no matter what your rating is. As it turns out, even though it sounds like it should be easy, converting winning positions can be very challenging - both because chess is a hard game, and also for psychological reasons.

In what is a long overdue post, I will try to share some wisdom and practical advice, giving many examples from my own games so we can learn from not just my own mistakes, but those of my opponents as well.

And you have been warned - since this is an important topic, this will be an extra-long post!

Let's start with some basics - the way I think about it, there are a few different types of "winning" positions:

1. Positions you can win very easily, practically in your sleep, against any player no matter how strong they are. I'm talking about the completely trivial situations where you are up an overwhelming amount of material (as in, you've taken all your opponent's pieces) with absolutely zero counterplay, or you are, for example, mating with queen and king versus king, or you have a theoretical king and pawn endgame or Lucena position that you know stone cold is winning, and you know exactly how to win it.
   
   For example:
   
   

   

   A very easily winning position

   
   As long as you have just a basic understanding of king and pawn endgames (which hopefully the majority of readers do), you can win this position with 5 seconds on your clock (plus some increment or time delay) against anyone, even an engine. There's basically no calculation required.
   
   
2. Positions where you know that you have a decisive material advantage, but there is still some "technique" left to do.
   
   These types of positions will range in difficulty, depending on how much of a material advantage you have and how simplified or imbalanced the position is.
   
   An easier example:
   
   

   

   A little technique still needed, but fairly easy

   
   Here white is simply up a bishop for only one pawn, and there's not much else going on. White still has to show some technique - i.e., not carelessly letting black's rook take all of your pawns. But winning this should not be too difficult.
   
   A somewhat harder example:
   
   

   

   Some more technique needed, please

   
   You can look at this position and see that white has a queen for a rook and knight, and even an extra pawn too, and conclude that this surely must be (easily?) winning. And you would be correct - this is a winning position. And you would think that it should be easy. But you might be surprised to know that I actually failed to convert this against someone 300 points lower rated! More on that game later.
   
   But, however easy you think this position with the Q+P vs. R+N should be, you probably can appreciate that it isn't quite as simple as the previous example where we just had an extra bishop with more limited material. And I think it is good to be aware of exactly why it is not quite as straightforward:
   
   (a) Material is not as simplified - i.e., not as many pieces have been traded off
   (b) There is more of an imbalance
   
   The following position can be even trickier:
   
   

   

   Those queenside pawns surely will never be dangerous ... right?

   
   Black is up a "clean" exchange for no pawns, but the structural imbalance makes this not completely trivial. This is exactly the kind of position where if you get sloppy, strange things can happen. And in fact, this position came from a blitz game I had against another player 300 points lower rated, where I even managed to lose this as black!
   
   Rule #1: In general, the more simplified and less imbalanced a winning position is, the easier it is to convert.
   
   That may sound obvious to some, but we forget this rule more often than we realize, which can lead to horrible mistakes.
   
   
3. The third type of winning position is a little more advanced. These are the positions where you know you have some decisive positional advantage, but you are not up any material.
   
   Here's a prime example, also from one of my own games (white against a 2000 player in a rapid time control):
   
   
   

   

   White has a dominating position, but it still has to be converted

   
   White has a decisive advantage, despite not being up any material. (I think this should be clear to anyone over 2200, but if you are not convinced, you can check with an engine to confirm this is between +2 and +3.) Now, I am a strong enough player that during the game, I understood I was winning here. However, just understanding that doesn't automatically give you the full point. White needs to act with some urgency here to win material before black eventually organizes his pieces to better squares.
   
   A strong move here is 24.e5!, aiming to trap the Nh5 next move with g3-g4 and hitting the c6 pawn. Of course I saw that idea, but I didn't want to calculate the ramifications of 24. ... f6!? or even 24. ... g5!?, when I thought there may be some tricks against my loose minor pieces on the e-file or my Rd6 and Kh2 being on the same diagonal. However, accurate calculation will establish that white is maintaining control and close to winning material after 24. ... f6 25.Nc5! or 24. ... g5 25.Nbd4! (although I wouldn't say it is completely trivial).
   
   Instead, I played the prophylactic 24.Kg1?! and after 24. ... Rc7 25.e5 Bf8 made the further mistake 26.R6d2? when suddenly after 26. ... Rac8! black was well on his way to generating some activity with ...c5-c4, and the game became unclear. Later I was even losing before eventually winning on time. (Instead of 26.R6d2?, white keeps a decisive advantage with 26.g4! Nhg7 27.Ng3! +- offering the exchange to prevent black from organizing ...c5-c4. But I did not sense the urgency in preventing black from activating his pieces.)
   
   In this situation, I find it helpful again to clearly put into words why white was winning here. It's not an advantage in material, nor is black's king permanently weak. No, it's because white had an overwhelming advantage in piece activity. But this is, strictly speaking, not a permanent feature like being up a bishop, which is the important distinction between Type 3 and Type 2 winning positions. More on this later.
   

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Now, let's dive in to how and why we mess up winning positions, and what we should do instead to convert them. Incidentally, I think having a good understanding of this also helps when you are resisting in lost positions.

Why we can fail to convert winning positions:

1. Relaxing too early

One reason we may relax too early is that we think a position should be "easily winning" while forgetting the most important Rule #1. Being up a full exchange with symmetrical pawn structure is usually very easy to convert, especially with pawns on both sides of the board. However, being up the exchange with both sides having passed pawns is not as simple.

The second reason this happens is when facing lower-rated players, because you do not expect as much resistance and just assume that your opponent will collapse soon. This is very dangerous thinking!

To see how much this matters - consider the following position:

Paciorkowski-Smith, Albany 2018

This came from the final round of the 2018 New York State Championship, and my opponent is a strong player - a grandmaster - who I knew would not go down without a fight. I would describe this as a Type 2 position which is not that easily winning. How did this game go? Well, I converted this without giving my opponent a single chance to save the game, despite his very stubborn defense.

Yet, the same person who played this nearly flawless endgame against Smith failed to win the below position, also in a classical game, against a 2100 player!

Paciorkowski-Kharroubi, Rochester 2021

"How can that have happened?", you might wonder. Well, against Smith, I was not relaxed at all; rather, I calculated variations almost every single move to make 100% sure I was controlling all of black's possible counterplay. I never assumed I would "just win" until he stopped the clock and shook hands.

Meanwhile, against Kharroubi, I played way too nonchalantly, just assuming that something would happen and my opponent would fall apart eventually. This made me lazy, not wanting to calculate many variations (something else we will discuss). After missing several forced knockouts of varying degrees of difficulty, we eventually ended up in this position:

Paciorkowski-Kharroubi, Rochester 2021

Incredibly, black has a fortress, and I had to acquiesce to a draw eventually. This debacle was entirely psychological! Had I not relaxed, and instead calculated variations with the same rigor and precision as I had against Smith, my game against Kharroubi almost certainly would have gone differently.

We are all vulnerable to relaxing too early against lower-rated players - whether you are a 1700 trying to convert against a 1400, or a 2400 trying to convert against a 2100.

2. Inability or unwillingness to calculate variations

Here's the unfortunate truth to Type 2 and 3 winning positions:

Rule #2: Unless you have a Type 1 winning position, never expect to win without having to calculate "potential" counterplay, which will invariably be connected with either creating/promoting passed pawns or attacking your king.

The point is that there almost always will come some critical moment(s) where you have to allow what may look like dangerous counterplay, but concretely does not work for tactical reasons. Calculation is most important in these critical moments.

As a simple example - pawn races. Your opponent may have a dangerous-looking passed pawn, but if you calculate the variations, you may see that you simply promote faster and will be winning. Here it is OK to "allow" the opponent's "counterplay" because it concretely does not work. You very rarely will be able to convert a winning position without having to allow something that looks like counterplay - especially if you are up against a stronger player who is defending stubbornly.

In general, the more imbalanced and less simplified the position is, the more important this rule is. Let me give you an extreme example:

Stolyarov-Paciorkowski, New York 2022 (white to move)

This was a 25-minute game (I was black), and my opponent is rated around 1950. It doesn't really matter what happened earlier in the game, but white is winning here. And I mean really winning, with an extra rook and no obvious threats against the king on g1 (engine gives about +6!). However, despite the huge material advantage, this still counts as a decidedly tricky Type 2 position. You will not be able to win this without calculating, as black still has many dangerous ideas to try and attack the king (i.e., counterplay). And you'd better believe that I will throw the kitchen sink at the king on g1, pulling every trick I know of trying not to lose. Black's attacking ideas ultimately do not work, but you must calculate variations to find the proper defenses.

The game continued 34.Rf3 (a good move, letting the Kg1 run away) 34. ... Nf5!? 35.exf5 Qh4 36.Rcc3?! (still winning, but there was nothing to fear in 36.Nxc8! Qh2+ 37.Kf1 Qh1+ 38.Bg1! +-) 36. ... Bxf5 37.Ne6! Qh2+ 38.Kf1 Bh3!? (D)

This bishop can simply be taken - in case of 39.gxh3! g2+ 40.Ke1! g1=Q+ 41.Bxg1 Qxg1+ 42.Kd2 +- the queen by herself is not able to cause any harm and white's king escapes safely. Instead, white panicked and played 39.Ke1?! Qh1+ 40.Kd2? (40.Rf1! Qxg2 41.Rcf3! +- was the only way to keep a winning advantage at this point) 40. ... Qxg2+ 41.Kc1 Qh1+ 42.Kc2 Bf5+ 43.Kd2 Qg2+ 44.Kd1 (D)

Black now has a perpetual (although I still wanted to win this game). I continued with the last-ditch attempt 44. ... a3!? and after 45.c7?? (45.bxa3 and I would have had no choice but to make perpetual check) 45. ... axb2 black is suddenly winning. 46.Rb3 b1=Q+ 47.Rxb1 Qxf3+ 48.Kd2 Qd3+ 49.Ke1 Qxb1+ 50.Ke2 Qd3+ 51.Ke1 Bg4 0-1 and white had to resign.

Perhaps my most ridiculous swindle. How did this happen? White had multiple opportunities on moves 36 and 39 to win even more material which would have limited my attacking ideas. Even on move 40, white could have found the cool-headed 40.Rf1! to defend. But these variations did require some precise calculation to make sure that I am not winning by promoting the g-pawn or throwing in a sudden ...e5-e4.

In this case, I do not think my opponent lacked the skill to calculate these lines (something that can and should be trained). Rather, he was unable to calculate because he had no time. When he played 34.Rf3, he had only 1 minute on his clock (there was a 5 second delay, but that's not much in this kind of position) to my 8 minutes. By the time I threw in the unexpected 44. ... a3!?, he was down to 3 seconds, at which point anyone, even Magnus Carlsen, can make horrific blunders.

Of course, there are other reasons why you may find yourself unable to calculate well. Perhaps you are distracted during the game, or you didn't eat/sleep well and have trouble focusing.

But on the topic of time pressure, this brings us to another important reason why we mess up winning positions:

3. Bad time management

Since we now understand that you will still need to calculate some variations to convert Type 2 or 3 winning positions, it goes without saying that if you leave yourself with no time to do so in critical moments, you dramatically increase your risk of throwing the game away.

Rule #3: Good time management is a necessary part of conversion technique.

In my swindle against Stolyarov, I would not say his real mistakes were on moves 36, 39 or 40. Instead, I would say his mistake was spending too much time earlier in the game on decisions he could have and should have made quickly. Even though his chess moves were good then, leaving himself with only 1 minute to convert a still tricky position ultimately cost him the game.

I'll also say this:

Rule #4: Don't beat yourself up too hard for failing to convert in fast time controls.

Because of the importance of calculating variations, we should now understand that this is just inherently difficult in blitz. If you only have 3 minutes for the whole game, of course you will not play perfectly. Even strong GMs have blundered away completely winning positions in blitz or rapid games, sometimes in comical fashion. So in these faster time controls, accept these conversion failures as a part of life. The faster you can calculate and the better your intuition, the better you will be at converting in blitz games - but you will still have your fair share of mess-ups.

However, in classical tournaments, where you have 1, 2 or even 3 hours for the whole game, there are no excuses for improper time management. In these longer games, time management is a skill that needs to be developed like any other, so that you always leave yourself with enough minutes on the clock to convert a winning position.

One more reason why we fail to convert winning positions:

4. We get nervous

Consider the following example:

Nikolayev-Paciorkowski, Rochester 2013 (white to move)

I played this game (as black) when I was 14 years old, with a rating around 1800. My opponent is a strong FM who out-rated me by about 600 points. Somehow, I had managed to outplay him earlier and reached what I knew should be a completely winning endgame (although I had missed multiple knockouts earlier), up an exchange and several pawns.

Just watch what happened: 49.Rxc5+ Kxc5 50.Nd3+ Kd4 51.Nxf4 Ke4?? 52.Nxg2 1/2-1/2

I even remember feeling lucky after 52.Nxg2 that my opponent offered a draw, since I felt like I would even find a way to get checkmated by white's lone knight in that position.

Needless to say, I was very nervous in this game. It was the first time I ever had a winning position against such a high-rated player, and I remember my heart racing at the time in disbelief. These nerves ultimately caused me to make a ridiculous blunder that under normal circumstances I would never make (time pressure also played some role).

Now today, I will admit that I still do get a little nervous when I have a winning (or even just clearly better) position against a strong grandmaster. I have also been on the other side of the coin, having a completely lost position against a super talented but clearly nervous kid, and escaping with a draw or even a win.

This is not only limited to kids - I've seen plenty of adults get nervous too when they know they are winning against much higher-rated opponents. Ultimately, I think this is a psychological phenomenon which gets better with playing experience.

Rule #5: Forget about your opponent's rating; focus only on the position in front of you.

(Easier said than done, of course...)

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Now that we understand the different types of winning positions and why we fail to win them, what should we do properly convert decisive advantages?

How to win a winning position:

I'll share my theory here in the last few rules:

Rule #6: Your goal is always to convert a winning position to one of "lower type".

Remember the three types of winning positions:

1. You have a clearly overwhelming material advantage with absolutely zero counterplay (i.e., you captured all your opponent's pieces), or you have a theoretical endgame position which you 100% know how to win.
2. You have a decisive material advantage, but it's not so simple that you can just win it with your eyes closed. Your opponent still has some pieces which could create counterplay.
3. You have a decisive non-material advantage which is often temporary in nature (e.g., more active pieces or a safer king).

So, suppose you know you have a dominating position (Type 3), but material is still equal. Then your primary focus is to win a decisive amount of material (or checkmate, if that is possible), transforming to a Type 2 position. (There are a few other important notes about Type 3 positions that we will touch on next.)

Or, let's say you have a Type 2 position, with what you know is a decisive material advantage. Your goal is to simplify the position into something elementary, often by trading pieces or winning even more material, until you get to a Type 1 position.

Rule #7: Feel some sense of urgency in Type 3 positions, but at the same time, do not "cash in" too early.

This one is difficult and in my opinion is trained mainly from experience. Consider the example below:

Black to move

Although material is equal, black has a decisive advantage because of white's passive pieces and weak king. We should feel some sense of urgency to win material, but we also do not want to settle for too little. In the game, black found a way to win a pawn: 28. ... Rxd4? 29.Bxd4 Qc2+ 30.Kf1 Qxb3 31.Qh3! suddenly white's pieces have new life, with a strong bishop on d4 and the queen ready to invade on d7.

Black should still be winning there with an extra pawn, but it would have been much stronger to build the position with a move like 28. ... Ba5!, activating the otherwise dormant Bc7. We will then continue to make threats or otherwise improve our position and trust that there will eventually be an opportunity to win a clearly decisive amount of material, more than just a pawn.

Unfortunately, it is not always obvious how to tell if you are cashing in too early. I think you build some intuition from experience, but in general I would note the following:

(a) If you have a dominating Type 3 position but don't see a clear knockout (e.g., winning a piece or checkmating), prioritize activating your last piece over winning a small amount of material.

(b) Be suspicious of variations where you win only a small amount of material but your opponent's pieces suddenly become active.

Rule #8: Do not hurry in Type 2 positions, and prioritize calculating variations to limit your opponent's counterplay.

When you have a permanent material advantage, you can afford not to rush, and will win by restricting your opponent's counterplay while thinking of ways to win still more material, simplify the position or otherwise transition to a Type 1 position.

But you still must be prepared to calculate! See Rule #2.

Rule #9: Improving your knowledge of theoretical endgames will expand the range of positions that are "Type 1" to you.

A simple example to illustrate - suppose you have what you know should be a decisive material advantage, and at some point in your calculations you see that you can force the position below:

(White to move)

Is white winning? And if so, how? If you know the theory behind opposite color bishop endgames, you will understand pretty quickly that white must be winning, since black cannot stop the pawns with the bishop on the same diagonal. However, if you lack this endgame knowledge, you will be unsure of how to evaluate this, and may miss an opportunity to go from a Type 2 to a Type 1 position.

To get better at converting winning positions, it is a useful investment to regularly expand your knowledge of theoretical positions which you can have in the future as being Type 1 to you.

Last but not least:

Rule #10: In Type 2 positions with reduced material, look out for unexpected fortresses or stalemate tricks.

My game against Kharroubi, seen earlier, is an example of an unexpected fortress.

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So to recap our 10 rule theory of converting winning positions:

1. In general, the more simplified and less imbalanced a winning position is, the easier it is to convert.
2. Unless you have a Type 1 winning position, never expect to win without having to calculate "potential" counterplay, which will invariably be connected with either creating/promoting passed pawns or attacking your king.
3. Good time management is a necessary part of conversion technique.
4. Don't beat yourself up too hard for failing to convert in fast time controls.
5. Forget about your opponent's rating; focus only on the position in front of you.
6. Your goal is always to convert a winning position to one of "lower type".
7. Feel some sense of urgency in Type 3 positions, but at the same time, do not "cash in" too early.
8. Do not hurry in Type 2 positions, and prioritize calculating variations to limit your opponent's counterplay.
9. Improving your knowledge of theoretical endgames will expand the range of positions that are "Type 1" to you.
10. In Type 2 positions with reduced material, look out for unexpected fortresses or stalemate tricks.

Endgame Corner 2: R vs. B with 1 pawn each

Welcome to the second edition of Endgame Corner, where we will be taking a deep dive into a different fundamental theoretical endgame each week. As with last week, our goals are to:

1. Learn key positions for each endgame, and their evaluations
2. Know which fortresses can be constructed by the defending side, and how to break any apparent fortresses.

Last week, we examined the pure rook vs. bishop endgame with no pawns. Recall there that the defending side can hold a draw quite easily by keeping the king in the opposite color corner of the bishop. The endgame is lost if the king is trapped in the same color corner as the bishop, or if the stronger side can get the opposition in the right situation, leading the rook to tactically dominate the bishop.

For this week, we will extend this topic to rook vs. bishop with one pawn each.

If the stronger side's pawn is a passed pawn, then the position as a rule is always winning, except if it is an a- or h-pawn. For example, the below setup is a useful fortress to know:

Position 1 (white to move)

This is a very easy draw to hold. Black can just sit and do nothing, moving the bishop back and forth along the a2-e6 diagonal. White can never force a mating net, nor be able to force the promotion of the h-pawn. The only thing black should be mindful of is not to carelessly allow white to achieve a pawn on h7 + king on h6 (which you already have to be quite cooperative for), but even then, as long as you can meet Kh6 with moving the bishop to the b1-h7 diagonal, the h7 pawn will be lost.

If black had a dark squared bishop, it is still a draw, as long as white cannot establish the pawn on h6 -- black should use the bishop at the right moments to take that square under control. If white does get the pawn to h6, then the position is winning by forcing a trade of the h6 pawn for the f-pawn, resulting in a pure R vs B ending with the defending king in the wrong color corner.

For other situations where the pawns are on the same or adjacent files, the most important principle of defense is to keep your pawn on the opposite color square as the bishop. If the defending side's pawn stays on the same color as the bishop, then the position is almost always losing, because the stronger side's king will be able to invade and then ultimately sacrifice the rook for the bishop+pawn to reach a winning king and pawn endgame

Although it looks a little scary when you see it for the first time, the kind of position below is a fortress:

Position 2 (white to move)

All black needs to do is not to allow the white king to touch the g6 pawn. The bishop can control f6 and g5 when needed, and f5 and h5 are covered by the pawn itself. This means that black must maintain control of f7 using the king. So after 1.Rc7+ Kg8! (or 1. ... Kf8) 2.Kd5 Bf6 3.Ke4 Bg7 4.Kf4 Bf6! black can always make sure that the white king is not allowed to directly attack the g6 pawn.

Now, it is actually important in this kind of position that the bishop has enough squares on the long diagonal not to end up out of moves. If the defending side's pawn is advanced just one square further, sometimes it is possible to break the fortress with zugzwang, as in the unfortunate case below:

Position 3 (white to move)

This position is winning for white! First, you have to understand that the goal is to get the white king to attack the g5 pawn. Then, you can work out the technique required to force the bishop away from the defense of the f5 square. This is done as follows: 1.Kd4 Bc2 2.Ke5 Bd3 3.g4 (useful just to gain a little more space and control h5 from black's king) 3. ... Bc2 4.Rb5! Kg7! (trying to open the g6 square for the bishop) 5.Rb7+! (forcing black's king back to g6, since black still has to prevent white's king from reaching f6) 5. ... Kg6 now white goes after the bishop 6.Rb2! Bd3 7.Kd4! Bf1 (only square!) 8.Rb6+ Kg7 9.Ke4! and black cannot prevent Kf5, after which white picks up the g5 pawn and has a winning position.

Endgame Corner 1: Rook vs Bishop

Welcome to the first edition of Endgame Corner, where we will be taking a deep dive into a different fundamental theoretical endgame each week. The idea is to accumulate a steady base of knowledge across a wide variety of endgames, with two specific goals:

1. For each endgame, to know the evaluation of certain key positions.
2. To know which fortresses the defending side can construct, or how to break down setups which may seem like impenetrable fortresses.

This is a key part of any strong player's toolkit, as frequently in a complex endgame we face moments where we can force a simplification to a theoretical position we may have studied. If we have exact knowledge of which theoretical positions we should be aiming for and how to win or draw them, it makes playing the more complex endgames that much easier.

We will begin with the most basic of positions, and will progressively be able to graduate to more complex positions once we know the basic ones.

For this week, our topic is: rook versus bishop (no pawns).

This should already be well-known to more experienced players but it is always good to practice the cases where the defending side goes wrong - you can definitely set up small tricks in a practical game.

Position 1 (black to move)

In the worst-case scenario, if the defender's king is cut off to the back rank, the position is drawn as long as defender's king is in the "safe corner" of the opposite color as the bishop. In this situation, 1. ... Rh2 2.Bf5 (white can move the bishop to any safe square along the b1-h7 diagonal) 2. ... Rh1+ 3.Bb1= and any rook move on the first rank would be stalemate.

There is also no way for black to create a zugzwang here, as the bishop will always have several safe squares to move to along the b1-h7 diagonal.

If black maneuvers the rook to give a check on a2, white will slide the king to b1, and any rook move back along the 2nd rank will allow white to put the king back on a1. For example: 1. ... Rh2 2.Bf5 Ra2+ 3.Kb1 Rf2 4.Bh7 Kb3 (if black keeps attacking the bishop it will just keep running away, staying on the b1-h7 diagonal, and checking on the first rank allows Kc2, escaping) 5.Ka1= back to the safe corner.

Finally, black could try to put the king on b3 and then give check with the rook along the a-file, forcing white's king to b1, and then try switch the rook back to "pin" the bishop to checkmate along the first rank. But even if black succeeds in making this "pin", white always has Bc2+ (an important resource) to escape. For example, from Position 1: 1. ... Kb3 2.Bf5 (white need not even play Bd5+) 2. ... Rf8 3.Bh7!? (just to illustrate even the "worst"-case scenario) 3. ... Ra8+ 4.Kb1 Rh8 5.Bc2+ Kc3 (5. ... Ka3 6.Ka1= is familiar to us) 6.Bf5= (or anywhere safe along the b1-h7 diagonal) and black is no longer threatening checkmate.

The main "trap" to be careful of here (and why you should always play it out in a real game, to test your opponent) is the following, still from Position 1: 1. ... Kb3 2.Bf5 (following our rule, just keep the bishop on this diagonal) 2. ... Ra8+ 3.Kb1 Rf8 and if white tries to be "clever" with 4.Bd3?? (instead 4.Bc2+ Kc3 5.Be4= holds) then 4. ... Rf2! (D) leads to an instructive winning domination position for black (although it is not immediately obvious that it is winning):

Position 2 (white to move)

White would need to be giving a check along the a2-g8 diagonal to save the game, but because of the unfortunate placement of the bishop on d3, this is not possible (although we wouldn't even be getting to this situation had we followed the simple rule to give check on c2 after 3. ... Rf8). After 5.Ka1 Ra2+ 6.Kb1 Rd2 -+ black wins the bishop, and the threat is anyway to play Rf2-d2. In case of 5.Kc1 Kc3! white is forced into 6.Bb5 (6.Ba6 Ra2 -+) when now 6. ... Rf5! forces back 7.Be2, and finally 7. ... Rg5! (D) dominates the bishop, winning it:

Position 3 (white to move)

This position really makes you appreciate why the rook is so much stronger than the bishop in an endgame. White loses the bishop after any of 8.Kb1 Rg1+ 9.Ka2 Rg2; or 8.Kd1 Rg1+; or 8.Bd1 Rg1; or 8.Ba6 Ra5.

So, going back to Position 2, the most resilient defense is to try and hide the bishop with something like 5.Ba6, but then 5. ... Rd2! 6.Kc1 (forced) 6. ... Rd4! (D) is another key position:

Position 4 (white to move)

On 7.Be2 or 7.Bf1, black is able to force the domination seen in Position 3 (it is a good exercise to practice it so that you know how to execute it properly). For example: 7.Bf1 Kc3! first setting up opposition so that there will be mate threats on the back rank 8.Be2 Rd2! 9.Bb5 Rd6! 10.Bf1 Rf6 11.Bb5 Rf5! 12.Be2 Rg5 -+. The try 7.Be2 Kc3! 8.Kb1!? is met with 8. ... Rb4+! 9.Kc1 (9.Ka1 Kc2! mates) 9. ... Rb2! and black eventually will achieve the Position 3 domination.

So from Position 4, more resilient is 7.Bb7 (7.Bb5 is similar), when black wins by setting up a second type of domination: 7. ... Kc3! again first setting up opposition for mate threats - the bishop is now confined to the b, c, or d-files as otherwise black can fork/pin it to checkmate 8.Bc6 (black is making good use of the temporary fact that white's king could not have escaped the mating net with 8.Kb1 because of the fork on b4) 8. ... Rd6 9.Bb5 Rd5 10.Bc6 Rc5 11.Bd7 Rc7 (D)

Position 5 (white to move)

The bishop is trapped. Either it goes off the b, c, or d-files and is pinned/forked to checkmate, or it is captured after 12.Bb5 Kb4+.

This second type of domination seen in Position 5 will help you appreciate why the endgame is lost if the defender's king is in the "dangerous corner" - the same color as the bishop:

Position 6 (black to move)

In this situation, if black ever checks on the back rank, blocking with the bishop on f1 will not lead to stalemate after a waiting move by the rook, but instead force Kh1 Rxf1#. But if black tries to go for mate directly with 1. ... Ra2? then 2.Kf1= and white will escape (2. ... Kf3 3.Ke1 Ke3 4.Kd1=). Instead, black wins by setting up a similar kind of domination to the one seen in Position 5 (another good exercise to practice, so that you know you can execute it properly): 1. ... Rf8! (other options also win; this is just the fastest) 2.Bh7 Rh8 3.Bg6 Rh6 4.Bf5 Rc6! and white is out of defenses, as the desired 5.Kf1 allows Rf6! pinning and winning the bishop.

Last but not least - white would still be OK if the king was cut off only "near" the dangerous corner, without actually being trapped in it yet. For example:

Position 7 (white to move)

We should be careful, and notice that black is planning 1. ... Rf3!, which would be attacking the bishop and simultaneously threatening ...Rf2+ followed by Kg3, trapping our king in the dangerous corner. For example, black to move here wins after 1. ... Rf3! 2.Be4 Rf2+ 3.Bg2 (3.Kg1 Kg3 and black will win as in Position 6) 3. ... Re2 4.Kg1 Kg3 -+

But as long as the bishop stays off the f-file, white is OK. We will hold the draw after 1.Bc8 Rc3 (in a practical game, black could also try to be tricky with 1. ... Rg8 hoping for 2.Bf5?? Rf8! followed by Rf2+ and Kg3) 2.Bb7 Rc2+ 3.Kg1 Kg3 and importantly, black does not yet have the rook on f2, so white escapes with 4.Kf1!=