Mathematical Problems, 3A - The Value of Pi

Back when I was doing my A-levels, I remember learning about how it's possible to evaluate pi in various ways, one of which was through calculus.  I can only remember the basics, and I'm sure I can't recall how to do it now - at least not without some help!

The value of pi is the ratio of the circumference of a circle (the distance all the way around the outside of the circle) divided by the diameter (the straight-line distance from one side to the other, through the centre).  It's been known historically to be about 3, but I'm going to make some approximations from first principles.

Firstly, drawing a square around a circle, so that the square touches the circle.  See the diagram above, with the square ABCD around the circle.

If the diameter of the circle is d, then the perimeter of the square is 4d.  We can see by inspection that the square's perimeter is longer than the circle's circumference, and we've called the circumference pi d.  Therefore, we know that pi is less than 4.

It's not a dramatic result, I know, but it's a start!

Next, we need to look at setting a minimum value for pi, and we'll look at this next time.

Mathematical Problems, 2 - The Tetrahedron Path

In this article, I want to provide another puzzle, and the solution to it (you'll need to look closely at the diagram below to understand the solution).  This follows on from my previous post, which was a puzzle about a spider and a cube.  The spider was a mathematical spider, and she wanted to walk around all 12 edges of a cube, in both directions (i.e. from left to right and then right to left) in a single continuous path.  In the original puzzle (devised in a BBC Micro maths adventure game), you had to tell the spider to turn either left or right at each corner.  Now I'm a little older, I use a pen and paper and a diagram...

Following on from the cube, I set myself the challenge of doing the same for a tetrahedron.  I can't say if it was significantly harder or easier, perhaps a little easier with fewer edges to follow, but here's the solution.  The path through the letters goes along each edge twice, once in one direction and then later in the opposite direction, starting and finishing at the same point.

My next post will be a brief discussion on how to calculate a very approximate value of pi from first principles (by which I mean a few diagrams and some basic geometry).

Here's my solution to the tetrahedron path puzzle:

Mathematical Problems, 1 - The Cube Path

Now that the X-Factory has finished its on-screen cash-making routine, I'm returning to more interesting and productive matters - in this case, a mathematical problem that I first came across nearly 20 years ago.  Yes, I'm that old.

This puzzle was posed as part of a text-based adventure game (remember them?) with a strong mathematical bias - you had to solve certain problems in order to progress through the game.  If I remember rightly, for each part you solved, you were given an item or a shape that would come in useful later in the game.  The game was on the school's Maths Club's BBC Micro, and although I can't remember what it was called, there was one puzzle which I didn't solve at the time (although a friend of mine, James Leeson,did, after we started working on it together).  The puzzle recently resurfaced in my mind earlier this week, and I sat down to apply myself to solving it.

Anyways, enough preamble.  In the game, you met a spider, who had a challenge.  She wanted to walk along each of the 12 edges of a cube in a single continuous path that would take her along each edge twice - once in each direction.  You weren't allowed to go directly back on yourself (i.e. reverse) but at the end of each edge, you had to type in if you wanted to turn left or right.  Although the problem didn't specify that you had to start and finish at the same point, this becomes evident through the symmetry of the problem.  And you have to walk along each edge twice (once in one direction, and once in the reverse) otherwise you're guaranteed to hit a dead end.

I can't say much about the theory behind the solution - or if there's more than one solution - but here's mine (and I'm quite proud of it, nearly two decades later).  Start with A and follow each letter sequentially.  If you label each edge with an arrow as you go along, you'll see that it's a valid solution.

Next time... the same puzzle for a tetrahedron!

Cheryl vs Wagner, 21 November 2010

Well, it's good to see the X Factory machine in full swing.  Last Saturday's X Factory Pantomime was filled with all the usual comments, criticisms and crowing that we've come to expect, and in addition, they even managed to get Jeremy Kyle's audience in too.

Big news was of course Cheryl Cole's desperate attempt to undermine Wagner's fanbase.  Realising that her acts are rapidly losing ground, popularity and votes, she's had to change her tactics in order to try and get him voted out of the show.  I'm pleased to see that it completely failed.  So, she, "doesn't normally have any constructive criticism," for him?  Why should this week be any different, eh, Cheryl?  That wasn't constructive criticism, that was a failed character assassination.  So Wagner pointed out that she used to live in a council estate and she's very lucky.  Her transparent, "You should think about how lucky you are," was a thinly veiled threat, and I'm happy that it didn't work.  Instead, with good grace, Wagner managed to completely turn the tables on her, and came up smelling of roses.

Of course, I'm biased.  Yes, The Sun reports it differently, but the fact remains that Wagner is still in, and this little escapade by CC has not done enough to dent his increasingly loyal fanbase.  I'd have liked to have seen Louis take the sing-off to deadlock, instead of eliminating Paije - if only because it increased the chance of Cheryl losing *another* act, the uninspiring rapper, Cher.

Still, Wagner remains, the votes count must be climbing, and we saw an inspired use of the, "No particular order," line.  More on that next time.

X-factor Update: Wagner to win.

So the previous weekend has seen the first serious contender leave the show, as John was voted out and some of the other less talented (but more entertaining) acts were left in.  Yes, I'm referring to Wagner, and yes, I really do genuinely hope he wins.  Last year, we had Jedward who brought in serious money for Mr Cowell (while they were still on the show, before they started touring) but who were unfortunate enough to get voted out before the final.  Consequently, the public had to wait until Christmas before we could deliver him a poke in the eye in the form of "Rage Against the Machine".  This year, we could deliver a serious prod before his show's even finished - it's just a real shame that we'll have to line his pockets to do so.  Personal preference would be for a *shock* Christian song to be number one at Christmas, but in the meantime, prodding the money-makers and giving them a pause for thought and a bit of a knock to their ego might help.

Until then, I'm backing Wagner.  No, I won't be voting for him, and no, I won't regret the fall of the other acts while Wagner stays in.  Last year, you may recall Simon keeping Jedward in at the expense of some other acts who could sing, so I won't be too upset at the public doing exactly the same.  Instead, I'll be watching the news about the Facebook groups, and smiling with a certain cynicism at Wagner's progress.

New blog in the blogosphere

An unrelated, random and probably interesting post today - a friend of mine has just started a thought-provoking blog, and I can recommend it very highly.  It's Chris Timbey's Blog and he covers a wide range of interesting topics (or will be doing in due course).

Lack of practice leads to poor playing

Well, it must be said that a lack of practice at Chess, and having your mind on other things, really does diminish your ability to play Chess.  I say that, dear reader, about you, knowing that it actually applies to me.  My Kasparov Chess computer, which I can beat at Level 6 at my best, is currently dealing me an education in Chess at just Level 4.  No, I wouldn't rank myself a beginner, I've been playing this game for over 20 years, but at the moment I feel a bit like a starter.

So, if you want to improve your Chess, the best thing you can do is at least practise occasionally, and more importantly, learn from your mistakes (and your successes too - I'll tell you when I next get one!).

X factor results, 10/10/10

"In no particular order," the results of the vote were announced.  The two strongest singers from last night got announced first, then Wagner was in the middle, and we're left with an authentic group, Lady Gaga and Nicolo Festa.  That was a surprise - I thought there were at least two other acts that were more likely to be in the bottom three - but what was less surprising, and actually quite pleasing, is that Nicolo got booted straight out.  Hurrah!  It's quite probable that the British public didn't like his attitude or his character, or his personality (or any combination of the above) - a case of too much X Factor, by the looks of it.  And now we're left with FYD and Lady Gaga.  In a few weeks' time, we'll all need to consult Wikipedia to remember who they were, let alone what they looked like.

The X Factor Pantomime

Okay, so it's really got nothing to do with Chess, at all, but I figure it's time I wrote down some of my thoughts about the X Factor.  I'm biased, I'm opinionated and I thought I'd point out some of its biggest flaws, and the things that annoy me about it, just to see if anybody else feels the same.

Firstly, there's the theme tune, composed by Simon Cowell and some other people.  I wonder how much of the composition is down to Mr Cowell's musical talent, and how much of his writing credit is down to getting royalties every time they play it (once at the start, once at the end, and twice for every advert break).  Just a thought...

Then there's the whole 'making a drama out of nothing'.  When Dermot O'Leary announces the results of the vote, "In no particular order," I will roll my eyes.  Rest assured that the results of the votes are announced in the order that will produce the most drama.  Some of the more shocking results will be given at the start, then the ones that are safer will be announced, then it'll come down to two of the bottom three.  Except that this week, there's a double elimination... well, if they allow in four more acts at the start, they need to get through them fairly quickly, don't they?

Most years, and this year has been no exception, we've had the manufactured boy band and the manufactured girl band.  Take four or five individual candidates and bolt them together as a group.  They suffer from a lack of practice time, and hardly know each other at all, but they shouldn't have to worry too much - after all, they have a good record for getting through to the live TV stages.... but then getting eliminated very quickly.  I sympathise for the authentic groups who can sing well, as their space has just been lost to a cynical marketing ploy.

I'll add just one more thing before closing (and rest assured I've got plenty more to rant about next time) - the cash cow setup.  Not content with aiming for Christmas number one (and such a *shame* they didn't get it last year) the whole setup is to get people to spend money on the vote.  And how much money?  Based on some rough mental arithmetic, if they had, say, 4 million votes for just the final last year, and 35p from each call is straight profit, then that's £1.4million.  Just from the final - not counting any of the previous rounds.  Last year, Jedward (a whole article of their own) were clearly the money-spinners, as people were voting to keep them in, contrary to Simon Cowell's overly loud  protestation (and much money-counting in the background). And yet, when the time came for him to eliminate them - the first chance he got - he kept them in and eliminated Lucie Jones (nobody can remember her, but she was a good singer).  The decision got the press it deserved, in a Daily Mail article and Simon Cowell kept rubbing his hands with glee.

Anyways, I'll close for now, as Joe McElderry has just sung his new song, in a hope to get a number one hit (since he didn't get it last Christmas, and needs all the publicity he can get).

Update

Yes, it's been a long time since I've updated the blog.  Real life getting in the way.  I've joined Chesscube.com, which I recommend for ease of use... all I need to do now is work out how to post my games here without having to do anything lengthy like cutting and pasting!

I've been playing the King's Gambit to good effect as white, so that'll probably be the subject of the next post!

DavidL defends the Patzer as Black

After my previous post, I said I'd give an example of how I've recently defended against the Patzer's Opening.  I've recently joined Chesscube.com and, as in almost all online Chess environments, any player who has no reputation, no ranking and no games played is often seen as easy prey - a Patzer.  My opponent, k_ermin, decided he'd have a go at the Patzer's Opening against me - and I was ready!


Played 29 April 2010, k_ermin vs DavidL

1.e4  e5 
2.Qh5 Nc6 
3.Bc4 g6 
4.Qf3 Nf6

At this stage, we've reached the classic Anti-Patzer position.  Black has successfully defended the immediate threats from White, and has a fairly good king-side development for it, while White is having to mobilise the rest of his pieces.
 
5. d3   Bg7 
6. Bg5  O-O 
7. Bxf6 Bxf6 
8. Bd5  d6 
9. Bxc6 bxc6 
10.Nh3  Rb8 
11.b3   d5 
12.exd5 cxd5 
13.Nc3  e4 
14.dxe4 dxe4 
15.Qe3  Re8 
16.Rd1  Qe7 
17.Nd5  Qe6 
18.Nxc7 Qc6 
19.Nxe8 Bc3+ 
20.Kf1  Ba6+ 
21.Kg1  Rxe8 
22.Qxa7 Qf6 
23.g3   Be2 
24.Rd7  Bf3 
25.Nf4  Ba5 
26.Qxa5 Qa1+ 
27.Qe1  Qxe1# 0-1

Coming up soon: DavidL defends the Patzer's Opening

Yes, I know it's been a long time since my last post, but I've been playing a few games - so that I've got something to comment on.  I've just joined Chesscube, http://www.chesscube.com/ and experienced something that probably everybody experiences when joining a new community - people trying to checkmate you with the Patzer's Opening.  I've got two games where I successfully defended 1. e4 e5 2. Qh5 Nc6 and I'll explain how, hopefully next week!

The Patzer's Opening (1. e4 e5 2. Qh5)

This post isn't about a game, but about how to defend against an over-enthusiastic, over-eager opponent who decides that you look easy enough to beat quickly. The Patzer's Opening is played by White when he (or she) reckons that Black should be a pushover, and makes some extremely aggressive moves from the start. With precise play you can gain the advantage against this kind of opening.

The Patzer's Opening starts like this:

1. e4 e5

2. Qh5

This is a very aggressive move by White, and breaks the general principle of moving the queen early in the game. The main idea for White is to bring the bishop to c4 and then deliver checkmate on f7 with the queen. However, the more immediate threat is Qxe5, taking Black's pawn. Black must address this threat, and there are two main lines which can be played - either d6 or Nc6. I'll cover both, starting with Nc6.

2. ... Nc6

3. Bb4

White continues with the attempt to deliver a swift checkmate. My favourite response to this is g6, but it's also possible to defend the f7 square with Nh6. Playing d5 will not work, as white can capture the pawn with the bishop, Bxd5 and the threat continues. I like g6 because it develops the kingside defence, but especially because it gives White a good prod!

3. ... g6

White now has to move his queen, and the most likely square is f3, repeating the threat of capture on f7.

A note at this point - don't be concerned if, as Black, you're having to make a series of very defensive moves just to stay in the game. You're developing your pieces well, and they're all in good positions. White, if he plays Qf3, has prevented his knight on g1 from moving to its best square, and even on f3, his queen isn't ideally placed for later in the game. You'll come through the opening in a strong position, as White can't maintain a huge attack while you're beating his pieces back!

A natural response to Qf3 is Nf6, using the knight to block the queen's attack on f7.

4. Qf3 Nf6

White's attack is now running out of steam, and you're well on the way to developing a strong defence for your king. The moves g6, Nf6 and then Bg7 are known as 'building the house', providing a relatively safe place for your king when you castle kingside.

An alternative to playing 2... Nc6 is to play 2... d6 which has a similar effect (protecting the pawn on d5) and I'll cover that in a future post!

Kettinoffski vs David L, B21 Sicilian, Smith-Morra Gambit

Kettinoffski vs David L, B21 Sicilian, Smith-Morra Gambit

This next game is one where I played as Black. My opponent opened with e4, and I decided on the Sicilian, although I have been known to play the Ruy Lopez as Black. To be honest, I rarely play anything else against e4. Years ago, I'd play e5 as a matter of course, until Garry Kasparov and the 1993 World Chess Championship Final against Nigel Short, where Kasparov frequently played the Sicilian Najdorf, and it became all the rage (at least among my peers, and we were all still at school!). My opponent either knew the Sicilian very well, or not very well at all, and immediately went for an unusual opening.

1.e4 c5
2.d4 cxd4

I don't know much about the Sicilian, but I know for sure I'm not going to let White build a massive pawn platform in the centre. If I don't take the pawn on d4, I risk him advancing it to d5 and really causing me problems - I'll have a lack of space and I'll be really cramped, struggling to get my pieces onto strong squares. I therefore decided to capture the pawn, and White decided to recapture with his queen - moving the queen early in a game isn't recommended, as it can be chased by lesser pieces:

3.Qxd4 Nc6
4.Qd1 Nf6



5.c3 e5
6.Bg5 Be7
7.f3



7.... Qb6

Since White has moved his dark-squared bishop and left b2 undefended, I have a look at it with my queen. Notice that once again, an online opponent has played c3 and f3 - there must be a real phobia in the online community about knights!

8. b4 O-O

9. a4

White advances his queenside pawns - an unusual way of protecting that half of the board, and an unexpected response to my Qb6 move. However, I realised at this point that White's bishop on g5 is not protected - and although I could have made this move earlier, I've not noticed it until now. I suspect we were playing a tightly time-controlled game - hence the less-than-perfect play.

9. ... Nxe4

I'm now threatening checkmate with Qf2#, and I'm also threatening White's bishop with mine. White has to capture the knight, and I grab the bishop - leaving me a pawn up. White then looks for some more initiative on the queenside, and I move my queen to the centre.

10.fxe4 Bxg5

11.a5 Qe3+

12.Ne2 Qxe4

13.Nd2 Bxd2+?

Not an ideal move - although it means I can keep my queen in the centre, it also means I lose a useful attacking piece in exchange for a defensive piece that's only just moved.

14.Qxd2 d5

15.Kd1


15. ... Be6?

Probably not the best move. It's solid enough, protecting the d-pawn, but I could have moved the bishop directly to g4, pinning the knight. As it works out, White siezes the opportunity to move his knight, and I give a bishop check anyway.

16. Ng3 Bg4+

17. Kc1 Qg6

18. b5?

White misses the opportunity to grab the d-pawn, and I take the chance to defend it with the knight. I'm planning to move my rooks over to the queenside, open the c-file and get some reinforcements for my next attack on White's king. White continues his development, and I'm able to grab some more space in the centre.

18. ... Ne7

19. Bd3 e4
20. Bc2 b6

21. c4 Rfc8



This sets up the possibility of a strong attack on White's king which could win me his queen. If now, White plays c4xd5, then playing the pawn to e3 threatens checkmate (Qxc2#) and also White's queen. It's always useful to put your rooks on the same file as your opponent's king - this is an example of why. Although this doesn't quite work out in this particular game, it's a good principle to follow.

22. axb6 axb6

23. Rxa8 Rxa8

Instead of having my rook opposite White's king, it's now on an open file, which is also a strong position. The game now ends very quickly, surprisingly quickly, as White makes two very weak moves and I obtain a swift checkmate.

24. Kb1? Qf6

25. cxd5? Qa1#

White's last two moves - moving his king to b1 and then not realising my threat on a1 led to the quick ending. Perhaps he played Kb1 to prevent me playing Ra1+ but I can't quite see what prompted cxd5 - and didn't see the idea behind Qf6. I know for sure that we were both under close time controls, which accounts for a great deal!

David L vs Bailamooos (English Opening A21)

I found this game in my archive - genuinely, an archive of printouts of games I've played from some years ago. This game was played on Yahoo Games, so probably had fairly tight time controls, and was between me and Bailamooos. I often play lesser-known openings on Yahoo Games, to avoid falling into my opponent's planned openings (more on this in a future post). In this game, I played the English Opening (and as I'm English, it only seems appropriate). This game was played on Saturday 13 September 2008.

1.c4 e5

2.Nc3

This second move is the English Opening (as I understand it!) although there are a number of options for White's second move. I expect 2. e4 or 2. Nf3 are both playable for White - I'm no expert on the English (I'm no expert on any opening!) but I can't see any major or immediate problems with either!

2. ... a6?

3. Nf3 h6?

Black's moves are typical for online games I've played in. For some reason, there's a general fear of White's knights coming to b5 or g5 (respectively) and attacking c7 or f7. Yes, f7 is a weak spot for Black, but this early in the game, I'd be more concerned about the centre than the wings. Still, playing ... a6 and ... h6 gives Black's position a certain symmetry. While Black is playing these moves, however, he's left his e-pawn undefended, and I decide to capture it.

4. Nxe5 Qg5

5. d4

Black plays Qg5 to threaten my knight. Moving your queen early in the game is generally not recommended, as it can be chased around by your opponent, who will develop his other pieces at the same time.

My response is 5. d4, which is the diagram position below. This move has a number of useful consequences. It protects the knight on e4; it occupies more space in the centre (and prevents Black from moving his bishop to c5), but it also attacks Black's queen. My bishop on c1 is now pointing directly at Black's queen - a discovered attack. However, Black doesn't seem to realise this...

5. ... d6

6. Bxg5 dxe5

Instead, Black plays d6, developing his pieces and attacking my knight again. I capture his queen, and he captures my knight. I decide to start attacking with my queen, leaving my bishop on g5 en prise - where it can be captured. This is a mistake by me - with correct play, Black would be able to capture my bishop.

7. Qa4+ Bd7

8. Qb3

Although I've made a mistake in leaving my bishop where it can be captured (I should have moved it immediately), I have managed to get away with it. I'm now attacking b7 with my queen, and then I'll be among Black's pieces. A good move for Black now would be b6, moving the pawn so that it's defended by the c-pawn. Instead, black makes a series of questionable moves that allow me to finish the game quickly. I can't remember what the time controls were, but they could have been quite tight (or perhaps my opponent was having a bad day).

8. ... Nc6

9. Qxb7 Nxd4

While I'm working my way through Black's queenside, he seems happy to grab a pawn in the centre. The end comes quickly - and throughout it all, my bishop remains on g5, and has a part to play in the final checkmate.

10.Qxa8+ Bc8

11.Qxc8# 1-0

The final position is shown below.

If you have any suggestions, observations or ideas on this game, please leave a comment below.

Update

Yes, it's been a few days since my last post, but a new game will be appearing in the next few days - after two Ruy Lopez games, and a tutorial on discovered checks, I think it's time for something different. In the future, I'll also include games I lost (and learned from) and games where I played Black.

David L vs Mi Kl (Ruy Lopez)

I played this game during the last few weeks of 2009, and it's an interesting game because of the number of discovered checks in it. A discovered check occurs when you move one of your pieces out of the line of attack of another piece, and the second piece attacks your opponent's king. It's easier to describe in the context of a game, as you'll see below. This game includes a number of discovered checks, and you'll see the tactical advantages that they can bring!

David L (approx ELO rating 1525) vs Mi Kl (approx ELO rating 1411), started 5 December 2009.

1. e4 e5

2. Nf3 Nc6

3. Bc4

I'm not sure why I didn't play the usual Ruy Lopez move, which is 3. Bb5. Instead, I decided on this move to secure the d5 square (I think).

3. ... Nf6

4. O-O Nxe4

My fourth move does allow Black to take the e4 pawn, but I'm hoping that my next move will gain me a longer term advantage, and also enable me to recapture Black's central pawn. Moving the rook to the centre also gives me an advantage in development.

5. Re1

The immediate threat is the capture of Black's knight on e4, and if Black moves the knight away, I can play Nxe5 and regain the pawn. Instead, Black defends the knight by playing ... d5, which attacks my bishop on c4. I play d3, to give his knight another nudge - and develop another central pawn, and defend my bishop. If Black captures my Bishop, then I can capture his knight with either my rook or pawn. My move is also a kind of waiting move, and maintains tension in the centre.

5 ... d5
6. d3

Black now has to move the knight, or capture my bishop - otherwise I'll play d3xe4 and win the knight.

6 ... Nf6

7. Bb5 Bd6

8. Bg5 Bg4

Black moves his knight away, and I move my bishop to avoid it being captured. Perhaps I should have moved it there in the first place - it didn't do much on c4. We both develop our other bishops, and pin each other's knights against our queens. However, I've noticed that I can use my rook on e1 and my bishop on c4 to co-ordinate an attack on Black's king, by using a discovered check. The first thing I have to do, however, is temporarily sacrifice my queen!

Although my knight is pinned against my queen, I can grab a pawn and then open the e-file to check Black's king.

9. Nxe5 Bxd1
10. Nxc6+

By moving my knight from e5 to c6, I've exposed Black's king to check by my rook on e1, and this is called discovered check. Black would like to capture my knight on c6 with his pawn, but he must respond to the check first! When he does, I shall be able to capture his queen with my knight.

10. ... Kd7

11. Nxd8+ Kxd8
12. Rxd1 c6
13. Ba4

Black moves his king out of check, and I capture his queen, which also gives another discovered check (moving the knight out of the way of my bishop). The king recaptures my knight, and I recapture the bishop on d1. This series of exchanges has now left me a knight ahead (Black's knight which I captured on c6 on move 10). I've also regained the pawn I gave up earlier.

13. ... b5

14. Bb3 h6

15. Bxf6+ gxf6

Although I let Black chase my white-squared bishop around the queenside, I seize the opportunity to start simplifying the position by exchanging my other bishop for Black's knight. This is a general principle to apply in Chess games - when you're ahead on material, simplify the position by exchanging pieces. The reverse also applies - if you're behind on material, try and keep the pieces on the board and make the position as complicated as possible.

16. c4 dxc4
17. dxc4 Kc7
18. cxb5 cxb5
19. Nc3 a6
20. Rac1

I've simplified the queenside pawns and kept some open lines for my bishop, although I could have captured Black's pawn on f7, I decide to develop my queenside knight to c3, and develop my rook by putting it onto the newly opened file.

20. ... Be5

21. Nxb5+ Kb6
22. Nd4 Rad8

23. Rc6+ Kb7
24. Rc4 a5
25. Nb5 Rxd1+

26. Bxd1 Rd8

27. Bf3+ Kb6

Black threatens my bishop, so I develop it and check Black's king. A better response for Black is Kb8. Kb6, followed by Bxb2 will lose the bishop, and subsequently does so. Note that while I've moved my bishop to f3, I can't now move it from the d1-h5 diagonal, otherwise Black can play Rd1#.

28. a4 Bxb2

White protects the knight on b5 with his a-pawn, and Black snatches the pawn on b2. However, this bishop is now unprotected, and can be captured with a sequence of moves (sometimes called a 'combination') starting with a check by the bishop.

29. Rc6+ Kb7

This move is forced - Black has no other move which will get him out of check.

30. Rc2+

Another discovered check! This time, the rook moves aside to deliver the bishop check, and white can then capture black's bishop on b2.

30. ... Kb6
31. Rxb2 Rb8?

This is an unexpected move, as putting the white rook on the same file as Black's rook makes it easier to exchange them and simplify the game again.

32. Nd6+ Kc7
33. Rxb8 1-0

The final position, where Black resigned. Even after Black captures the Rook on b8, White's material advantage will be overwhelming, and Black has no counter-play, and so resigned the position.

David L vs Belraim Penhaligon: (Ruy Lopez)

This first game was played on iGoogle Chess, and was between me (approx ELO rating 1361) and Belraim Penhaligon (approx ELO rating 1063) on 2 December 2009.

1.e4 e5

2.Nf3

At this stage, I was expecting to play a classic Ruy Lopez, where Black responds with Nc6 to protect his pawn on e5. However, the game took an unexpected twist.

2.... f6

3.Bc4 Ne7

Maybe my opponent was concerned that I was going to capture his knight on g8, and hence moved it. I wasn't - I was looking to develop my pieces. However, his unusual play at this point led me to try something unusual of my own - a knight sacrifice to disrupt his pawns and to bring my queen quickly to the kingside.

4.Nxe5 fxe5

5.Qf3

5. .. Ng6

This defence was not enough to prevent a checkmate. The f7 square is a weak spot for Black (for White, the corresponding square is f2) as it is only defended by the king. It's important to defend this area early on - especially if it's being attacked, as it was in this case, by your opponent's pieces.

6.Qf7#

1-0

Introduction

The purpose of this blog is for me to discuss the Chess games I've played; games I've read about, or studied. I'll be providing basic commentary (with the emphasis on 'basic') and inviting discussion on lines I've missed, mistakes I've made and other general blunders and ideas. I'll be updating with plenty of diagrams (because I can't play blindfold Chess at all and I need to have a board permanently set up in front of me!) to make sure my ideas are clear.