Reckless Chess, Part 2

My online Blitz Chess games seem to be developing a pattern, and it's a trend which is suiting me very nicely.

1. e4   e5
2. Nf3  Nc6
3. Bc4  d6
4.  0-0  Bg4
5. Re1 Nf6
6. h3  Bh5
7. g4  Nxg4

This is now the second time I've been able to pile in with this king-side sacrifice, and it's going fairly well.  Clearly it's wrong-footing my opponents, but it removes two of the three pawns in front of his king, and gives me a some entertaining games playing with my queen in front of his king:

8. hxg4 Bxg4 
9. Re3 Nd4 



Piling on the pressure, and developing my pieces while White's pieces stay in their starting positions.

10. c3 Nxf3+ 
11. Rxf3 Bxf3 
12. Bxf7+ Kxf7   

13. Qxf3+  Ke8 

Maybe my opponent thought a counter-sacrifice would work, but all he's done here is give me more material - I'm now ahead by the exchange and a pawn - and he's kindly opened the f-file.

14. d4 Qh4  - direct Chess at its most fun.
15. Kf1 Be7 
16. dxe5 Rf8 
17. Qe2 

Black (me) to play, played dxe5 and missed Qh1#

17.   ....   dxe5 (missing Qh1#)
18. Qb5+ c6 
0-1

The threats piling up around the white king include Qxf1# and if Qe1 then Qh1#.  There's also cxQ if White doesn't move his Queen.

As I said, I am enjoying the sacrifice on the g4 square, and so far it's reaping its benefit against people trying to play some form of Fried Liver Attack, with Nf3 and Bc4.

More to follow, I'm sure!

Some of my other Chess games:

My very earliest online Chess game
My most bizarre Chess game
My favourite Chess game

Review: Space Force, Episode 2: "Save Epsilon 6!"

CONTAINS SPOILERS

The second episode of Space Force follows immediately from the first episode; with General Naird and Doctor Mallory witnessing (via an implausibly powerful telescope) the sabotage of the Epsilon 6 probe they had just launched.

There's an F-bomb from each of them, before they return to mission control to work out what's happened and what can be done about it.  It seems the language in this show is the only thing that's definitely strong, because the characters, plot and script are definitely not quite there yet.

This episode focuses on the struggle to reattach the two solar panels to the Epsilon 6 probe - there's problem-solving, brainstorming and so on.  The struggle is largely between the inept but in-charge General Naird, and the sensible but obstructive scientists (we meet more of them in this episode).  The General wants to use a bomb to blow the solar panels back onto the probe (there's a convenient plot device which states that the panels only need to touch the probe to work).  After all, in the Air Force, using a bomb is always the best answer - is that a political comment, or is it funny; neither, or both?
The scientists want to try a more elegant approach, which is, in all honesty, probably more likely to succeed, and they are conveniently sidelined.  This episode is about the relationship (or lack of it) between Naird and Mallory, and the pressurised situation of trying to rescue the Epsilon 6 is a good background for it.  Both men have skills and knowledge that the other needs, but neither of them will accept that yet.

One character who is not conveniently sidelined is the social media marketing idiot, Tony.  I'm sorry, but he brings nothing to the story at all, and if anything, he detracts from it.  He is an obstruction to the story and the plot, and a distraction from the better characters (as in, all the other characters).  He needs toning down or kicking out.  At the end of the last episode, Naird had put him in jail, which worked for me.  Sadly however, in this episode, he's back and getting in everybody's way.
The final solution that Naird proposes is to use a monkey from a nearby orbiting spacecraft (convenient, but it works) which was recently launched, and get it to fix the Epsilon 6's solar panels.  Cue visual comedy about communicating with a very unhappy monkey through sign language, and finally persuading it to fix the Epsilon 6.  The visual comedy reached farcical proportions as the monkey used a power drill/power screwdriver to reattach the solar panels - when the bolts stopped turning, the laws of physics dictate that the drill needs to start turning instead, and the monkey (still holding the drill) starts spinning around at several hundred rpm.  Which is funny enough, until the monkey lets go and is launched into space.  Hmmm.

The Epsilon 6 is fixed.  However, the monkey is now on a collision course with the Sun, and so the brainstorming switches to 'how do we get the monkey back?'.  The question is rendered moot by the end of the episode, as the Chinese space vessel (which had sabotaged the Epsilon 6) has completed an orbit, and intercepts the monkey.  Coincidence?  Farce?  Yep.

The episode concludes with the team working out how to escalate this international (interplanetary?) incident... we shall see.

I rate this episode marginally better than the first, but if things don't improve, I'll find myself returning to planet earth and finding something else to watch.  7.5 out of 10.

Review: Space Force: Episode 1

Space Force:  is it a mockumentary?  Is it a sitcom?  Is it just plain funny?  To classify it, I'd call it a sitcom, bordering on farce.

Steve Carell is definitely funny.  He knows comic timing and how to deliver a gag - physically and verbally. But this is not The Office. And one thing I will include at this point is that the language in Space Force is unnecessarily bad - the series is rated 15 for language and it shows. It's almost as if the producers realised their show isn't laugh-out-loud hilarious and threw the profanities in to compensate.

Anyway, back to the comparisons.

Michael Scott is accidentally competent, unaware of how his team's success is their own work, and often despite his management, rather than because of it.  His career is largely successful (best branch in the company) and this success allows him a lot of leeway in using his own personality to manage.

General Naird is largely unsuccessful despite all his best efforts. He has almost no control over his life: he's been given a promotion to a four-star general rank, and despite expecting to take on leadership of the Air Force, he's been given the task of founding and running Space Force. He's totally out of his depth.

He has no control over his family life: for reasons not yet revealed, his wife is in prison. His daughter is pushing his boundaries and she's started dating a Russian astronaut stationed on the space base.

He has no authority over his space programme, despite being responsible for it. He wants to launch a rocket, but the resident  head of science (an annoying character played by the typecast John Malkovich) says he can't due to bad weather.

He even has no control over his office: in the first episode, there is an unannounced and uninvited guest in his office every time he walks into it (except one occasion, where he escapes to his happy place).  His personal assistant or receptionist or however you'd like to refer to him, is an incompetent waste of space.

The General feels the pressure of his space programme ("Boots On The Moon") at all times, and in contrast to Michael Scott where he's an appalling manager with a successful team, the General is a good manager (out of his depth) surrounded by critics, detractors and obstructions.

So, Space Force is nothing like The Office.

The first episode could be summarised as "General has to demonstrate some return on all the investment into Space Force, and in order to do so, prematurely launches a prototype weapon which explodes on the pad, but contrary to scientific advice, successfully launches a new unmanned rocket into orbit." with a twist, "Another spacecraft severs the new probe's solar panels leaving Space Force with a predicament to solve."  It introduces the main character and his colleagues, who are some of the most irritating characters on Planet Sitcom.  I've already mentioned John Malkovich's character, Dr Adrian Mallory (as annoying as he was in Transformers Dark of The Moon); joined by F. Tony Scarapiducci (played by Ben Schwartz, who played the utterly infuriating John Ralphio in Parks and Recreation), who is the entirely superfluous social media manager.

Is Space Force funny?  In parts, yes, but not in the way that The Office is funny, or Parks and Recreation, or any other mockumentary or sitcom.  If anything, I'd have to liken it to the more serious episodes of Brooklyn 99, but without the slapstick.

One thing it certainly has is accidental relevance. In a week where the Space X Dragon launch was postponed due to the weather, this was very timely.  The handover of Space Force to General Naird is accompanied by the line that The President wants to protect the Internet and Twitter as information is bounced off satellites.  In a week where Donald Trump has loudly attacked Twitter, this was certainly an unplanned piece of cultural commentary.

Do I like it? I think so, but I am not convinced. The tone of the General constantly under pressure to perform does  not lend itself easily to comedy, and apart from wastefully spending taxpayers' money in failed launches, there's not much to laugh at in the first episode.   I'm rating it 7 out of 10, and will persevere for another few episodes at least.  I even managed to make it as far as watching and reviewing Space Force Episode 2.

Crazy Blitz Chess

Chess is a complex game - sometimes you win, sometimes you lose; sometimes you deserve to lose and still manage to win.  This is probably the craziest game of Chess I've played - Blitz again - but I was very pleased with the way I wrapped it up.  Firstly, the step-by-step video replay:



I played White, and selected my standard Queen's Gambit opening.
White "davidleese1010"  vs Black "tarekamine"

1. d4     d5
2. c4     Nc6 
3. Nc3   Bf5
4. Qb3   Na5
5. Qa4+   c6
6. cxd5   e6
7. e4   exd5
A blunder from which Black never really recovered.  

8. exf5   Qe7+
9. Be3   Nc4
10. Bxc4  dxc4
11. Qxc4  Nf6 
12. Nf3   Ne4 
13. O-O   O-O-O 
14. Rfe1  Qd6 
15. Nxe4  Qc7 
16. Ne5   Rd5
17. Rad1  f6 
18. Nf3   Rxf5 
19. d5   cxd5 
20. Qxc7+ Kxc7 
21. Rc1+  Kb8

22. Red1  

Setting a cheeky trap.  Black cannot capture because Rd8 is checkmate.  And now, I've centralised both my rooks.

22. ...   Bb4 
23. Nc3   Rd8 
24. Nd4   Rh5 
25. a3   Bd6
26. b4    Bxh2+ 

Missed that one.  But at least I have an easy escape square, and now my pieces gravitate towards Black's King.

27. Kf1   Be5 
28. Ncb5  a6 
29. Ne6   Rd7 
Forcing Black's Rook off the back rank, with my Rook on c1 now waiting.

30. Ba7+  Ka8
31. Rc8+  1-0

Final position: my pieces are so precariously placed that my only option was to keep moving forwards at maximum speed!

Some of my other Chess games:

My very earliest online Chess game
My most bizarre Chess game
My favourite Chess game

Reckless Chess for Fun

Way back when I first started this blog, it was going to be a place where I shared my games of Chess.  Over the years, it's changed - the name has changed twice, and the content has changed constantly, although it does tend to gravitate towards maths and web analytics (and Star Trek).

Here's a recent one-off Chess game - five minutes of Blitz.  I was Black, and I was clearly in a reckless mood:



Starting with move 9. Bh5, where I deliberately allowed my bishop to become trapped.  Yes, it was deliberate.

1. d4 d5  
2. Nf3 Nc6
3.  e3 Nf6  
4. Bd3 g6  
5. O-O Bg7  
6. b3 O-O  
7. Bb2 Re8  
8. Nbd2  Bg4  
9. h3 Bh5 

Reckless, but with the deliberate plan of getting two pawns for the knight, then opening up White's king with ... e5 and Qg5 or Qh4

10. g4 Nxg4
11. hxg4  Bxg4  
12. Qe1 e5
13. dxe5 Nxe5
14. Bxe5  Bxe5  
15. Nxe5  Rxe5

Recapturing in the centre, with my queen now ready to sweep into the kingside.  I have, however, missed an opportunity since White's move 12 Qe2 to play Bh3 and trap White's rook.  This is blitz Chess, and such mistakes are not uncommon.
 
16. Be2 Bh3  (I saw it!)
17. Bf3 Qg5+
18. Kh2 Bxf1 (finally capturing the rook, bringing the game closer to material parity) 
19. Qxf1  Qh4+  
20. Kg1 Rg5+  
21. Bg2 Rh5
22. Nf3 Qf6
23. Qe2   Re8?  (missing the chance to play Qxa1, but bringing in reinforcements)

24. c3 Qxc3  
25. Rd1 c6  (I couldn't think of anything better than this solidifying move)
26. Qd3  Qb2  
27. Qd2 Qf6  
28. Qd4  Qf5  
29. Qxa7  Re4 

I have decided to play some more reckless Chess.  I don't need those pawns, I need to launch my pieces at White's King - now!

30. Qb8+ Kg7  
31. Qg3    Rg4  
32. Qe5+  Qxe5

I didn't want to exchange Queens, but I had to - White had been pushing to trade for several moves, and here he managed to force the exchange.
 

33. Nxe5  Rxe5  ... but I got an extra knight for it, and now I'm ahead on material, and have an outside passed pawn ready to roll.
34. Kf1 f5  
35. Ke2 Rxg2  a blunder from white, which I didn't miss.  This is now winning for me.
36. Kf3 Rg4  
37. Rc1 h5  
38. a4 h4    "Always push passed pawns"
39. Rh1 g5  
40. Rh2  Rge4  
41. Ke2 f4  
42. Rh3 d4
43. Kd3 dxe3
44. fxe3  fxe3
45. Ke2   Rd5 

A very pleasant position for me.  I'm going to play Rd2+ and keep pushing the e-pawn, and I've got the g- and h-pawns too.  My opponent's next move surprised me.

46. Rxe3  Rxe3+  
47. Kxe3  h3   and now, apart from dodging any stalemate traps, it's plain sailing.
48. Kf3 h2  
49. Kg2 Rd2+  
50. Kh1 g4  
51. b4 g3  
52. b5 cxb5  
53. axb5  Rd1+  
54. Kg2 h1=Q+  

I won't annotate the rest, but rest assured I wrapped up the game in the next five moves.

And here's the full PGN file of the game.

Reckless Chess - it's the way forwards!

Some of my other Chess games:

My very earliest online Chess game
My most bizarre Chess game
My favourite Chess game

Summing Square Numbers and Triangle Numbers

"A grocer stacks apples in pyramids made of layers of equilateral triangles. How many apples will he need to fill four levels of apples?  A second grocer stacks apples in pyramids made up of layers of squares - how many apples will he need to fill four levels of apples in each tower?"

Firstly, let's borrow a picture for the first grocer's tower - this one contains the first five layers.

This is the series of triangle numbers:

The first row is one apple
The second row is three apples
The third row is six apples
The fourth row would be ten apples
Total = 1 + 3 + 6 + 10 =20 apples

And for the second tower, which is the series of square numbers:

The first row is just one apple.
The second row is four apples
The third row is nine apples (three squared)
And the fourth row would contain 16 apples (four squared).

1 + 4 + 9 + 16= 30 apples

These are the two ways of most densely packing spheres - in triangular fashion (left), or in a square fashion (right).  I've covered the density of sphere packing in hexagonal planes in a previous blog.

Extension Task

Now, to extend this simple problem a little further:  how many apples would be needed to produce a triangular tower (like the first grocer), or a square tower (like the second grocer) with n rows?

We need to determine expression for the nth term, and we can do this by taking differences between adjacent terms, and then the second (and if necessary) the third difference.

Triangular Tower (Tetrahedral)

The terms for the total numbers of apples are 1, 4, 10, 20, 35, 56 and so on.
The first difference is 1, 3, 6, 10, 15, 21 (the triangular numbers)
The second difference is 1, 2, 3, 4, 5, 6
And the third difference is 1, 1, 1, 1.

The third difference means that this is a cubic expression, and the value of the third difference (1) needs to be divided by 6 to give the coefficient a in the expression ax³ + bx² + cx + d
Hence we know that the expression is x³/6 + bx² + cx + d

We now have to subtract x³/6 from each of the xth value, and calculate the differences again (to determine what the coefficient b is), and then repeat the process to determine c.

Following this process, we can see that the expression for the nth term is

Tetrahedral Tower:  T_n = n³/6 + n²/2 + n/3

The Twelve Days of Christmas

This has one practical application:  if you recall the song 'The Twelve Days of Christmas', you'll see that each row, starting at the top, is the number of gifts given by 'my true love'.  On the first day it's 1, on the second it's 2+1, and on the third day it's 3+2+1, and so on.  So, if you're ever asked the question, "How many gifts in total were given during the twelve days of Christmas?" then you can whip out your calculator:  12³/6 + 12²/2 + 12/3 = 1728/6 + 144/2 + 12/3 = 288 + 72 + 4 = 364.

Square-based tower

The terms for the total numbers of apples are 1, 5, 14, 30, 55, 91 and so on.

The first difference is 1, 4, 9, 16, 25, 36 (the square numbers)

The second difference is 1, 3, 5, 7, 9, 11

And the third difference is 2, 2, 2, 2.

The third difference means that this is a cubic expression, and the value of the third difference (2) needs to be divided by 6 to give the coefficient a in the expression ax³ + bx² + cx + d

Hence we know that the expression is x³/3 + bx² + cx + d

We now have to subtract x³/3 from each of the xth value, and calculate the differences again (to determine what the coefficient b is), and then repeat the process to determine c, and d if needed.

Following this process, we can see that the expression for the xth (or the nth) expression is

Square-based Tower:  T_n = n³/3 + n²/2 + n/6

(As an aside, these solutions remind me of the puzzle I solved last year: 1/a + 1/b + 1/c = 1)

Other posts similar to this that you may be interested in:

The Fibonacci Series
Pythagorean Triples
Ulam Sequences: Up, Up and Away