Saturday, November 26, 2011

Probability of a Coin Flip

The probability of a coin flip landing on one side is 50%. This of course assumes that the coin is fair and the probability of heads or tails is thus even. The probability of a coin landing on heads or tails twice in a row is 25%. The reason is that there are now four possible outcomes: heads, heads; tails, tails; heads, tails; tails, heads.

The probability of a coin landing on heads or tails three times in a row is only 12.5% or one in eight. The reason is that there are now eight possible outcomes. With one flip the probability of one outcome is 50%. With two it becomes 25% and with three 12.5%. With each additional flip, the percentage is halved.

With this knowledge I decided to flip a 100 won coin three times in a row and repeat this eight times. Since the probability of heads resulting three times in a row was only 12.5% or one out of eight, I thought that I might get three heads in a row once out of eight tries. Here are the results of my experiment:

1) heads, heads, tails
2) heads, tails, heads
3) tails, heads, tails
4) heads, heads, heads
5) tails, heads, tails
6) heads, heads, tails
7) heads, heads, tails
8) tails, tails, tails

From my eight series of flips, I got three heads in a row once. I also got three tails once in a row. However, I got heads thirteen times and tails eleven times. This was not an even split. Instead of 50% heads and 50% tails, the result was 54% heads and 46% tails. Nevertheless, this was close to 50-50.

Based on this simple experiment, it may be that results are often close or identical to theoretical probability. I got three heads in a row once out of eight times which was exactly as predicted. I also got tails once out of eight as predicted. I did not get an even number of heads and tails but the results were very close to theoretical probability.

Wednesday, November 23, 2011

Exposed King

In a game of speed chess at chessgames.com, I managed to destroy the pawn shield around the enemy king and expose him to an overwhelming attack. My opponent was Rajantnr87 of India who played black. Here are the moves of the game along with my commentary:

1. e4 e5
2. Nf3 d6
3. Bc4 h6

Black makes an unnecessary move. Be7 and Nf6 are better moves.

4. h3 a6

I prevent Bg4.

5. a4 Nc6

I prevent b5.

6. d4 exd
7. Nxd4 Ne5
8. Bb3 Nf6
9. Nc3 Be7
10. 0-0 0-0
11. Bxh6 gxh6

I sacrifice my bishop to destroy the pawn shield around the black king.

12. Qd2 Kh7
13. f4 Ng6
14. Nf5 Rh8

Black makes a bad move.

15. Bxf7 Bxf5
16. exf5 Nf8

Black has four pieces on the back rank.

17. Rf3 Kg7
18. Bg6 N8d7
19. Rg3 Kf8

I place my rook on an open file.

20. Re1 c6

Black prevents Nd5.

21. Ne4 Qb6+
22. Kh1 Bd8

Black makes another bad move.

23. Qxd6+ Be7
24. Qe6

Black resigns. At the moment of resignation, black has an extra piece but three fewer pawns. The material count is even but black is helpless to prevent mate. I have control of f7. The only way for black to delay mate is to play Rh7 but I can then play Bxh7. With the realization that he cannot save the game, black decides to resign.

The keys to victory in this game are the exposed black king, the lack of coordination of the black pieces and my control of the light squares. Though black has one more piece, his pieces are very passive. He never manages to activate his rooks. For these reasons, he decides to resign on his 24th move.

Wednesday, November 16, 2011

Clearance Sacrifice

In a game of speed chess at chess.com, I used a clearance sacrifice to win material. A clearance sacrifice is a sacrifice which clears space. In this game, my sacrifice allowed my queen to control an important diagonal and capture my opponent's rook. My opponent was Mychessplay of India who played black. Here are the moves of the game along with my commentary:

1. e4 e5
2. Nf3 Nc6
3. Bb5 Bd6
4. 0-0 a6
5. Ba4 b5

I opt to keep my bishop.

6. Bb3 Nd4
7. Nxd4 exd4

I must make sure that black does not trap my bishop.

8. e5 Bxe5

I sacrifice my pawn. This is a clearance sacrifice because now my queen has access to the f3-a8 diagonal. I do not play Qf3 right away because then black can counter with Qf6 and my queen cannot capture the rook on a8. With the clearance sacrifice, my queen can control the f3-a8 diagonal on my next move.

9. Qf3 Nf6

Black's move prevents Qxf7#.

10. Qxa8 0-0
11. h3 c6

Black wants to trap my queen.

12. d3 Nh5

Now I can develop my dark-squared bishop.

13. a4 Qh4
14. Nd2 Qf4

Black threatens Qh2#.

15. Nf3 Qf6
16. Nxe5 Qxe5
17. Bd2 Qe2
18. Bb4 Re8
19. Rfe1 Qxe1+

Black must capture to avoid Rxe8#.

20. Rxe1 Rxe1+

Black resigns. On my next move I can play Bxe1. This leaves me one piece up. Even worse for black, I threaten to capture his bishop on c8 which cannot move because it is pinned. With the loss of his queen and pinned bishop, black realizes that his position is hopeless. For this reason he resigns. My clearance sacrifice on move 8, e5, is one of the key moments of the game.

Sunday, November 13, 2011

Debuccalization

Debuccalization is a sound change in which a consonant becomes a glottal fricative or glottal stop. It is a common sound change which is also found in English. Debuccalization can be considered a weakening process.

Many speakers of English glottalize a /t/ when it is word-final and followed by a consonant and when it is followed by a syllabic nasal or liquid. This can occur in the following environments:

hot coffee
not much
quite good
button
mountain

In Cockney English, an intervolic /t/ is replaced by a glottal stop, i.e., later, latest, city. In Canadian and American English, however, the /t/ is normally flapped here.

In Spanish, debuccalization also occurs. However, it is not a /t/ which becomes a glottal but rather an /s/. In many Spanish dialects such as those of Cuba, Venezuela and Panama, it is common for a syllable-final /s/ followed by a consonant to become an /h/. This happens in many words such as fresco (fresh), fiesta (party), and costa (coast).

Debuccalization is a common sound change. It can be classified as a subcategory of weakening, also known as lenition. With this sound change, the place of articulation shifts from the oral cavity to the glottis.

Monday, November 7, 2011

Miscalculation

Many chess games are lost because of miscalculation. Such was the case in a game of speed chess at chess.com. My opponent was FaduljoseA of the Phillipines who played white. Here are the moves of the game along with my commentary:

1. e4 c5
2. Nf3 d6
3. d4 cxd
4. Nxd4 Nf6
5. Nc3 a6

I prevent Bb5+.

6. Bg5 e6
7. Bc4 Be7
8. 0-0 Nc6
9. Nxc6 bxc6

White makes a mistake. The capture Nxc6 allows me to strengthen my pawn centre.

10. a3 0-0
11. Re1 h6
12. Bh4 Bb7

The white bishops are more active than mine.

13. h3 Qc7
14. Ba2 Rad8
15. Ne2 Rfe8

Black's last two moves are passive.

16. f3 Nh7

I want to exchange white's active bishop for my passive bishop.

17. Bxe7 Qxe7

I am happy to exchange bishops.

18. Nf4 d5
19. exd cxd
20. Nxd5 Qc5+

White miscalculates. He plays Nxd5 because if I play exd5, I lose my queen. However, I can safely play Bxd5. What white fails to notice is that he cannot win material. My queen is protected and I have two pieces attacking d5. I can play Bxd5 but I first decide to put his king in check and attack the pinned knight with my queen. With the realization that he will lose material, white resigns.

White loses because he fails to see that his combination is flawed. He thinks he can exploit my inability to play exd5 but does not notice that my protected queen prevents a gain of material. This is the difference in the game.

Wednesday, November 2, 2011

Accents of Canadian English

The English of Canada is remarkably uniform. Despite a large area, Canadian English is more uniform than that of Britain and the United States. The main accents of Canadian English are the West-Central, Maritime and Newfoundland accents.

The most widely-spoken Canadian dialect is the West-Central. It also includes the accent of Quebec. In contrast to the English of other provinces, Quebec English includes a number of French words such as "autoroute" for freeway and "metro" for subway.

The Maritime accent is the accent of Nova Scotia, Prince Edward Island and New Brunswick. The Lunenburg accent of Nova Scotia is the only non-rhotic accent of Canada. In the Lunenburg accent, the "r" in words such as"farmer," "farm" and "world" is not pronounced.

The Newfoundland accent is the most distinctive Canadian accent. In this accent, many words are pronounced with different vowels than in other Canadian accents. For example, the word "sun" is pronounced with the vowel of "ma" and "pa." It is a more open vowel. The "a" of "father" tends to be pronounced with a more fronted vowel, similar to the vowel of "cat." The "a" of "car" is also pronounced with a lower vowel so that it sounds similar to the vowel of "cat." Also notable about the Newfoundland accent is a syllable-final "r" which tends to have a longer duration than in the rest of Canada.

Although Canadian English is not so varied, it nevertheless has three main dialects. They are the West-Central, Maritime and Newfoundland. Of these three, the West-Central is the most widely-spoken and the Newfoundland is the most distinctive. The Maritime dialect includes the Lunenburg accent, the only non-rhotic accent in Canada.