Boggle

Lately, I have found myself deeply attracted (addicted?) to Wordtwist, which is basically Boggle with a weirder scoring system. Let's explore methods of scoring well in Wordtwist on a good board (one with many words available).

Firstly, an example board:

b x o p
y e t h
o n a s
k e s w

Let's look at the board and talk about it in general.

Sure, the game tells us that there are many words to be found (a pre-game accessible table tells us, with a bit of computation, that there are 316 words waiting to be found), but where do we start looking?

The 'x' near the top left corner is not badly placed. It contains obvious words (which are rewarded with bonus score thanks to the presence of the "weird" letter 'x') such as exo and oxy. In fact, there are 6 3-letter words containing an 'x' in this board: exo, oxy, hox, pox, yex and tex. It pays to know your 3-letter words (I didn't; oh well).

There are 6 other words containing 'x': poxy, next, nexts, oxen, onyx and ethoxy, which is admittedly hard to find.

The other "weird" letter of this board is 'k'. 'k' contributes to surprisingly many short words to those unfamiliar with Boggle-like games: kas, ska, ken, kent, kon, and whatever not. In fact, for this board, the 'k' words are: kon, kons, ken, kens, kea, keas, oke, okes, nek, hank, sank, keno, kent, kents, tank, wank, yoke, yokes, kente, sanko, shank, snoek (and edible marine fish, what the...), snoke, stank, swank, thank and bethank. Of these, kon, kons, ken, kens, kea, keas, oke, okes and nek are 3-letter words and s-plurals. If one recognises 'nk' as an ending stem, one could in theory locate the words hank, sank, tank, wank, shank, stank, swank and thank with some degree of consistency (a glance would give hank, sank, tank and wank surely, and the rest are not that hard to locate if you're looking for words ending with 'nk').

Next, we might take a look at 3-letter words (with some repetition):

yon yok yex yet yen yea wat was wan wae top toe tho tex ten tea taw tas tan tae sny sha sen sea saw sat san sae pox pot poh pht pho oye oxy opt ony ons one oke ohs oes nye nth noy net nek neb naw nat nas nah nae kon ken kea hox hot hop hoe haw hat has han hae exo eth eta ess eon ens ene eat eas ean bye bey bet ben ate ass ash any ant ane ahs

We theorize that most 3-letter words are of the form . Words that fit this bill are:

yon yok yex yet yen wat was wan top tex ten taw tas tan sen saw sat san pox pot poh noy net nek neb naw nat nas nah kon ken hox hot hop haw hat has han bey bet ben

This kind of breaks my hypothesis to bits, accounting for only half of the words. Yet these 3-letter words are the easiest to find. Relooking at the board:

b x o p
y e t h
o n a s
k e s w

One might have a deeply organised attack on these words which go:

 xop xot xoh pot poh tox top toh hot hop hox bex bet ben bey xeb xet xey xen yet yeb yex yen tex ten tey teb neb ney nex net yon yok noy nok kon koy nat tan tah tas taw hat han has haw nat nah nas naw sas sat sah san saw was wan wat wah

This covers all the 41 words in the reduced list above, and took me slightly above 1 minute to type out in full. Knowing the words well could likely reduce this to about 40 seconds, minus away some consistency due to flawed recognition of words. Also, doing it with a more stable presence of mind will probably help in locating the plurals, such as hats, nats, tans, hans, haws and wans more easily.

The remaining 3-letter words:

yea wae toe tho tea tae sny sha sea sae pht pho oye oxy opt ony ons one oke ohs oes nye nth nae kea hoe hae exo eth eta ess eon ens ene eat eas ean bye ate ass ash any ant ane ahs

6 are plurals of 2-letter words:

ons ohs oes ens eas ahs

The rest are weird; go figure:

yea wae toe tho tea tae sny sha sea sae pht pho oye oxy opt ony one oke nye nth nae kea hoe hae exo eth eta ess eon ene eat ean bye ate ass ash any ant ane

The remaining words according to classification where I can find them:

Seeming plurals/third person present tense of 3-letter words:

yens yeas wats wans waes tens teas taws tans taes seas saws sans pots opts ones nets nats hots haws hats haes eths etas eons enes eats eans bets bens ants anes

Others:

yont yean yeah ybet wate wast wash wase wany want wane toph toey toea thaw than thae tene tass tash tane swat swan stop stey sten staw snye sneb snaw shot shop shoe shaw shat shan sent sene sena seat sean sate sash sant sane pote poet phot phat onto noes ness neat hote hate hast hant haet haen eyne etna esne eath east ease bets beth beta bent bene beat bean atop ants ante aeon

5-letter words (words with apparent 4-letter stems are bolded):

yenta yeast yeans yeahs waste wants waney wanes tophs toeas thaws thans thane tense tenes tease tawse tasse swats swath swash swans stens steno stean staws stane snaws snath snash shote shaws shans sents sente senas seats sants santo sanes potae poets phots phase netop neats neath hoten hawse haste hants hanse haets etnas enate eaten beths betas bents bento benes beats beath beast beany beans beano aeons

6-letter words:

yentas thanes swaths steans steane stanes sneath snaths snaste senate potass potash potaes hasten ethane ensate beaths assent

7-letter words:

washpot waeness teashop steanes sneaths shantey hotness hastens ethanes beneath

Notably, waeness and hotness both have the -ness stem.

Random notes that didn't fit in anywhere else:

b x o p
y e t h
o n a s
k e s w

With the letters n, e (x2), a, t, s (x2), we can form (not exhaustively):

eta, etas, tea, teas, tae, eat, eats, ate, east, sate, sae, eas, tas, sat, ass, tass, neat, neats, tane, stane, stanes, stean, steans, steane, steanes, net, nets, ten, tens, sten, stens, sea, seas, sen, ens, nas, san, sans, sane, ane, ean, eans, tan, tans, nat, nats, sene, ene, tene, tenes, taes, sent, ant, ants, sant, sants,

all of which are rather common words with my 5 favourite letters, 's', 't', 'a', 'n' and 'e'. In fact, a square containing 'teas' has 22 words, which are:

tea, teas, tae, taes, eat, eats, eta, etas, ate, ates, sat, tas, set, tes, est, sea, sae, eas, seat, seta, east and sate.

For 'nats': nat, ant, tan, ans, nas, san, tas, sat, tans, nats, ants, sant
For 'nets': ten, net, sen, ens, set, tes, est, nets, tens, sten, nest, sent
For 'sane': san, nas, ans, sea, eas, sae, ens, sen, ane, ean, nae, sean, sane, anes, eans, sena
For 'tane': tan, nat, ant, tea, tae, eat, eta, ate, ten, net, ane, ean, nae, neat, tane, etna, ante

The Two-envelope Problem

  Well, this is one of the recurring problems we've probably all seen, time and time again, with various "obvious!"-style solutions as well as a nice wall of text explaining away the paradoxes by claiming that it was all a case of confusing phrasing -- with an inspiredly sneaky re-expression of the problem, the paradox dissolves! However, there is more or less no true escape from the true Mathematics of this problem. Wikipedia has a nice and technical exposition on the various "solutions" and solutions of the paradox, and equally sneaky reformulations of the problem to expose the holes in the "solutions". You should read it if you actually want a formal explanation, but I believe mine follows the Wikipedia article somewhat faithfully, up to at least somewhere in the middle.

  The first thing to state is the question in a text-wall format, so that we can demolish it later for clearer insight. Well, here I go: Two envelopes are on a table. One contains twice as much money as the other, and there is no way to tell the contents of the envelope until you open it. You choose one, taking extreme caution not to open it (and cleverly avoid revealing the contents of the other as well, you sneaky person). You think to yourself: If I open this envelope and find X dollars, then the other envelope could contain X/2 dollars or 2X dollars. Those two outcomes have equal chance, since I pick either the larger or the smaller (contentwise) envelope randomly. My expectation of money in the other envelope is hence 5X/4 dollars. This does not make sense, since the expectation of money in my envelope is now also 5Y/4 dollars, where Y is the amount contained in the other envelope. We get X=25/16*X. That's depressing, since it solves to 0. :( In my depression, I claim a paradox!

  Well well, not the most accurate formulation of the problem, but at least somewhat intelligible. Now I shall point out an interesting feature of this problem which is usually ignored in discussion for being somewhat impossible to prove -- Consider, in a train of thought very far removed from the original paragraph, the following paradox: "X is 1. X is 2. Therefore 1=2. Contradiction?!". This is clearly a matter for the logicians out there to name. I'd personally file it under the classification of "Lies" and trash it. But, the thing is... our problem seems self-consistent... up till the paradox. So now let's rephrase it without the envelopes:

  I pick a number (call it X), and map IDs #1 and #2 randomly to the two positive numbers X and 2X. Now, you pick either #1 or #2 and we define the number it maps to be Y. Now the other number could either be Y/2 or 2Y with equal probability, and the expectation is 5Y/4. The problem statement is clearly sound, since these are more or less mathematical formulations, and if a contradiction exists, the subject would fall apart and all I learnt in school would be totally useless!!!!! We therefore call it a confusing argument and try to explain it away.

  Clearer (albeit somewhat spoilt by the ending). So now for "solution" 1. We notice that Y can either be X or 2X. As such, Y is inconsistently defined. We therefore redefine it in terms of X and 2X and it all works out to an expectation of 3X/2. The world is saved!

  Clearly this violates the principle of the matter. It's like saying: "Why don't I get dough when I mix flour with kerosene?" and answering it with "Everything is well if you just buy the dough directly from the supermarket, you twit. After all, they've derived the dough from flour as well.". This resolves the paradox by more or less ignoring it, so let's just make the paradox more annoying and harder to sidestep:

  Both the number mapped from #1 and #2 have equal expectations by symmetry, and the smaller of which is further defined to be a random positive real number. You pick #1. It maps to X. Now, the expectation of the value of #2 is (X/2 + 2X)/2=5X/4, since the probabilities of the pairs [X/2,X] and [X,2X] are equally probable. The problem is: the expectation of the other number is always higher than your no matter what it is, so on average, knowing a number causes the other number's expectation to be 5X/4, which is 5/4 times its own expectation. Based on that, before you even know what #1 maps to (ok call it f(1), and similarly define f(2) -- this is getting tedious), you know that f(2) is on average 5/4*f(1). OMG contradiction!

  The resolution for this is a one-liner (Note: see Zagier's one sentence proof for an idea of how a mathematical line might look): X*5/4=X, where X is the cardinality of positive real numbers (commonly known as infinity, though not the only infinity). Well the thing is that since positive reals stretch indefinitely, the chance of choosing a finite number is infinitesimal. And for infinities, the statement f(1)=5/4*f(1) can make perfect sense.

  One last sneaky trick to throw in (and a solid text wall to help obfuscate matters just that little bit more):

  "We shall now be so nice, going out of the way to help you define just a specific case of the problem, and we'll even babysit you by stating precisely how we chose the numbers. More formally, we shall enlighten you as to the probability distribution of the amounts in the envelopes. We have an old friend here, called Mr. Fair Coin, who is a truly erratic fellow at the best of times and completely random at the worst of times. Now, we all know that Charles Dickens once famously said "It was the best of times, it was the worst of times", but you see, truly erratic and completely random are consistent with each other, so you're not getting a paradox for free. We first choose the smaller number by setting it as 1, and then tossing Mr. Fair Coin until he lands on his head (that clumsy fellow!). For each toss where he does not land on his head, we double the value of our numbers (the charitability in me!). Oh and I unconsciously neglected to mention, since it was so banally trivial, that since Mr Fair Coin is so fair, he does not have a preference to landing on heads, nor does he have a preference to landing on tails, and is most assuredly not inclined to land on sides, but lands on one of the three with equal probability. Then we double our number to generate the second number."

--Awkward seconds pass--

  "That's quite close to a random number generator, isn't it?"

  Disregarding the disconnect in common sense, he makes a fair point. Let's list the argument in point form:

P1.1: If the number you choose turns out to be 1, the other is 2, which is truthfully larger than 1.

P1.2: If the number you choose turns out not to be 1, but instead is X, the expectation is 3/5*X/2 + 2/5*2X = 11X/10. The other number is expected to be larger anyway!.

P1.conclusion: CE[f(2)]>f(1) for all possible values of f(1), where CE denotes conditional expectation.

P2: The chance of f(1) being infinite is limit (2/3)^n as n --> infinity = 0. Therefore f(1) is finite, and CE[f(2)] is finite as well. Therefore the previous argument regarding infinities does not hold.

  Final resolution (for this post): (highlight for spoilers below)

  The number of real numbers between 0 and 1 is a humongously huge infinity, infinitely (lol) greater than the number of positive integers. If we were to pick a random number from 0 to 1, therefore, the probability that it is any particular number is in fact 0. But this does not mean that it is impossible, i.e. P(A)=0 does not mean A is impossible, since the number randomly generated from the first try between 0 and 1 will have occurred, despite having 0 probability of occurring.

Shame

[Sente "benzoicacid"]
[Gote "sszx"]
[Date "2013.08.04"]
[Event "?"]
[Round "-"]
[Result "1-0"]
[SenteGrade "1162"] (me)
[GoteGrade "1289"]

1. P2g-2f P3c-3d 2. P2f-2e B2b-3c 3. P7g-7f P4c-4d 4. S7i-6h R8b-4b 5. S6h-7g
K5a-6b 6. P9g-9f P9c-9d 7. S7g-6f G4a-5b 8. B8h-7g S3a-3b 9. B7g-6h S3b-4c 10.
P9f-9e P9dx9e 11. L9ix9e P*9c 12. N8i-7g S7a-8b 13. P5g-5f R4b-2b 14. K5i-4h
P4d-4e 15. P4g-4f P4ex4f 16. B6hx4f S4c-5d 17. S6f-5e R2b-4b 18. P*4g G6a-7b
19. S5ex5d P5cx5d 20. P2e-2d P2cx2d 21. B4fx2d R4b-2b 22. B2dx3c+ R2bx2h+ 23.
S3ix2h R*9h 24. G6i-5h N2ax3c 25. R*2a S*5a 26. B*4d K6b-6a 27. N7g-6e B*8d 28.
K4h-3h G7b-6b 29. S*5c P7c-7d 30. S5cx5b+ G6bx5b 31. N6e-5c+ K6a-7b 32. +N5cx5b
N3c-4e 33. R2ax5a+ N4e-5g+ 34. +N5b-6b K7b-7c 35. G*7b K7c-6d 36. +N6bx6c
K6d-6e 37. S*6f B8dx6f 38. P6gx6f K6ex7f 39. P6f-6e P*6f 40. +R5ax5d +N5gx5h
41. +R5dx7d K7f-6g 42. B*8i P*7h 43. B8ix9h +N5hx4i 44. B4dx6f K6gx6f 45. R*6h
P*6g 46. G*7g K6fx5f 47. G7gx6g K5f-4e 48. P4g-4f K4e-3e 49. P3g-3f K3e-2e 50.
N2i-3g K2e-2d 51. K3hx4i S*4g 52. P3f-3e K2dx3e 53. G6g-5g S*4h 54. R6hx4h
S4gx4h+ 55. K4ix4h R*6h 56. N*5h R6h-6i+ 57. P*3f K3e-2f 58. S*3e P3dx3e 59.
+R7d-2d 1-0

Random words (July)

Tenon
Duars
Stipend
Supertax
Prate
Repine
Visage
Countenance
Mien

Go try eets AWWSUM

Wonder where it goes...

How to blunder a rook and still win

Changed to a hyperlink for your convenience!

xkcd what if?

First of all, if you haven't been reading xkcd, I recommend you start reading it soon! It's an awesome webcomic, perfect for people who actually bother to research on the multitude of references inside, ranging from movies to quantum physics!


Next of all (after you've convinced yourself of the worth of reading the main strip of comics), do check out the sideline series of articles by the same author (Randall Munroe) "what if?".


Today's article will randomly make comments on the 44th what if? issue: High Throw. Here's the link: http://what-if.xkcd.com/44/ . I'm not of the opinion that what if? is substandard. In fact, I do think it's awesome and enjoy reading it. But that shouldn't stop me from commenting about it and trying my very best to poke loopholes... right? :)


Quote: "A timing error of half a millisecond in either direction is enough to cause the ball to miss the strike zone... To put that in perspective, it takes about five milliseconds for the fastest nerve impulse to travel the length of the arm."


Comment: This might have something to do with systematic errors being cancelled out: since the time to throw the baseball is determined beforehand by the pitcher, possibly in the brain (and if it's reflexive enough maybe part of it is generated in the spine), there is a fixed amount of delay between giving the signal to swing the arm around and the signal to release the ball in order to hit the strike zone, and this is possibly learned through trial and error, since nobody is THAT good when they were first introduced to baseball. An example of a similar phenomenon can be observed when timing the timespan between two of the same events with no warning (eg. 2 lightning flashes), where the reaction times tend to cancel each other out almost completely (In my experience, my reaction time varies less than 0.03 seconds when doing the "drop a ruler to find out reaction time" test, whereas my reaction time is close to 0.2 seconds. Note that this is still out of the 0.5 millisecond range mentioned by about 3 times. Maybe that's why I don't play baseball.)


Quote:"But we could also sidestep the whole problem by using a device like this one:

It could be a springboard, a greased chute, or even a dangling sling—..."


Comment: This is actually unlikely to be efficient. The first problem is that the entry angle is unlikely to be sufficiently exact for it to just slide up as depicted in the picture. It's likely to bounce around a bit, which tends to lose energy quite well. The second difficulty to overcome is, as in most physics problems, friction. No I'm not talking about air resistance, that has already been (somehow) accounted for in the what if? comic. I'm talking about friction with the deflector. Firstly, let's talk about an instantaneous deflector (eg. a stiff, hard 45-degrees-to-horizontal board). This will cause a great big bounce, which loses energy according to the coefficient of restitution (COR). "Generally, the COR is thought to be independent of collision speed...(except when collision speeds are in the range of 1cm/second)". The highest permissible COR for a tennis ball, according to the international Table Tennis Federation, is about 0.92, on a standard steel block (Wikipedia). This means that about 8% of the energy is lost in one bounce, or about 8% of the height is lost (with an uncertainty of a factor of 2, considering air resistance). This is close to half a giraffe of height. For a baseball, this is likely to be much more, although to be fair, colliding with a board at 45 degrees will probably lessen the impact.


The second kind of energy loss through friction with the velocity converter is the friction that comes when the ball slides along the (for brevity) chute. Usually, when dealing with such dynamic (or kinetic) friction, we can use a formula:

"The coefficient of friction (COF), often symbolized by the Greek letter µ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together." -- Wikipedia, yes again.

Lubricated steel on steel has a coefficient of 0.16, again from Wikipedia (what a glaring testimonial to the unreliability of this article!). So, where does the normal force come from? It turns out that there has to be normal force acting on the ball, since it changes its velocity, and hence this means it accelerates, and using the standard F=ma, we can see that the Kinetic friction is Fric= ma = m(v^2/r), where r is the radius of the chute (Yes that's the formula for centripetal acceleration). So how much energy is lost? We shall make the simplifying estimate that velocity is somewhat constant throughout the ride (else it would be a bad idea anyway). We get:

Work done (against friction) = 2(pi)m*v^2

Well, not quite. After all, can't the ball roll? (The coefficient for rolling friction tends to be a lot lower, which is why cars are even remotely efficient) Turns out that even if it rolls, it won't go as high anyway, because the kinetic energy will be converted into rotational kinetic energy, which doesn't really cause the ball to go higher. (Note that this is in particular because it is a ball; projectiles such as bullets are typically given spin so that they stabilise in an aerodynamic position, a phenomenon known as the gyroscopic effect)


As an aside, note that r is not quite the radius of the chute (I lied.). r is actually the difference between the chute and the ball (Details are left as an exercise to the reader, but rest assured everything tends to cancel out.). There is an interesting special case, which will probably lead to the discussion of a bounce, which I shall not discuss due to its theoretical complexity (i.e. r=0.). And I've been using ".)." too often (Right.).


Yet another point he neglected to discuss (probably too boring) was whether we could thin out the air resistance, for example by climbing to the top of Mount Everest, where the air is thinner (minus some power to account for altitude sickness), or possibly from a hovering helicopter even higher up (Baseball probably would instantly fall downwards from the downwash of the helicopter's rotors or just plainly crash into it).


And one last thing: I don't get the caption for the last comic drawing.

Runescape skills and their applicability to real life

To start off, I just checked the skills present in Runescape, having unconsciously drifted away from the game for quite some time. As it turns out, the f2p (free to play) world has recently gotten access to p2p (pay to play, aka members) skills up to level 5. This isn't a very significant level, but it is a significant step in the expansion of f2p, since updates to the f2p world are as rare as my blog posts. It turns out there are 25 skills, namely *draws deep breath* Attack, Defence, Strength, Constitution, Ranged, Prayer, Magic, Cooking, Woodcutting, Fletching, Fishing, Firemaking, Crafting, Smithing, Mining, Hebrlore, Agility, Thieving, Slayer, Farming, Runecrafting, Hunter, Construction, Summoning and Dungeoneering.

That's a lot to process.

Firstly, I will begin with a few observations on those skills which will eventually save me time.

Observation 1: Dungeoneering and slayer are very forced skills, i.e. skills for the sake of having more skills.

Observation 2: There are a few almost exclusively combat skills, which can be lumped together to save discussion. These are Attack, Defence, Strength, Constitution and Ranged (as well as the combative part of Magic, but hey, Magic is a dual-purpose beast).

Observation 3: Runecrafting is... specific. Let's disregard this for the sake of a glimmer of hope at conciseness.

So we shall begin with the resource gathering skill. Ah... still uncomfortably many: woodcutting, fishing, mining. Out of these, woodcutting and mining are ridiculously industrialised, and are unlikely to be useful unless you happen to work in one of aforementioned industries. Fishing, on the other hand, is an incredibly useful skill, as I have found out personally. It is one of the most effective ways of countering boredom I know, boasting one of the highest used time to productivity ratio. And unlike staring at chess puzzles, people actually pretend to understand why you're doing it.

Next up, resource processing, the monstrous group of skills. This includes: Cooking, Fletching, Crafting, Smithing, Herblore and Construction. We shall do this in a list form, as any prose will result in an unwieldy paragraph that I have learned to shun.

Cooking: One of the useful skills in life, with applications starting from preparing instant noodles, which can save precious seconds and snag you the unbuyable you never wanted! (See: Neopets restocking) This obviously extends to more complex procedures such as barbeques when you happen to be stranded in a forest! (This has been happening surprisingly often to me; sadly I have yet to acquire such mighty levels of this skill)

Fletching: Another important form of entertainment in abovementioned stranded-in-forest situation. Note: Suitable arrows may actually be tougher to find, would do good to prepare those before getting stranded.

Crafting: The rings I know best are tend to exhibit resonance. I shall pass upon detailed discussion.

Smithing: Despite the apparently relation to fletching, smithing is not a viable option due to the disappointing lack of workable metals in forests. Tools may also be disgustingly unimprovisable.

Herblore: Definitely a useful skill, from forest survival to staying awake mugging the dynamics of Neopets using the power of ginseng (anecdotally proven to work).

Construction: Useful insofar as it relates to making a DIY computer. Speaking of which, it might be time to borrow skills from certain friends to improve on this artefact of a computer (a.k.a. mine). Further uses of this include the design of fantastic physical contraptions to do work such as strategically hold down a specific key on your keyboard for various sneaky purposes ranging from games such as Anti-Idle: The Game to Guitar Hero III (TTFAF intro anyone?)

Next up: combat. As somebody who is low in attack, strength and defence (and ranged too, unless it's badminton), I must say I do prefer agility.

This leaves a mere handful of skills that I have left out, probably by accident: Firemaking, Thieving, Farming, Summoning and Prayer, and last but not least, Magic.

Firemaking: This blog does not advocate arson.

Thieving: This blog does not advocate theft of any physical sort, but *borrowing* puzzles, ideas and questions are always encouraged. After all, information is a public good, defined as one which is non-rivalrous and (to a large extent) non-excludable.

Summoning and Prayer: Prayer can be useful in a wide variety of situations, ranging from international chess to chinese chess to shogi to RJT chess to even unexpected niches such as reversi, Go, Connect Five, Transfer Chess and even crazy things like double board RJT chess! (Do try: you'd probably be too befuddled to regret it!). Also, in a last-ditch attempt to make this post remotely relevant, we shall offer a last-minute prayer and invoke the spirit of U+3374 to offer us insights on the uses of magic.

Magic: Coming next^x *next* Thursday, where 1<=x<=3 is a positive integer.

Great eyepow... foresight!

Finally, the backshadowing has caught up. And it isn't even Thursday yet!

I hereby present to you the following guest post, which incidentally, comes without an explicit title:*

In the interest of not having to appear at a certain location in Serangoon on a certain Saturday evening, this article explores the possible topics which may be interesting enough to warrant appearing in the future. In other words, another post ought to be appearing on Thursday! (“Which Thursday?” “Next Thursday!" ”Isn’t that today?” ”No, *next* Thursday!”)

Clearly there are a few classes of possible blog posts. The kind that probably occurs most frequently amongst most blogs simply talks about recent occurrences in one’s life. But, looking at the nature of the previous posts on this blog (as well as the other blog owned by a certain contributor), this is clearly not the way to go (unless you’re talking about recently occurring chess games). Why write about the trifling details of your daily happenings when you can write about the trifling details of your greatest chess failures/cheapoes? Maybe when the (immensely limited) audience begins tiring of annotated chess games (with pretty unsound annotations at that), we can start writing our thoughts on (gasp) other games, like GGbranch-ferrying DotA. (Actually, writing a blog post thinking of strange handicaps and games you can play on a DotA map might be pretty interesting. Next Thursday might happen earlier than expected yet!)

Other than the category of “things that have happened”, there’s the category of “things that are true without needing to happen to us first”** (also known as “facts”). Like maths. And more maths. And even more maths. However, as kindly pointed out, none of our names are “Galois” (who apparently, while younger than us, did something so imba*^3 I still don’t understand it), so we’re kind of short of interesting true things to talk about, even if they do happen to be true. Our work in this area is most likely going to be restricted to generic surveys and discussion of existing results, or reinventing trivial things that we haven’t seen before, but maybe can be found in one of Ramanujan’s notebooks somewhere (though probably too trivial for that). Maybe if we ask a particular penguin*^4 to write something algorithmy rather than pure maths-ish we’ll get something less trivial. Or maybe we can start attempting some original research in some area that hardly anyone’s touched before, which will probably begin not merely next Thursday, but next *next* Thursday!

However, on a more plausible note, I’ve seen quite a number of interesting and not-hardcore-researchy programs written in quite a few areas. The aforementioned penguin has done a couple of interesting machine learning / AI ones, and there are more, like the Twitter iambic pentameter generator, or the genetic algorithm Mona Lisa painter, or the text classifier for “that’s what she said” jokes.  Perhaps when I go and read machine learning or AI or NLP or whatever stuff I’ll write some funny miniprojects up and stave off badminton for yet another week/month/year/millennium. Computer graphics projects are also pretty cool; got to learn that stuff someday.

Of course, instead of writing “facts”, we can instead be cheapskate and contribute our opinions on such facts. Like annotating our chess games. Or coming up with strategies for strange self-DotA-mods*^5. Or maybe writing the fail thought process of spending 5 hours solving some trivial maths/algo question. Or writing a scathing critique of a post detailing the fail thought process of spending 5 hours solving some trivial question. Scathing critiques of scathing critiques could probably be worth a week of writing by themselves!

The last category I can think of is “things that aren’t really constrained by trivial details like fact”. This doesn’t include just fiction (which I’m not really sure any of us are good at writing anyway, but maybe we’ll try someday), but other creative thingumajigs. If a text game ever gets round to being created (coming next next *next* Thursday! My, our Thursdays are going to be really busy, aren’t they?), some interesting aspects would probably end up here, like quest and storyline creation ideas. Art and music also spring to mind, except that we can’t draw and we can’t compose. We can do passable imitations of noob people playing certain instruments, though, but nothing we’d really dare to unleash upon the world online, lest civilization collapse. I suppose what we *can* do is make stuff like puzzles (ought to write another cryptic crossword someday too!), though that borders on fact instead of being pure unadulterated smoke. Also, come to think of it, we do have a decent poet, at least judging from the contents of his other blog. Maybe he can  throw some on this side as well! In addition, next next next *next* Thursday  I’ll probably write a series of articles attempting to formalize a magic system for fantasy settings, so you can wait for that as well.

Thus ends some thoughts on stuff that might appear on this blog in the future. If any of our limited audience has further requests for articles, written by guest posters or otherwise, he or she should feel free to contribute further ideas. Note that the list of banned topics include anything to do with certain units of pressure, especially pertaining to atmospheric pressure, as well as certain martial arts moves featuring in karate. Do will die, don’t ask why.

Happy waiting for future articles! Hope you’ve got a really thick book to read in the meantime.

*Annotations by pH42, yours unfalsely; changed some typos/speeling errors

**Read Anathem for a discussion about this at great length. Like, really great.

***Imbalanced, typically used to refer to something on the overpowering side. Alt. spelling: Imbar

****Preferred spelling: penquin, to better distinguish for penguins.

*****Note parallel to RJT Chess.

The post below is the title

The title above is the post

Yet another Chinese Chess Match

I've no idea why, but I'm by far more likely to post a chinese chess match score on here than an international chess one. But I assure you this was completely trolling a weaker opponent.


START{
 1. C2.5 c8.5   2. C5+4 a6+5   3. H2+3 h8+7
 4. C5-2 r9.8   5. C8.5 h2+3   6. P7+1 h7+5
 7. H8+7 c5+3   8. P5+1 e7+5   9. P5+1 h5+7
10. P3+1 h7+5  11. H3+5 h5+7  12. H5+6 h7+5
13. E7+5 h3-2  14. R9.8 c2.4  15. P5+1 h2+1
16. H6+8 c4.2  17. H8-9 c2.4  18. H7+6 r8+4
19. R8+7 p1+1  20. H9-7 h1+2  21. P7+1 h2+3
22. P7+1 r8.4  23. H6-4 c4+7  24. R8-7 c4.6
25. K5.4 h3+4  26. K4.5 h4+2  27. E5-7 h2-3
28. E3+5 r4+5 }END

Up Goer Five

I suffered at its hands, anything more to say?


'Singapore' is a small state city at an end of 'Asia', which is a really big piece of land. Actually, 'Asia' is the biggest land in this world.

Although 'Singapore' is so small, it is a very interesting place with many different things to do. One of these things to do is to eat many different kinds of food. Because of the many different kinds of people living in one small state, they usually change each other in small ways, and one of the changes is in the way we make our food. Because the set of people can't be exactly found in another place, the food that we make can't be exactly found in another place as well. People who live in 'Singapore' think that food is one of the things that make it a better place to live in.

Another thing good about 'Singapore' is the green all around us: leaves on trees, leaves coming straight from the ground. The green is all around, no matter where you go. All this is part of a plan to make it a "Clean and Green" place to live in.

However, all these are just about things that we can see and touch. There is more to the city state than all these; there are some things that you can't see, hear or touch, no matter how hard you try, like the state of being happy or sad. There is a sense that people living there are all the same in some areas, like having the same past. I think it goes past that, and most people who live there also have the same dream. As such, they work together to make the dream come true. This is shown by having a set of words people accept as true and so say it together, and it is called the 'Pledge'. What it says is something like:

We live in 'Singapore'. We will be one people, no matter our race, our tongue or our gods. We will build a 'Singapore' that gives all the people the same power to give power to other people who will have power and work for them. It will give everyone the same start, and it will be just, so as to make the people happy, well off, and be able to move on.

Needless to say, I scammed, not just with the '' syntax, I believe that's fine because I explained the terms within, but the true scam was with the different senses of the word. Eg. Leaves and Just.

Uncertainty

This blog post is just a poke at the uncertainty theory learnt in school, so...

Student A is a studious physics student, and thinks about physics even after school (shock!). In fact, the very moment he noticed that there was a newly installed solar panel installed at the side of the hill near his home, he decided that it would be great to calculate its power output, and put his knowledge of uncertainties to the test as well!

Via a protractor-bob improvisation, he manages to guess the slope of the solar panel via triangulation. However, as he is lazy to climb the hill, the way he derives the length of the solar panel is via subtracting the height of the lower edge of the panel from the height of the top (using a map to measure the distance from his house to the panel). As a result, the uncertainties are not exactly small, and he estimates the length of the (square) solar panel at 12 meters plus or minus 5 meters.

Using that value, he calculates the area of the solar panel.

Following that, he realises that the amount of sunlight received is somewhat unknown to him, due to poor geographic knowledge of his own surroundings. As such, he decides that the intensity of sunlight would nominally be pegged at 1000W/m^2, give or take 100W/m^2.

Lastly, he realises that he does not know the efficiency of the solar panel. Through internet research, he pegs it at 15% plus or minus 3% (i.e. 12% to 18%).

Finally, he computes his answer, and is feeling extremely satisfied with himself... until he calculates the uncertainty. He then concludes that he made a mistake somewhere in his calculations and goes back to clearing his usual piles of homework.

Valuations in Chess Speed (Where 'Speed Chess' barely does justice to the speed)

After a hiberation, a slumber, a hiatus, a timeless lullaby,
Bright sparks flew, entropy increased, and chaos streaked the sky;
This poem heralding the surreptitious reanimation of chess on this blog is brought to a rhymeless, rhythmless end upon the author realising how meaningless it might get if he tried to keep it up.

     Anyway... this blog post seeks to describe the valuation of pieces in bullet chess, described in the title as Chess Speed (no, Speed Chess doesn't do enough glory to the speed in it; it's like calling Chicken Chops Chops Chicken: just getting the order of importance wrong in the particular context).



     Firstly, let us talk about how computers evaluate a position. Rybka pseudo-famously evaluated position X as +1.47. What does this mean? It means that Rybka believes that objectively, there is an advantage due (by convention it is in general...) White worth the equivalent of 1.47 pawns randomly thrown onto the board in a generic otherwise equal position. Messy? Not quite. Unintuitive about the 0.47 pawns hanging in limbo? Perhaps. A third question necessary to complete the triad? (What was the word again??) Definitely not.

     And what might the significance of such a wispy number detailing non-integer, but nevertheless rational approximations of expected multiples of quantum superpositions of pawns on arbitrary expectations of generic boards be? (Note: expression might not make complete sense) Well, to me, the main significance, and the reason why we find joy and pride in the construction of a program able to derive the aforesaid wispy number from an arbitrarily set up board, is that it can be easily interpreted, with a simple function, the probability the said position is winning for White (or Black).

     If my memory serves, and as I remember it does, a +1 evaluation on Rybka means that on average, Rybka has a 95% chance of winning the position against perfect non-antagonistic play. So let's use half that yardstick, and declare a statistical +1 to be vaguely equal to that which gives me the same probability of winning as that closed integral up till 1 standard deviation after the mean of a normal distribution. Basically an arbitrarily, unnecessarily complicated definition of an imprecise yardstick, because. Ah well, this is an inexact science after all riiight?

     So to start of with a simpler to understand idea, I am playing at approximately a 1450 playing strength according to the chess.com bullet rating, which is rather inflated at lower levels I believe. As a yardstick, I believe that when playing opponents of slightly weaker strength (circa 1350), I tend to hang a piece for absolutely no reason about 1 in 3 matches, counting mostly those I notice after browsing through the match afterward.

     Hence, it may come as no surprise that I estimate that for me, a knight or a bishop can be evaluated, in the abovementioned badly designed scale, to be a +0.5. That means, if I am up a bishop or a knight for nothing, I am expected to get about 0.69 points from the match... against an opponent of my playing strength.

     Time to bring out the table of values... (justification later)

Knight -- 0.5
Bishop -- 0.6 early game, 0.4 if diagonal is blocked by pawns, 0.5 in general
Pawn -- 0.2 in early game, 0.15 in mid game 0.25 in endgame
Rook -- +0.7 if won, -0.4 if lost in early game and 0.7 otherwise
Queen -- 1.5 until mid game, 1.2 in endgame.
Doubled pawns -- -0.05
Passed pawn -- 0.2+0.4/(5-turns to promote) in early to mid game, and pretty much unfixed in endgame
Kingdrift -- Hard to evaluate. Quite a lot.
Pawn towards center -- 0.06 per square
(total value of your remaining) Time -- -30/(seconds remaining)

     Attack is important. Most chess instructional manuals will tell you that, but in bullet chess, it is important both objectively as well as psychologically. We all know that one failed step in attacking may lose you the game, but it probably isn't until about 15 moves later when being down a queen really starts to make its full impact felt. That could take 10 seconds, or 17% of the game time (rounded up in full bias). On the other hand, a blunder allowing a mate in 1 could end in well... 1 move. By contrast, blundering in a defensive position feels a lot worse. People tend to be tempted into trying harder not to blunder in such situations, and hence play more passively and more slowly. Big exploit there. Hence, in general do try to attack, and try to make the attack last. Seek not to sac unsoundly and expend all your material *just* to drain 30 seconds of your opponent's time. 30 seconds is a lot to kill with when you are up a queen, 2 rooks and 2 minor pieces.

     Knights are sneaky. However, they are relatively equally sneaky throughout the game, awarding them 0.5.

     Bishops make your opponents feel insecure if you point them at your opponent's king, preferably with 2, so it's harder to clog both colours with pawn chains. As a crucial part of my playing psychology, I fully recommend it. However, bishops aren't as sneaky in endgames, so they tend to lose a little bit of value in endgames.

     Being up a pawn is important in the opening, both to make sure your opponent thinks that objectively he might actually be losing, and to possibly control 2 squares (preferably in the center). This 2 randomly chosen squares, if properly centralised, can mess your opponent's favourite developing squares with happiness-inducing probabilities.

     Rooks. I don't like using them in the mid game (hard to get out sometimes), and when I lose them it tends to mean that my opponent has just moved a knight about 5 steps before sending it into a corner. On average, this means my pieces are sufficiently more active than his to ensure good counterplay... on the KINGside. Also, it is arguably the most straightforward piece in game, in a game where confusion plays a huge part. *pause* But in an endgame it helps greatly to have your rook still in existence. Ah well...

     Queens are awesome. They are the easiest way to bruteforce out a mate in early to mid game. Without a queen it tends to be a lot harder and opponents unafraid. So even if it in actuality is useless in your lines to get out a blundered mate, do consider keeping it safe and aggressive-looking. They are rather straightforward in the endgame as well, in the sense that they are harder to use in the probably 15 seconds left than to defend against (probabilistically).

     Doubled pawns. A small liability. In case you Do get into an endgame.

     Centralisation of pawns: see argument about accidentally controlling key squares in the center.

     Passed pawns: the kind of pawns that can sneakily move up the board VERY VERY fast (since it's a fast game) and hence catch your opponent rather unawares. Works a surprising portion of the time, and it functions as if your opponent has a second king. Many players treat a queening like an immediate lost, and will take very definitive actions to stop it. Use this to drain time severely and get a strong endgame advantage, even if it means losing the pawn eventually.

     Finally, time, the ultimate killer, has an evaluation that doesn't need explanation. With this, I end my blogpost and wish everybody enough sense not to believe what I just wrote.

P.S.: It isn't Cohm-pleet nonsense. Much of it works in low-level practical play! To the best of my knowledge anyway.

   

A few mysterious definitions

Ch: English dialect for I
Chop: A downward cutting blow or motion, typically with the hand
Ho: A derogatory term for a woman/ imitation or representation of the sound of a deep laugh
Hop: Jump on one foot
Hops: 3rd person singular present tense of hop
Op: Operation
Ops: Operations

This is of course, very definitely not a representation or foreshadowing of things to come.