Now, there are two possible things you might want to do with your coin pressure.

The first case is that you want to maximize your coin pressure. Why would you want to do this? Get rid of the change you are carrying of course. This is easily achieved by merely carrying a lot of change around – but most of us don't carry a coin purse, or anything that can hold substantial amounts of change. So what is it you can do to maximize coin pressure?

What you can do – is to always carry around a fixed set of coins and notes. Your meals would usually not exceed 10 dollars. (If they do, then it might be time you stop caring abount coin pressure and start caring about wtf you're eating.) This means that you should carry around enough change to pay anything from $5 to about $15 (just in case there was a want or need to splurge on drinks, dumplings, soup, or whatever nonsense was.)

Let's simplify the problem to just carrying $4.95 in coins – you can carry a $5 note and a $10 note to make sure you can cover the ranges extremes at $5 and $10. To be able to cover every possible change situation from $0.05 to $4.95, in Australian coins:

• 1 x 2 dollars
• 2 x 1 dollar
• 1 x 50 cents
• 1 x 20 cents
• 2 x 10 cents
• 1 x 5 cents

This is obviously a very specific case, since there's not many 1 cent coins in circulation in Australia (if any) – so in order to maximize coin pressure, you only need to carry 8 coins in total. Very manageable for most wallets (unless you don't have a coin pouch or holder).

If you live in a country where there are no $2 coins or notes, and you do still have 1 cent coins, then to cover $0.01 to $4.99 you would need to carry:

• 4 x 1 dollar
• 1 x 50 cents
• 1 x 20 cents
• 2 x 10 cents
• 1 x 5 cents
• 4 x 1 cents

13 coins – which could pose a problem. But if you live in Malaysia – you have RM1 notes! (and 1 sen coins are gonna get phased out eventually anyway, but 5% taxes at food places make it annoying.) And if you have $1 notes, you then only have to carry 9 coins – which is again manageable.

Of course, this guide is only good if you happen to have a huge stack of coins at home and want to get rid of them – if you keep reloading your wallet from your stash like this, you'll see to drop in size quickly enough. Obviously, this guide only works if we assume coins are in some decreasing order of size (barring the Australian dollar and two dollar coins). It's entirely possible that this is not always true (for example, the US nickel, 5c, is a lot larger than the US dime, 10c, and there's that 25c coin that'll just annoy your math if you're used to 20c coins.) – just adjust accordingly.

The second case is that you want to minimize your coin pressure (or in other words, create a change vacuum.) Why in the world would you want to take change? There are various reasons – number 1 – you need the change, since the notes you are carrying are way too big. This usually happens if you're walking about with 50 dollar or 100 dollar notes – which are almost always too big to spend on anything small (sub-$10).

It's pretty simple to achieve – carry around very big notes, or if you feel like turning your friends into portable ATMs (that are sometimes difficult to collect from, like malfunctioning ATMs ) – carry around a credit card, preferably one from the same country. Don't want to get caught up in messy exchange rate risk now, do we?

(Note: Look – no photo. What did I tell you about me not maintaining any trend?)

Look again at the one who has been seen inside but hasn't been seen entering.

Look once more at the one who has been inside but doesn't have a map.

Look once more – and you will find the one who knows everything.

While I'm not gonna post photos of them, since they're no longer out on show like they used to be in my Arrow apartment, and they were pretty stupid purchases since nobody I knew appreciated them. Anyone who knows me also knows that I'm pretty bad at controlling my spending. I buy loads of random stuff on a whim, and it's usually worked for me.

I tend to think a lot when buying stuff, and this is one of the two really impulse purchases I've ever made. The other one is a story for another day. So, like always, I bring back some bulky box into my small Arrow apartment, stuff them into the storage (my apartment was a corner, so it had a small storage space). Anyway, I took them both out to examine. I found one of them lightly damaged, nothing I couldn't fix – so I put up the other one with a view to alternate every once in a while.

Needless to say, having a fox on somewhat of a stage/pedestal that looks like some kind of extravagant deity in addition to my already slightly strange behaviour – led to my housemate asking me whether or not I pray to the thing. And he wasn't kidding. *sweat*

After moving to my new place, I didn't display either since I didn't have the table space for them. (Arrow had these low drawers that I couldn't really do much with, so I just put the resin statue on one of them.)

Well, so here, there are in storage and not doing anything at all! Cool eh? Well – at least no one will think I pray to a nine-tailed fox deity and a monstrous looking forest spirit – right?

Now that you know the big picture – does my original argument still hold? To see whether it does, let us consider what happens when we choose to cross at the first traffic light if it is green.

If we do, our problem is simplified to this:

Using our original assumptions of independent Bernoulli trials, you can see simply that you have a 87.5% chance of being able to cross at one of these set of the moment you come to one. This are significantly better odds than you had before (50%) – but it is still unable to beat the result from skipping that first green traffic light (100%). (Yes, crossing at that north T junction vertically DOES NOT require you to wait for a traffic light.)

Surely, there must be a point to me writing about this. The point is simple:

Minimize the number of traffic lights you have to cross
to minimize travel time.

Why is this important? It will help you understand some decisions you can choose to make during my journey to university when I get to that – and the path I chose to minimize travel time, while minimizing disutility while travelling to university. Next up: why you might decide against lower travel time.

]]> http://cfgt.net/blog/2008/04/26/extending-the-traffic-light-problem/feed/ 0 http://cfgt.net/blog/2008/04/23/the-law-of-coin-pressure/ http://cfgt.net/blog/2008/04/23/the-law-of-coin-pressure/#comments Wed, 23 Apr 2008 05:02:19 +0000 cfgt http://cfgt.net/blog/?p=579

(More)…]]> I remember have this strange theory that is usually true. I might have even mentioned it on this blog before maybe even blogged about, but this is a post entirely devoted to this funny subject.

In a contracted form, it simply says this: The more coins or small change you have, the more likely you are to give them out – and the less likely you are to receive them. I call it “coin pressure” as a reference to air pressure. Air flows from high pressure areas to low pressure areas – and so do coins. This is typically the case when you go out with friends.

Imagine the case where you go out with friends to eat. Being students, going Dutch is standard practice. There is no arguing over who pays the bill. Everyone pays the bill. Now, some places do cater to students and allow you to pay separately for items on the bill. This means that there is conversation going: “You owe this much from that, and you're supposed to pay for that, and I'm supposed to pay for this.”

Usually you relegate this calculation to the accounting major students by just using the excuse that usually goes: “Let's give this to the accounting majors to sort out.” In real life, there's probably a better mental mathematician at the table than the accountants (in fact I think in our case it was a management major student) – but hey, anything to not do the work.

After it gets sorted out, then everybody gets the numbers. Sometimes the numbers can get pretty bad change wise, for example, $8.90 per person. That means to pay exactly, you need one $5 note, one $2 coin, one $1 coin, one 50c coin, and two 20c coin – and that's already the simplest possible. 6 pieces of change to pay off your bill.

Of course, if you have the change, you just pay your part. If you don't, you take on more and more change – in general, the bigger the currency note you have to pay with, the more change you will have to carry when you leave. It follows that the opposite holds true, the more small change you have, the less small change you will have to carry when you leave. (Hence, the origin of the law.)

There is the largest possible denomination of currency – a credit card. If you are paying the bill on behalf of the table by credit card, then you effectively collect all the payment by everyone else – since you had the lowest “coin pressure”.

Of course, there is such a thing as too much coin pressure. If you carry around 200 5c coins just so that you will always have enough coin pressure to pay off any possible bill within $10 – nobody will want to have to split a bill with you.

Moral of the story?

Carry a good variety of coins and small notes with you.

Try to never leave any coins at home unless it's in your piggy bank. Coins at home have this bad habit of accumulating to ridiculous numbers since you leave more and more and home – and leaving coins at home reduces your coin pressure, hence increasing the probability of you receiving even more coins.

There are many considerations when trying to get somewhere by walking. How many traffic lights are on the way? Are there any diagonals you can use to get there faster? No matter how far you walk, you'll sometimes find yourself facing what I like to call the Consecutive Traffic Lights problem.

What is this problem I've randomly given a name to? It's really simple if you look at my diagram.

The arrow being the pedestrian, and X being the destination. If the first set of traffic lights turn green – do you cross the road at the first junction and then go to the second? If you said yes, then you have probably been wasting a lot of time waiting for traffic lights.

Why? Think of it this way. Assume the traffic lights behave independently of each other and their state when you get to them is random – and the chance of a green light in either direction (when you arrive at the lights) is 50%. This also means that the lights last an equal amount of time. As with most lights in Melbourne, crossing the junction horizontally, and then vertically or vice versa, you wait a minimal amount of time (about 15 seconds).

OK, so to my first example – the state of the first set of lights is green. Say you cross – then there is a fifty percent chance that you will get to the second set of lights in the right direction. If you don't cross – you have a 100% chance that you will get to the second set of lights in the right direction. This is just based on completely independence of the two sets of lights.

In truth (the real life scenario that I do walk every day), the lights are synced. This means that the go green in the same direction almost the same time. The problem with this? Crossing the junction and making it to the second set of lights is enough time for the second set of lights to change twice – what does this mean? There is an 80-90% chance that when you arrive at the second set of lights -> it will be red for the horizontal direction and green for the vertical direction you just crossed. Ah ha!

If you've been following this closely, you'll see that this argument doesn't hold water if you can get to the next set in three light changes – which alters the argument the other way round. However, this doesn't reduce travel time – all it changes is whether it matters that you crossed at the first traffic light or not.

This means that the dominant strategy is to ignore the first traffic light and go straight for the second set of lights, since this will probably reduce the expected travel time. Why? Since even if you don't have any information on how well the traffic lights are synchronised, you will get to cross when you arrive at the second junction. This is true as long as you can cross on all sides of the road, and some set of pedestrians can cross at any given time.

I've decided that now I've moved to a new place, it's time I update it with my new table! The last time you saw my table, it looked like this:

I've changed the layout of my room and now have a new desk lamp!

I won't be numbering everything like last time (since it's not that cluttered), but I think it's always a good idea to tell you what's in the photo so you can look for it.

Let's take a closer look at the left side of the photo:

Items in the photo:
1. Empty IKEA food container.
2. Spindle of Verbatim DVD-Rs.
3. Left speaker.
4. Chimei 22″ monitor – if you can guess what website this is, heh.
5. Pack of sweets.
6. Electric shaver.
7. fx-570w calculator
8. Green highlighter
9. Plug converter.
10. Ruler.
11. Safeway receipt.
12. IKEA receipts.
13. Green USB hub.
14. Apple Wireless Keyboard.

Then, what about the right side of the photo?

Items in the photo:
1. PowerBook G4 1.5GHz
2. Right speaker.
3. Pair of IKEA scissors.
4. Yellow highlighter (not easily visible)
5. Camera.
6. Toilet paper.
7. Loads of stationery and receipts.
8. VX Revolution.
9. MX610.
10. Plastic spork/foon.
11. 1GB thumbdrive.
12. Desk lamp! Woo-hoo!

Underneath the table:
13. All-in-one printer.
14. Box of Magic commons.
15. File of stuff to settle with uranium238.
16. Box file for books and stuff.

What is not in any photo but underneath the table:
Consoles and CD files containing games for those consoles, headphones, loads of AC adapters (I mean LOADS.)

And then today, I logged in the XBox Live Marketplace to see this really nice ad.

*cue extreme annoyance and anger*

If you'll excuse me, I'll go back to writing out cover letters for potential employers after lunch, by when I've hopefully cooled off somewhat.

(Btw, if this is Microsoft's way of telling me to get the PS3 version, I'll be more than happy to do so. As soon as Play-Asia gets the stock to send me.)

Update: Just thought I'd post my gamercard.