Morpheus on… Two Clever (?) Ideas

I once heard a story about a young man who was propositioned by an old man on a long-distance train. It was not THAT sort of proposition, however. This one involved GAMBLING.

Despite having been warned by his mother about the dangers of gambling with strangers on trains, the young man listened.

The two men had a compartment to themselves, which had a small fold-down table positioned between them.

The old man removed his jacket and hat, rolled up his shirt sleeves and produced three two-inch discs. On one, there were two identical, plain crosses – one on each side. The second was blank on both sides. And the third was blank on one side, with a cross on the other.

He explained the methodology thusly. Each would take it in turn to place the three disks into the hat, give it a shake and hold it under the table – and then the OTHER would remove one disk, clench it in his fist and slap it down on the table. At which point, the first would have to guess whether the UNDERSIDE was blank, or had a cross on it.

The old man pointed out that since the other was drawing the counter, cheating would be impossible.

He further stipulated that either party could examine and re-examine the hat and/or the disks at any time – as many times as they liked.

The young man examined the counters carefully. Without doubt, the crosses WERE identical – precisely centred and PRINTED onto the counters. All were perfectly flat, with clean edges.

He then examined the hat, which proved to be mundane. He even checked the old man and determined he had no concealed mirrors or trick glasses – not even contact lenses.

At which point, the young man said okay then, what was the point? If the cross was on top, the disk could not be the double-blank – thus it had to be either the cross-blank or the double-cross. The odds were fifty-fifty.

And likewise, if the top was blank, it could not be the double-cross. Therefore it had to be either the cross-blank or the double-blank. Again, fifty-fifty.

Plus, the discs had the same number of crosses and blanks, evenly distributed on their faces. Yet again, fifty-fifty.

Precisely, said the old man. He went on to explain that since the train journey they were on was a long one, a fifty-fifty game would pass the time more quickly – without either of them being in danger of losing a significant amount of cash.

Having established that both parties had fifty pounds on them which they could afford to lose, they decided on that sum as a “ceiling”. And since their money was not in single pounds, they would keep score on a piece of paper, which would be placed on the table – in view of both at all times – and settle up when one of them reached the ceiling or they both reached their destination.

And so they began to play. At first, the game proceeded pretty much as the young man had expected, with neither man moving ahead. However, after a while, the old man’s fortunes appeared to improve.

The process was gradual – but slowly, the old man’s total began to approach the fifty pounds.

Despite the young man having examined the discs and hat a number of times – with no anomalies detected – the old man finally hit the agreed sum, a few miles before the journey’s end.

The young man paid up – and asked the old man for the secret. Their time together had been good-humoured, so the old man let him into the secret.

He pointed out the young man had been INCORRECT when he had determined the game to be fifty-fifty. He said that in fact it was two-thirds/one-third. The trick was in the NUMBER OF COUNTERS. There were THREE – not two.

Thus, if one bet on the hidden side being the same as the top side – one would be correct two times out of three. Therefore, if one said the hidden side was the SAME, MORE than fifty percent of the time – in the LONG TERM, one would have an EDGE.

Obviously, if one ALWAYS said the underside was the same as the top side, the other person would realize what was going on and COPY them – and therefore, while they might not understand the principle, they would neutralise the first person’s advantage.

The trick was to exploit the advantage enough to show a profit – without alerting the other player to the method used.

The young man considered fifty pounds to be a fair price for having learned an interesting ploy – and having an equally interesting anecdote to tell his friends.

They shook hands and went their separate ways.

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

Which brings us (and not a moment too soon) to Clever Idea Number One.

Bearing the above story in mind – I devised a System For Winning At Roulette.

Now, I HEAR you – roulette has been around for over two centuries and the grounds of the casinos of the World are littered with the corpses of those who thought THEY TOO had a system.

So what was MY system, I hear you ask, expectantly. Well, it was thus…

You attend a wheel and watch the play, writing down the numbers that come up on it. Few casinos mind this – they are keen to attract ANY punter, provided their “system” does not interfere with the game. In fact, some casinos will even PROVIDE you with the list of numbers that have come up during the last hour.

Either way, once all of the numbers have come up one time each – you examine your list and place a bet on the number that has not come up for the LONGEST time.

You play this number for each subsequent spin – the same amount of money each time – taking care to continue listing the numbers that come up. When your designated number DOES come up, you take your winnings and check your list to see which is NOW the number that has not come up for the longest time. Then you play THAT, until it comes up – and so on.

This means that you are continually playing the number which is the most “DUE”.

Now, casinos are out of my league – so I decided to run this one around the block to see if the wheels would fall off, using something I COULD afford. A douse – singular of dice. (I was just checking to see if you were still with me – the word is of course DIE – appropriately enough).

So what I did was this: I threw a good quality die into a box (with a flourish, to ensure it was a “good” throw) and noted the number that came up. I then repeated the action FIVE HUNDRED TIMES.

Using the same system described above, for roulette, I deducted a point for every wrong number – and awarded myself six points every time the right number came up.

I figured that five hundred throws ought to give me a fair average, with my “total” being only one – or at the most, two – percentage points off.

So you can imagine my surprise when – after having computed that total – I discovered I was almost TWENTY-FIVE PERCENT UP!!!

Resisting the temptation to smash my piggy bank and head for the Riviera, I determined to ask a smart friend I was meeting in the pub later – what his thoughts were.

After we had sat down in the pub, I told him BOTH of the above stories. He mused for a bit. You’re assuming a perfect wheel, he asked. Oh, yes, I replied. (I knew the underside of roulette wheels have grub screws to adjust the divisions between the numbers, to allow them to be calibrated to be as true as possible).

He mused a while longer and finally told me that it would not work. He pointed out the wheel has no memory. Even after a number has come up three times consecutively, the next spin STILL gives you the same odds it will come up again. Thirty-seven-to-one against (thirty-eight in America – The Mob were more greedy).

In fact, he said, if the wheel was NOT perfect, you would actually be betting AGAINST the odds, using my system.

I told him I’d already considered ALL of that. AND the fact that if it were really that simple – during the two hundred-plus years people have been playing the game, someone would already have THOUGHT of my idea.

But then I directed him to the result of my experiment with the die. Twenty-five percent, mate.

He replied that any worthwhile experiment HAD to be repeatable and advised me to do it AGAIN and see what happened. I figured a sample of five hundred ought to have been enough – but agreed to try it again, the next day. We then moved on to other matters.

And so it was that the following day I got out the die, the cardboard box and the notebook and pencil – and gave it ANOTHER five hundred goes. This time, the variation from the norm was AGAIN nearly twenty-five percent, except on THIS occasion I was twenty-five percent DOWN!!

DAMN!

I can only attribute the ENORMOUS variation – and the fact that it was UP the first time and DOWN the second – to bloody MURPHY. It had SEEMED like a Clever Idea…

– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –

And so, we finally arrive at Clever Idea Number Two.

This has NOTHING to do with the above – apart from the fact that it emerged from the same brain (mine). This time, it concerns aeroplane landing gears (a bit different from roulette systems, but stay with me).

It is no secret that a plane’s most hazardous moments are experienced on landing (particularly if it is in the Hudson). Aside from those CROSS-WINDS (see elsewhere, in these columns) the SHOCK when a number of STATIONARY wheels hit a concrete runway, below a four-hundred-tonne aircraft doing around one hundred and forty miles per hour – is MASSIVE.

Tyre blow-outs are common. In fact, when it happened to Concorde, pieces of rubber were known to rupture the wings’ fuel tanks. It is a wonder the fire and crash that ENDED Concorde’s career did not happen much earlier.

So what can be done to minimise this SHOCK to an aeroplane’s underparts?

Well – how about a row of half-cups, attached to the wheels?

Think ANEMOMETER.

With a row of large half-cups forming the outer face on each one of an aircraft’s wheels (or perhaps two, smaller ones – or a row of sloping slats) – if positioned correctly, when the gear was lowered they would cause the wheels to ROTATE in the direction of travel.

And once the optimum size had been established (through experimentation) the wheels would reach a speed that would almost be that of the groundspeed – ensuring that instead of them having to overcome that monumental INERTIA as they made contact with the ground, they would be rotating at the right speed to ensure a landing so soft, that no longer would little old ladies ask the trolley-dollies whether they had just landed – or been SHOT DOWN.

Bliss.

But like my roulette system, the concept is hardly rocket science – so why has no-one THOUGHT of it before? Aeroplanes have been around for over a century and some pretty wild ideas have been tried (many with fatal consequences).

As with the roulette thing, I have tried to think of snags. Obviously, aeroplanes’ landing gears present major DRAG – which is why they took the expensive and difficult step of making them RETRACTABLE. Thus, the half-cups or whatever would exacerbate that problem.

However, by simply dropping the gear more gradually and accounting for the drop in airspeed…

Then there is the speed of the wheels. But I would have thought that balancing the force exerted by the half-cups against the friction set up by the wheel’s axles (by designing the SIZE of the half-cups correctly) would allow the wheels to PEAK at the desired speed.

Plus any major amount of head-wind could be dealt with using some sort of governor – or simply by ensuring (again, by design) that the wheels’ speed was significantly LOWER than the groundspeed.

Indeed, even if the wheels were only rotating SLOWLY – surely this would still EASE the shock caused by the INERTIA of those STATIONARY wheels?

If anyone who has stumbled across this piece and read it this far has specialist knowledge (perhaps YOU are an aircraft designer – and I do not mean paper darts) I would be obliged if you would leave any information you possess as a “comment” on this piece.

I (and I am sure, others) would be fascinated to know if this Clever Idea HAS been tried – and if so, why it DID NOT WORK.

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2 responses to this post.

  1. Numbers confuse what little brain I have so I took in very little of the train ride story, ditto roulette because casinos are of no interest to me. Any device to drive the aircraft undercarriage wheels around would add weight. I guess it has been preferable to upgrade the spec of tyres to keep up with the increase in jet-liner weight. I guess fans of flying boats lost their cause once pneumatic tyres got really good.

  2. Posted by Vincent on May 12, 2011 at 1:16 pm

    Nah – trust me – WEIGHT would not be an issue. The wheels would merely have a series of “ears” moulded into the side, instead of just being hollow.

    Flying boats were COOL – but not so good for flying to Houston, Beijing, Moscow, Berlin…

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