Winning Strategies For Games Of Chance

In an Olympic year it might be churlish to gainsay the founder of the modern games, Baron Pierre de Coubertin, whose mantra was that “the most important thing in the Olympic Games is not winning but taking part; the essential thing in life is not conquering but fighting well”. That is all very well, but for some psychologists and game theorists rock, paper, scissors (RPS) offered the opportunity to develop strategies that reduced the impact of the implied randomness of the game.

A fascinating article published in Physics and Society in April 2014 by some researchers from Chinese universities described the cognitive processes involved in the game. Taking 360 students and breaking them down into groups of six, they asked them to play 300 games in random pairings allowing them to observe how the players rotated through the possible options. To incentivise them, the players received a small cash prize each time they won.

While there was a slight bias in favour of rock and scissors (35 per cent each) compared with paper, players selected their options randomly on average. However, there was a distinct pattern to the way players behaved after the result of a round of RPS. Those who had won were more likely to stick with their selection, whereas those who had lost not only were prone to change their choice but also to follow a clear sequence, choosing paper after rock, scissors after paper, and rock after scissors and so on.

An understanding of this process, which the researchers called a “win-stay lose-shift strategy”, opens the way to developing a winning strategy. The key is to be a reactive rather than a random or reflexive player, concentrating on reacting to how your opponent plays. As most winners stick to their choice and losers alter their choice in a cyclical fashion, this can be turned to advantage.

The researchers do sound a note of caution, though, by pointing out that opponents who also adopt a reactive strategy will be more difficult to beat. However, they observe that facing an opponent who is confident enough to break away from the “win-stay lose-shift strategy” is rare and basing a strategy on the assumption that most players will stick to a reflex-based strategy will, on average, improve the chances of winning. Extending the concept, Neil Farber, writing in Psychology Today in April 2015, provided a handy list of nine strategies to adopt against non-random players of RPS.

Weighty matters have been decided by a game of RPS. In 2006 a Federal Judge in Florida, Gregory Presnell, ordered the two sides in a lengthy case to settle the matter with a game while three police officers were reprimanded in 2015 for allowing a underage drinker to avoid a fine after beating them at RPS. Even august auction houses, Christie’s and Sotheby’s, resorted to playing a game, under their client’s instructions, in 2005 to determine who would have the rights to auction a collection of impressionist paintings. Taking advice from the 11-year-old twins of a director to choose scissors, Christie’s won, earning a sizeable commission from the subsequent auction.

In the days of yore when our rivers were not full of effluvia, a game of Poohsticks was a pleasant way to spend a summer’s afternoon. It is simple enough, competitors dropping sticks off a bridge into a river upstream with the winning stick the first to reach a designated spot downstream. To avoid unseemly arguments, perhaps to be settled by a game of RPS, each stick should be personalised in some way. AA Milne introduced the game, which he had played with his son off Posingford Bridge in the Ashdown Forest, to a wider public in his The House at Pooh Corner (1928), attributing its invention to Winnie the Pooh.

While 57% of Britons surveyed believe that Poohsticks is a game of pure luck, it too has fallen prey of game theorists. Dr Rhys Morgan of the Royal Academy of Engineering has developed a formula which enables a competitor to gain an edge, expressed as PP (a perfect poohstick) = A * E * Cd, where A is the cross-sectional area, I the density, and Cd is the drag coefficient. In layman’s terms the stick should be long and thick, heavy but not so heavy that it will sink, and with quite a lot of bark to catch the flow of the river like paddles.

Just 11% of the 2,000 respondents, the survey found, instinctively selected the right sort of stick while 30% went for a long, thin stick, which, according to Dr Morgan, is only half right. If you want to test his findings, head to one of these bridges, designated by VisitEngland, as the twelve best for Poohsticks.

Rely on your instincts or pay heed to the game theorists, the choice is yours!  

The ABC Murders

A review of The ABC Murders by Agatha Christie – 240323

The thirteenth novel in Christie’s Hercule Poirot series, originally published in 1936, is generally regarded as being one of her best and it is so well known and has been so well analysed by critics and reviewers that it is difficult to find anything original about it. It does contain some unusual features which keep those he feel that she too easily slips into a tried and tested formula on their toes.

In format it starts out as an inverted murder mystery where the reader is given advance warning of who the killer is and we can smuggly watch the sleuths grapple their way through a morass of clues to reach the conclusion that we knew from the start. However, Christie knocks any smug complacency out of the park with a ferocious twist in the tale that upsets all preconceptions. Inspector Crome’s case against the prime suspect seems so convincing but there are a few little details that do not quite fit into the overall picture he has painted, enough to worry Poirot and set his little grey cells whirring.

There is more than a little humour in the book, perhaps more than I would normally expect from Christie’s pen. She enjoys through Poirot pointing out the differences in approach between her sleuth and Conan Doyle’s Sherlock Holmes, evidenced when Poirot pulls Hastings’ leg by plucking a description of the murderer out of the air from little or no evidence like the occupant of 221b Baker Street. She also references poetry, or at least a nursery rhyme, “and catch a fox/ and put him in a box/ and never let him go”, which gives a telling insight into the psychology of the culprit and alerts the reader that the inversion is going to be inverted.

Hastings makes a return, narrating the mystery, although he adds a few chapters here and there which are not from his journal but which, he hastens to assure us in the preface, he has verified with the best possible sources including Poirot. Always a man to state the bleedin’ obvious Hastings earns his spurs by making a banal observation that is so perceptive that it causes Poirot to reconsider his theories and come up with an alternative and radical solution to the problem at hand.   

Unusually for Christie, she has a serial killer on her hands who seems to strike at random albeit with an overarching scheme. First Alice Ascher is murdered in Andover, Betty Barnard in Bexhill, and Sir Carmichael Clarke in Churton – you get the sequence. The murder leaves their calling card, a copy of the ABC Railway Guide placed under or by the victim, and each attack is preannounced by a letter addressed to Poirot himself issuing him with a challenge to apprehend the culprit if he can. The fourth murder, in Doncaster, seems to follow the same pattern but the victim is George Earlsfield.

There are aspects of the second murder that worry Poirot and he wonders why the letter announcing the third murder was misaddressed so that he and the police had no opportunity to prevent it. Indeed, why send the letter to him and not to the police or the press? Convinced that there is a causal link between the first three murders, Poirot pulls together a working party made up of relatives of the victims and through that discovers that a travelling salesman, selling stockings, had been in the vicinity of each murder at the relevant time.

However, Poirot cannot believe that the individual languishing in the police cells, having collapsed and given himself up in Andover, has either the intellectual capacity to challenge Poirot as an equal nor the personality needed to sweep a flighty young girl off her feet and arrange a nocturnal assignation on a beach. The true culprit, although superficially charming and eager to help, is a thoroughly nasty piece of work who has manipulated a psychologically damaged character to act as their fall guy. As is often the case, the plot is an enormously risky and unnecessarily complicated way of getting your hands on an inheritance.

The characters may be unrounded and the dialogue wooden, but you do not read Christie for a polished piece of literature as you would a Nicholas Blake, Gladys Mitchell or Josephine Tey. You pick up her books to be royally entertained, forget your cares for a few hours, and exclaim “did that really just happen?”. She achieves this in spades with The ABC Murders.

Cefn Coed Viaduct

The third largest in Wales, Cefn Coed Viaduct was built to carry the Brecon & Merthyr Railway over the River Taff near Merthyr Tydfil in South Wales. Designed by Alexander Sutherland and Henry Conybeare, it consists of fifteen arches, each one with a span of almost forty feet, and is 257 yards long with a maximum height of 115 feet. Described as a graceful and majestic structure, it has an impressive and elegant curve.

The designs were prepared by Alexander Sutherland and Thomas Savin and John Ward, managers of the railway company took responsibility for the build. However, they soon hit problems when the company, which had been paying a guaranteed five per cent dividend to shareholders, ran into financial problems. Sutherland stepped in to save the day, choosing an alternative route for the section.

The revised route avoided Cyfartha Castle, the property of local ironmaster, Robert Crawshay, by going down the west side of the valley, increasing the engineering complexity of the project but earning the gratitude of the influential landowner. It is alleged that a sizeable bribe eased the pain of the redesign.

A further problem hit the project when, in February 1866, stonemasons went on strike. The intention had been to build the viaduct out of limestone, like the nearby Pontsarn, which Savin, Ward, and Sutherland had also built. Instead, the company was forced to buy 800,000 bricks and employ bricklayers which is why bricks line the underneath of the arches while the rest of the structure is made of stone.

Eventually, on October 29, 1866, Mrs Sutherland was able to lay the final stone and the viaduct was declared open. It had cost £25,000 to build and was used until the line was closed to passengers in 1961 and the last goods train trundelled over it on August 1, 1966. It has since been renovated and now forms part of the Taff Trail walking and cycling route.

Eight To Nine

A review of Eight to Nine by R A J Walling – 240321

The curiously titled sixth novel in Robert Walling’s Philip Tolefree series, also known as The Bachelor Flat Mystery, originally published in 1934, is another story where the movements of suspects at a particular time hold the keys to the mystery. The hour in question is between eight and nine, when housekeeper Mrs Pilling is off duty at Elford Mansions, hence the title, and seasoned readers of the detective fiction genre will soon realise that the empirical evidence of time is not necessarily to be trusted.

The story also centres around a femme fatale, an actress by the name of Millicent Vane, a woman with a past and to whom several rich and eligible bachelors are attracted like bees to a honeypot. One such is Bill Chance, son of Lord Greenwood, and the worried nobleman engages Tolefree, insurance broker and amateur sleuth, to dig around and find if there is any scandal attached to the woman. Curiously, we never meet Miss vane. Despite his distaste for the task, Tolefree accepts the brief and accompanied by his faithful Watson, a ship broker by the name of Farrar, begins his investigations.

Acting on a hunch to visit rich playboy, Howard Klick, at Elworth mansions, Tolefree finds that the comedic Mrs Pilling has fainted and that there is a body of a murdered man in the flat occupied by North. Despite the assumption that the murdered man is North, Tolefree discovers, courtesy of a feather and an Australian penny, that the victim is Australian and that he is Pendleton, the husband of Miss Vane whom, when he was imprisoned for fraud down under, she left to come to England and seek her fame and fortune. Understandably, Pendleton was a bit miffed and when he was released sought his revenge.

The police investigation is led by Pierce and while he and Tolefree have perfectly amiable relations, they approach the case from radically different angles, coming up with two different culprits. Tolefree engages in a masterful piece of filibustering to prevent Pierce making a fol of himself and incurring the wrath of his fierce Scottish boss.

It is a tale of timetables and alibis with a reasonable number of red herrings and witnesses whose accounts are not entirely reliable. One credible suspect is summarily dismissed because he sailed from Australia to London in the Orlando second class and second and first class passengers never mix.     

After much toing and froing, including a nighttime expedition to the wilds of the Fens, much to the discomfort of Farrar who had to tail a car at a speed above which he was comfortable driving at, Tolefree concludes that the culprit is someone who sailed on the Orlando at the time Miss Vane did, lives in Elford Mansions, maintained a flat for Miss Vane in Kilburn, and who had a rendezvous with Pendleton on the Thursday night in question.

These criteria together with the disappearance of the feather and Aussie penny from the scene of the crime seals the identity of the culprit. In Poirot style he lays out his findings before Lord Greenwood and an assembled group of suspects, demonstrating that Pendleton’s death was committed in self-defence rather than a premeditated act of murder.

It is a complex plot and the story is well told in an engaging style, Walling uses short burst of staccato-like sentences to inject some urgency into the narrative. I could not help thinking, though, that a chat with Miss Vane would have saved a lot of time.

Waterloo Station Clock

Where do you meet on a crowded railway concourse? The obvious place is under the station clock as it is usually centrally positioned so that it is visible from each of the exits from the platforms.

One of the most iconic meeting places is under the railway clock at Waterloo station, famously the meeting place for Laura and Alec in Noel Coward’s 1946 film Brief Encounter, although the scenes were shot at Carnforth station, and of Del Boy and his future wife, Raquel in the Only Fools and Horses Christmas special in 1988, Dates. Curiously, despite its iconic status, whenever I have arranged to meet someone there, there has been hardly anyone else staring anxiously and vacuously into the distance.

Manufactured by Gents of Leicester, on its installation it was described by the Daily Mirror in its edition of November 19, 1919 as a “two ton clock…of novel construction”. What was unusual about it was that it used within its mechanism an electric “synchronome”, which ensured that each of its four faces told the same time. It also had twenty-four hour faces, well before British Rail adopted the twenty-four hour clock as standard in 1964.

Waterloo’s clock was originally positioned in front of the taxi rank between platforms 11 and 12, platform 11 being the terminus for the Ocean Liner Expresses, and the Bournemouth Belle. When the Windsor train shed was demolished to make way for the International platforms, two new platforms, 12 and 13, were opened and the original platform 12 was redesignated 14.

It did not take long for the clock to be established as a meeting place. Londonist in their blog notes that in 1924 a short story syndicated in the press featured a meeting under the clock, another from 1927 spoke of an “under the clock” tradition for meeting at Waterloo a rendezvous that formed the basis for a romantic liaison in a 1935 short story.

Next time you are at the station, see just how many people are waiting under it. It might just lead to an exciting adventure!