You cut, I’ll choose

Winning depends on initial attitude

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When I was a nipper and my older brother and I were offered something like a cake to share, he would say, “You cut, I choose.” Of course, it would be nonsense for him who cuts also to choose, for then he’d cut himself a nice fat piece of cake, and leave the crumbs for the other. But, it is visually easy to discern which of two slices of cake is the larger. All my brother needed to do was decide which was bigger and leave to me the motor skills of cutting one cake exactly into two halves. Not once did he ever say, “I’ll cut, you choose.” Nor was there any suggestion from him that we cut and cut and cut until we both agreed the portions were the same. One cut. He chose.

What seemed like a manner of proceeding that guaranteed fairness was in fact predicated on exploiting the immature cutting skills of the younger party: my brother didn’t reckon I could cut straight, but reckoned he could judge straight and, if I can’t wield a knife, that’s my bad luck. Shall we say, it’s a method that doesn’t exactly foster a mutual feeling of trust.

Casinos offer games at a variety of odds, and roulette is one of them. Take paire/impaire or rouge/noir, where the odds are even: 50:50. No number can be both odd and even, both red and black. But there are numbers that can be neither. One is 0 and another, at some tables, is 00 and there are even tables with a 000. These bear the colour green and any mathematician will confirm that none of them is either odd or even. When you land on 0, 00 or 000, you lose any stake placed on red/black or odd/even, regardless of what you bet on. The odds for any given roll of the ball, therefore, are always stacked in favour of the house. What is sold as fairness is in fact pretty unfair.

Regular casino visitors probably know all the odds on all the games, but don’t sit there calculating them: anyone who even remotely looks as if they’re calculating something in a casino is liable to be ejected summarily. In any case they’re not there for the winning; they’re there for the flutter of the flutter. I once won a jackpot on the one-armed bandit in New York, New York, Las Vegas, and rejoiced in the thousand times my stake that I’d garnered: a full 50 dollars. And, almost immediately, wished I’d played the dollar machine instead of the nickels.

“It’s not fair”: the classic plaint. Play the roulette, and the odds aren’t quite what they’re announced as being. Play the utterly fair mechanical bandit, and we want yet more winnings, even when we win.

It is possible to make roulette more fair, by doing away with the zeros at the top of the wheel. But, because a casino visit is far more than simply wagering, with its complimentary drinks and cheap meals and entertainment on hand, gamblers forgive the odd iniquity for the sake of a whisky and soda.

New research announced in VRT NWS’s website today reveals that deciding a yes/no matter with a toss of a coin is, likewise, not entirely fair. Apparently, there is a greater tendency for a coin to land showing the side that is showing at the time it is flipped. The researchers flipped coins of all types of currencies at 12-hour stretches for 350,000 flips and concluded that you’ll more likely get heads if you start with heads; tails if you start with tails.

This brings us back to “You cut, I choose”, because anyone armed with this knowledge, as you are now, could tip the odds in their own favour, the custom being that he or she who is not flipping the coin calls: heads or tails.

However, the research is, to my mind, disingenuous. A skilled tosser (of coins) will show the upper face of the coin to their opponent, flip it and catch it in their palm, and immediately invert their hand over their other hand, thus reversing the result that occurs when it’s simply caught in the palm. In any event, it is at that point that the opponent chooses heads or tails. In other words, the success or otherwise of calling heads or tails is dependent on exactly who calls, whether it’s simply caught or caught and turned onto the back of the other hand, and, so it seems, what knowledge the caller has of the coin’s initial attitude.

If the opponent doesn’t know, then, whether the coin was heads up or tails up to begin with, it actually makes no difference (they will simply name one or the other as their guess), and, indeed, the pure guesswork is heightened if the opponent doesn’t know in what attitude the coin started its airborne trajectory. Since it is the opponent’s guess that is decisive, and as long as the opponent has no knowledge of the starting attitude, then the guess is fair.

After the call and decision, the both faces of the coin must be shown to the opponent, to verify that it is not a double-header or double-tailer. But even then, if it is one of those, that is immaterial: if the opponent doesn’t know that the coin is a double-header, then guessing heads will guarantee his success, and the tosser cannot change that; guessing tails will mean the tosser loses, however, because then the toss is void, and he loses by default for trying to cheat. So that a double-header or -tailer will guarantee that the tosser loses, and therefore surely would never be deployed.

The percentages by which the researchers determined which was a likelier outcome, heads or tails, are nothing to write home about: it’s just 51% for either call (e.g. start with heads, end with heads; start with tails, end with tails).

The conclusion is that there are remarkably simple means to re-establish fairness where unfairness is perceived to be a feature of any system, whether that system is sharing cake, roulette or tossing a coin.

But there are many systems that are entrenched or embedded or traditional that are not only perceived to be unfair but in fact are unfair and they don’t ever get recalibrated according to what is deemed fair. And that seems unfair, because some of these systems are pretty important.

Take UK elections, and their first-past-the-post system. The fairest practicable election system is not Britain’s traditional one but proportional representation based on the Sainte-Laguë system.

Or take US elections. As in the UK, in order to enhance fairness, they are secret ballots; yet voters need to register to vote in an election (with one exception) and, in some areas, to declare allegiance to a particular political party in order to do so. That would tend to militate against the idea that impels a secret ballot, but whether it’s widely recognised as unfair is outside my knowledge.

What is widely recognised as unfair is the Electoral College, an assembly of state representatives who are not bound to adhere by the mandate issued by the voters in their state. What’s more, the mismatch between College representatives and state size means that some candidates are voted in by a minority of the voters, such as Donald Trump was.

The US has a Supreme Court that has as good as declared itself to be above the law on the disclosure of financial interests, which I view as an astounding proposition; and the US Congress is flailing around to find a means to bring its most senior court to heel. Whether that’s fair or not, and, if not, unfair to the court or to Congress, is, again, outside my knowledge. But the mere fact that the question is there itself raises questions: there should be no question as to the fairness of a nation’s judiciary.

Fairness is a product of checks and balances. Without them, fairness can exist, when those who enjoy free rein to do as they please nevertheless rein in not only others but also themselves, in a spirit of benevolence, understanding and compassion and a sense of the greater good.

However, that is increasingly not the case. Although there are manyfold stories of such humanity and openness of spirit to be read and heard the world over, and it is possible that equity and equilibrium are indeed to be found in many places, of which, again, I am unaware. That is not an issue.

What is the issue is that fairness can be perceived and proved to be lacking so often and yet there is a lack of will to ensure unfairness is eliminated. The flexing of military muscle between Russia and Ukraine, Azerbaijan and Armenia, Israel and Gaza, in Niger, in Sudan, and in hotspots across the world, like Nanterre’s quartiers chauds in France: they all stem from some sense of unfairness, and they all induce some sense of unfairness, and yet eliminating the individuals or groups seen as the source of the putative unfairness is seemingly perceived as the sole course of action available.

Whereas eliminating the unfairness itself is so easily ridden roughshod over in the rush for the armoury: you don’t need to negotiate with dead men.

One cuts, the other bleeds.