Backgammon

I have a confession to make. I am addicted to backgammon. I am addicted to playing backgammon on my phone. My productivity and sociability have lately been decimated by my addiction to playing backgammon on my phone. The app is called Backgammon NJ. (The "NJ" is a mystery to me. Is backgammon big in New Jersey?)

Currently, I can beat my phone at backgammon about 50 per cent of the time on the "Medium" skill level. When I have overturned these statistics and gained a positive advantage over "Medium", I will move on to "Hard" and subsequently "Expert". Trouble is, my win rate has been about 50 per cent for some weeks now. I am stuck. I am Heracles chasing Zeno's tortoise. I can never catch up. What am I doing wrong?

I am convinced that my phone is cheating. It rolls itself fantastic dice and dances gaily around the board, while leaving me with the dregs – rubbish 1s and 2s that get me nowhere and leave my pieces trapped and exposed. I love playing my phone at backgammon, but it often drives me to tears. It is an thoroughly punishing, self-destructive addiction and I need help. Help.

The role of cheating is not taken into account in my theory of games. Here's my theory of games.

In most games, there are three variables that determine the outcome.

1 Your own skill
2 The skill of your opponent(s)
3 Luck

The best games are those in which luck and skill have a comparable degree of influence, but skill must always be the more decisive and interactive element.

Luck is, of course, an important factor in every card and dice game, but it also has a part to play in some sports. In Test cricket, one team may be favoured by the weather, which may change suddenly, and the result of the coin toss may prove critical to the overall shape of the game, but skill will normally be the critical factor, unless rain rescues one team from defeat.

Golf is a game in which the weather can be a variable, and might in theory favour the technique of one player over the other. But since the position of one player's ball has no influence on the other's, the game is not interactive. This is exactly what makes golf a stupid game, but not as stupid as darts, in which chance environmental factors are taken out of consideration altogether. The opposition of one player to another is entirely artificial, and they may as well be aiming their arrows at different dart boards in different countries at different times of the year.

Most sports, like darts, attempt to minimize any environmental factors that might favour one player or team over the other. They do often this enforcing a change of ends. Games such as tennis offer an interesting example of this, but it is technically possible to win a game purely through the lack of skill of your opponent, without touching the ball. A series of double faults will give you a game, but the players swap service as well as ends to correct this anomaly.

Other games – such as ludo – are interactive, yet feature more luck than skill in them, so they tend to produce random outcomes. In the case of casino games, the luck is weighted in favour of one of the players (as I suspect it is in the case of Backgammon NJ). The ultimate game of luck, in which both skill and interactivity are excluded altogether, is Snakes 'n' Ladders. (Yet even Snakes 'n' Ladders somehow seems less stupid than darts.)

At the opposite end of the scale are skill-only games such as chess, which constitute a completely interactive battle of wits. Although these involve the purest form of contest, the games that demand an interplay of skill and luck are the most compelling and addictive. These are the games in which bad luck can be overcome by good play and good luck can be squandered. The losing side can choose to console themselves that they were cheated by fate. At the conclusion of each game, both winners and losers are eager to start again, to see if the result can be replicated or overturned.

The two games that illustrate this the best are Test cricket and backgammon. They are the greatest games ever invented, with the exception of such games as "love" and "improv". If "life" is a game, then success and happiness consist in recognizing and understanding the interplay of skill and luck – in other words between those things that are in our control (our own abilities and attitudes), those that are not (the abilities and attitudes of others) and the things from which we may allow to affect us either positively or negatively (chance events).

The reviews on the App Store for Backgammon NJ are mostly glowing. But its perfect 5-star rating is compromised by a handful of malcontents.

★★★★★ Works well both offline and online. Can't fault this app. I didn't think it would be as good as this.

★★★★★ Only trouble is I spend too much time playing backgammon!

★★★★★ Brilliant.

★★★★★ The AI is brilliant and it's a great learning tool.

★ Sorry but I have to agree with others here in that the luck seems to be hugely in favour of the computer opponent. I have lost count of the number of times that the exact numbers required are thrown whenever a computer opponent's piece is "captured" and the enormous weighting in favour of the computer throwing doubles.

The accusations of cheating levelled against Backgammon NJ have forced its creators to issue lengthy statements explaining how the dice rolls are generated according to the Mersenne twister algorithm, which produces what we are assured are "high quality random numbers". We are invited to print out the dice rolls in advance or to roll the dice ourselves rather than rely on the makers' word alone, so as to test and prove Backgammon NJ's superior AI.

In spite of my humiliating record of 50 per cent success at this excellent game, and a gnawing resentment at its apparent flukiness, it is my duty to come out in defence of the creators of Backgammon NJ. For surely, if my suspicions of cheating were to be correct, I would have to presuppose a far greater conspiracy – namely, that the assurances offered up by the makers of Backgammon NJ are a fabrication, and that they have gone so far as to create a fictional cover story for their deception – a remarkably dishonest bluff. They would need to have developed a quasi-random algorithm that gave the impression of being fair, sufficiently subtle to fool most of the people most of the time, while introducing a significant mathematical advantage at an undetectable level that stood up even to critical analysis.

Firstly, if they were going to go to such enormous lengths, why shouldn't they just spend that time and trouble developing an AI that was just really good at calculating backgammon moves? Secondly, why should they perpetrate such a fraud in the first place? In order to cheat and win against random members of the public, customers of the App Store whom they will never meet in person? What sort of vain, tortured, love-starved freaks to they believe these Backgammon NJ programmers are?

I still have a great deal to learn about this game. As it is in backgammon, so it is in life. Think upon that, the next time you're tempted to complain about all the bad luck you've been having lately.