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Fixing problem gamblers with math

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https://aeon.co/essays/a-mathematician-a...into-a-bar

INTRO: A mathematician, a philosopher and a gambler walk into a bar. As the barman pulls each of them a beer, he decides to stir up a bit of trouble. He pulls a die from his pocket and rolls it ostentatiously on the bar counter: it comes up with a 1.

The mathematician says: ‘The probability that 1 would come up is 1/6, and at the next throw it will be the same. If we roll the die infinitely many times, the relative frequency of the number 1 will converge to 1/6, that is, to one occurrence every six throws.’

The philosopher strokes her chin, and remarks: ‘Well, this doesn’t mean we won’t get the number at the next throw. Actually, it’s physically possible to have the same number on the next 1,000 throws, although that’s highly improbable.’

The gambler says: ‘I know you’re both right, but I wouldn’t bet on that number for the next throw.’

‘Why not?’ asks the mathematician.

‘Because I trust mathematics, and so I expect that number to come up about once every six throws,’ the gambler answers. ‘Having the same number twice in a row is a rare event. Why would that happen right now?’

The gambler’s ‘argument’ is a mix of conceptual inadequacy, misinterpretation, irrelevant application of mathematics, and misleading use of language. She thinks that she has some new information that will increase her chances of winning – that there are now five numbers to choose from instead of six, and as such the randomness of the game is ‘losing its strength’. This sort of belief reinforces a gambler’s impulse to bet – it won’t make her quit the game, but rather continue gambling.

Some people believe that confronting problem gamblers with the ‘reality’ of mathematics – a kind of mathematical counselling, often called ‘facing the odds’ – can help them overcome it. After all, since our earliest school days, many of us have learned to trust mathematics as the provider of necessary and logical truths. But we also trust our senses, as well as the patterns we discern from our experiences and the words we use to communicate with one another. Mathematics has its own language, and the extent to which we should trust mathematics depends on how we interpret these words, especially when applied to physical reality. In fact, understanding gamblers’ relationship to maths reveals something deeper about the nature of mathematics itself.

I don’t gamble, and I suspect few mathematicians do – or at least, they don’t gamble to get rich. In my youth I was fascinated by games of chance, and loved to play them so I could to watch probability ‘at work’. But after studying mathematics and its philosophy in more depth, my interest in such games vanished. I came to see them as simply mathematical models wearing sparkling clothes. Instead, I wanted to figure out how I could help other people to see them in the same way.

All games of chance – whether casino games such as roulette, craps, blackjack and slots, or lottery and bingo, or card games such as poker or bridge – rely on certain basic statistical and probabilistic models. Uncertainty is built into them, which is what makes games ‘fun’ to play and also explains their continued existence. Casino games would never run if ‘the house’ wasn’t confident that they’d always win in the end. The mathematics of the games, including their rules and payout schedules, assures the house will profit in aggregate, regardless of individual behaviour... (MORE)
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