I don’t like to think of myself as insufficiently cynical, but every once in a while I hear something that reminds me I still retain the shreds of a naive and misplaced faith in humanity, institutions and other people’s inherent sense of fair play.

It happened again on Monday morning: I was half asleep, listening to AC Grayling talking about his new book Democracy and its Crisis on the radio, when he questioned whether the leavers had bet against themselves at the bookies ahead of the referendum to slash the odds of a remain victory and suppress remainer turnout.

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I sat up in bed. Nothing this cynical – or clever – had ever occurred to me. I’ve always thought of bookmakers as super-accurate alternative pollsters. I just figured they were financially incentivised to get it right. Could Grayling have been right?

So let’s look at what actually happened in June 2016, when bookies were taking fewer, but much larger bets on remain. At William Hill 69 % of the individual bets were for leave, but 68% of the total money went to remain (these percentages, incidentally, were almost exactly mirrored in the betting on the US election). The average leave bet taken at Ladbrokes was £70; the average remain wager was £400. As a result the odds shifted in favour of remain in the last days of the campaign.

I couldn’t begin to calculate how much money a small group of people would have to spend to tip the odds significantly, but in a two-horse race it would be simple enough to reduce your losses by simultaneously betting against remain on an online exchange instead of one of the high-street chains whose odds are routinely cited in national newspapers.

My son, who has a better grasp of both maths and gambling than I do, points out that longer odds naturally attract smaller stakes; that in the recent Mayweather v McGregor fight there was more betting on Conor McGregor, but more money on the favourite, Floyd Mayweather. I can only attribute his position to a youthful naivety. The scales had fallen from my eyes, but now it seems I have to put them back.

Goodbye to Gorka

Facebook Twitter Pinterest ‘Sebastian Gorka was always the oddest fish in the White House bowl.’ Photograph: Mark Wilson/Getty Images

So long, Sebastian Gorka, former White House security-something-or-other who has either resigned or been fired, depending on who you ask. Either way he’s managing to spin his departure into some kind of triumph, explaining how much more effective he will be at furthering Trump’s agenda now that he’s been relieved of the burden of actually working for him. I think the world is probably a tiny bit safer as well.

Gorka was always the oddest fish in the White House bowl, perhaps not counting Donald Trump himself. He’s a counter-terrorism expert whose expertise is questioned by most other counter-terrorism experts – one said “he needs to sit down and read a few books that he didn’t write”. He counts himself an alpha male – as opposed to the “limp-wristed Pajama Boys” of Obama’s administration – but his only real role was as Donald Trump’s most devoted attack dog. I’m tempted to mark Gorka’s departure from public service with a few choruses of the television comedy Parks and Recreation’s Bye Bye Li’l Sebastian, but I looked up his height and apparently he’s 6ft 5in. Never mind.

Quids in

Facebook Twitter Pinterest ‘Some businesses just aren’t bothering to sort new pounds from old when they bank them.’ Photograph: Oliver Dixon/Rex/Shutterstock

The removal of the old pound coin from circulation has hit a snag: apparently up to half of the coins handed in by businesses are actually the new ones. Again, I don’t claim to know much about odds, but I would hazard that’s no better than chance. Even blindfolded you’d be bound to weed out more than half the 12-sided ones. It’s more likely that some businesses just aren’t bothering to sort new pounds from old when they bank them. At this rate they may miss the 15 October deadline for retiring the old coins, which is good, because I’ve yet to use a parking meter that takes the new ones.

• Tim Dowling is a journalist for the Guardian