So I decided to introduce my two-year-old son to the world of video games. Before you accuse me of hobbling my offspring's mind, I'd like to point out that a) television is 2,000 times worse, so shove that up your Night Garden and b) I also decided to counterbalance the gaming with exposure to high culture. For every 10 minutes of Fruit Ninja during daylight hours, he'd get 10 pages of a critically acclaimed novel at bedtime. We're currently halfway through The Magus by John Fowles, which he's enjoying immensely. He finds some passages so moving that his protracted sobs drown out my reading completely, and when I return to the beginning of the chapter to start again, he leaps up screaming, trying to snatch the book out of my hands with delight.

Like any self-respecting 2014 toddler, he can swipe, pat and jab at games on a smartphone or tablet, but smartphone games aren't real games. They're interactive dumbshows designed to sedate suicidal commuters. And they're not just basic but insulting, often introducing themselves as free-to-play simply so they can extort money from you later in exchange for more levels or less terrible gameplay. Either that or they fund themselves with pop-up adverts that defile the screen like streaks on a toilet bowl.

I don't want him playing that horrible bullshit. I want him mainlining proper games as quickly as possible. And proper games are played with a keyboard and a mouse, or a weighty controller embellished with an intimidating array of buttons and sticks and triggers – one that melts ergonomically into any experienced gamer's hands, but makes newcomers feel like they've just picked up a Rubik's Cube designed by Salvador Dalí.

So I handed him a controller. I tried him on Super Mario World, but he didn't understand that you could move and jump at the same time, which limited the fun. My fun, not his. He was perfectly happy to press one button repeatedly to make Mario leap up and down on the spot. But he wouldn't time the jumps properly. He kept getting killed by the same Goomba, endlessly waddling towards him. It was excruciating to watch. So I switched the Nintendo off and tried a different console. He screamed with enthusiasm, or possibly despair. Maybe even hunger. It was getting quite late.

Eventually, after a few more missteps, I stumbled across the perfect game: Trials Fusion. It looks like an action game, but it's actually more of a physics-based puzzle. You're meant to continually adjust the stance of a motorcyclist so he doesn't fall off as he rides at speed over spectacular courses full of ramps and chasms. Despite its high difficulty level, he could make entertaining progress just by pressing the accelerator. The rider fell off all the time, but when he did he plummeted into ravines and bashed against photorealistic scenery, screaming in terror. My son found this hilarious, which is fine, OK, because it is hilarious. After each tumble he hurriedly tapped "retry", which is the second button he learned to locate.

Things soon escalated. One afternoon he threw a tantrum in a supermarket and I, in desperation, downloaded the iPhone version of "the Motorbike Game" (which is what he calls it), and handed it to him as he writhed screaming in the trolley seat. Bingo. Instant calm. He couldn't have been happier. Or quieter. I had to prise it from his hands later with a shoehorn, but that seemed a reasonable exchange for 30 minutes of peace.

But as with free-to-play games, the price was higher; the sting came later. Shortly afterwards, we went on holiday. He had a meltdown on the plane, so out came the Motorbike Game. Wouldn't sit still in a restaurant. Out came the Motorbike Game. Strayed perilously near the pool. Motorbike Game. It was too tempting: like having a toddler with a pause button. Inevitably, he got hooked. Hopelessly hooked.

I want the Motorbike Game. I want the Motorbike Game. That's all I heard all week, apart from him singing the theme music. Just like smoking, each individual cigarette satiated the immediate craving, while increasing his overall dependence.

Worst of all, in the iPhone version – which surprise, surprise masquerades as "free" – the bike runs out of fuel now and then, and the only way to refill the tank it is to wait for a countdown to expire (slightly harder for a two-year-old than completing a tapestry), watch an advert (evil) or to purchase in-game petrol from the App Store. I first became aware of this when he screamed and hurled the phone across a restaurant table in a fury. I caved in immediately and, illustrating everything that's wrong with human progress, found myself spending real money on non-existent petrol for a non-existent motorbike in a desperate bid to appease an infant. Spending money to shut him up felt transgressive and undignified – but worse still, I was literally fuelling his addiction.

On our return we realised he was shunning his regular toys in favour of the Motorbike Game. There was nothing else for it. He had to go cold turkey. The Motorbike Game had to die. I deleted it from the phone and hid the Xbox controller. Neither action went down well. Having been introduced in order to avert meltdowns, the Motorbike Game was now causing them on an epic scale.

Eventually, after several days of endless and often furious requests for the Motorbike Game, he passed through the five stages of grief and came out the other side.

I walked into the kitchen where he sat calmly on the floor, playing with his wooden blocks for the first time in a week.

"That's nice," I cooed encouragingly. "What are you doing?"

"I'm playing the Motorbike Game", he replied, a little sadly.

I looked again. He was re-enacting the game. One block was the motorbike. The rest were the scenery.

It wasn't as good as the original. But it was, at least, his own.