Putting the words "gender" and "games" into the same article can often be a very combustible mix, especially if you also add the hint of "sexism", but as the dad of a three-year-old daughter, I've begun to notice how few games let you switch easily between male and female lead characters.

We often play games together on a tablet or phone, and I first saw what an effect the gender of the lead character had on my daughter with the game Temple Run. The default character is a male explorer, but my daughter had noticed that there were female faces on the upgrade page. One night, I absentmindedly played it for ages on the iPad while watching football, collecting enough coins to unlock the cunning escape artist Scarlett Fox. Once I'd done that, I selected her as the character to play with, and then waited to see what my daughter's reaction would be.

When she picked it up the next day, she nearly exploded with joy. "It's a girl – just like me!" she shouted (even though in truth you only see the character very briefly from the front before a pretty gender-neutral ponytail becomes the only indication that she is female).

But I really noticed how much it meant to her the next time I let her play it on my phone. The game wasn't synced on this device, so Scarlett wasn't available. When she started playing it, she was horrified. She'd had a glimpse of being able to play as a woman, and she didn't want to go return to the game's default position – that escaping from rabid mutant-skulled monkeys is a man's job.

Now we've started on Sid Meier's Pirates for the iPad. I didn't intend it as a shared game, but she spotted the pirate icon on the screen and kept asking if she could play pirates. I explained that it involved lots of reading, which made her suspect it might secretly be work for a while, but eventually I showed the app to her, saying she could watch me play it for a little bit. Of course, within 90 seconds, she'd seized the iPad, taken control of my fleet, and was barking out orders for me. Kids can be like that. She won her first sword-fight when she said she wanted to try one, which filled me with a mixture of pride at how quickly she'd picked up how to do it, and horror at how naturally fighting had come to her.

I've started a new game and named the pirate after her, but that is the most customisation I can do. The story will remain that a resolutely male Mr Emma is trying to avenge his family's disgrace, and win the hand of the daughter of one of the colony overlords. I'd love her to be able to have the adventure as a swashbuckling female pirate instead.

Now, there is of course an open question about whether a three-year-old should be trying to escape from rabid mutant-skulled monkeys, or playing pirate games at all. It is very difficult to gauge the right level of exposure to games. We enjoy playing them together and have a lot of fun, but she does plenty of other things like puzzles, card games, drawing and jumping into muddy puddles too.

I was a good few years older before I had access to handheld electronic games, although I remember a friend having a Casio watch that played a Space Invaders style game when I was at school that we all coveted. My dad, on the other hand, didn't get a TV at home until he was in his teens. Our children grow up taking the technology around them for granted, and I think there is a lot of value in getting my daughter familiar with computers and touchscreen tablets. There are apps on the phone that are helping to teach her phonics and learn to do maths, and she can already both write and type a few words. Kids aren't scared that they are going to "break" a computer or "do the wrong thing" in the way that adults tend to be when approaching technology.

But it is the gender thing that has intrigued me most. Mike Hoye has made himself a hero among techie dads by hacking a computer game to allow his daughter to play it as a girl. He said that "It's annoying and awkward, to put it mildly, having to do gender translation on the fly" when reading out the text adventure game they were playing together, and so he edited the game's binary code to change all of the pronouns and replace all the references to "swordsman" and "my lad".

I was really taken aback by how strong my daughter's affinity with the female character was at such an early age – it obviously really meant something to her, even though I've never really noticed her pay much attention to gender before. She chose a Barbie once when we let her pick a toy to buy from a local table-top sale, but she also likes robots, dinosaurs, a lion cub she has that she has to feed milk to, and she says that she wants to go and watch football when she is "a little bit more grown-up". I hope she'll grow up to be the kind of girl who hands in this kind of response to homework assignments suggesting toys only belong to boys or girls.

I'm not skilled enough to do something like Mike Hoye did – and you'd struggle to do it with Apple's closed iOS systems anyway. But I'd really like to just have more games which made it easy to switch genders, and had strong female lead characters for us to play together as she grows up.