When I was a little kid, I used to watch bigger kids play all sorts of video games. From Golden Eye 007 to Mario Tennis, both of which referring to the Nintendo 64, I observed unsatisfied of not being part of the action. At a very young age, I was quite shy. Over time though, I began asking to join in. Sometimes I'd get a "no", but others I was accepted into the fun.
Some people liked to take advantage of me by going full force and beating me repeatedly. Others would let me have a handicap. (For Golden Eye 007, you can adjust individual's maximum health. For Mario Tennis, you can adjust your partner's artificial intelligence, so the lesser skilled player could have a better playing partner than a more experienced player.) However, I did not want such an advantage.
It is true to say I had nothing good besides a lucky shot here and there, so I didn't contribute much to the gameplay. Yet, I continued playing like that for years to come. While I only provided good slaughtering material, heh, I still continued. My reason for doing so is simple: I felt like one of them. Using a handicap, like using smaller stones and melons, would only glorify my weakness, so I wanted to participate on equal terms.
It is true that I didn't add much to the gameplay, but I felt good that I was a part of something bigger than me. Looking back over my day, I could say to myself, "I played with bigger kids today on their terms." Whether I made a fool of myself or not, it didn't matter. I had fun, and I was proud knowing that I didn't make things easier despite having such unfair situations. I could very well be wrong, but perhaps Ducky and Petrie viewed playing games with bigger kids for these, if not similar, reasons.