I do, but only with local multiplayer games. (I couldn't care less about online players) Letting people win against me in video games increases my enjoyment quite a bit. Let me explain. I play local competitve games for two main reasons: 1.) to overcome difficulty, and 2.) to bond with friends.
If I'm dominating a game, there is obviously no diffficulty to overcome. Therefore, a significant contributing factor in my enjoyment is nonexistent. I've seen people dominating games for hours on end and I see them having the best time of their life. I cannot understand this. If I'm playing someone of a considerably lower skill level than myself, I'll take it easy on them. When I do this, I give my opponent an advantage that counters or even surpasses my skill advantage. By giving a lesser skilled opponent a substantial advantage, I present myself with a challenge. I'm put in a position where I actually have to test my skills. I have to put forth a decent effort to overcome difficult odds. I feel like I'm actively trying and competing and a video game. I actually get to enjoy games this way. On the contrary, if I hadn't given my opponent an advantage, I wouldn't have have any challenge at all.
I can't have fun if my opponent isn't having fun. In conjuction with challenge, the other significant factor in my enjoyment is the bonding with friends. A large motive for playing video games isn't just to have fun playing video games; it's the usage of video games as a means of developing & maintain a comrodery. When I'm done with a gaming session and I reflect on how much fun I had, I don't think of how often I won versus how often I lost. I think of my interaction with my friend. If I sense my friend isn't truly having a good time, whether he admits it or not, then it's hard for me to have a good time. It's hard for me to be pleased at the cost of my opponent being bored or demoralized. When I have local multiplayer sessions, my maximum enjoyment level is limited by the enjoyment of my friend. I guess seeing others happy makes me happy myself.
As you can see, I'm more concerned with the experience of gaming. Contrarily, others may not truly care for the experience - they're more focused on the arbitrary title as 'winner' or 'loser.' I know people with this mentality and I don't truly understand it. I cannot understand what's so fulfulling about the mere winning or the losing. It's like the old saying "It's not reaching the top of the mountain that's important. It's the climb and the journey to the top." Or something like that. Basically, it's my experience during a match that counts - the thinking, the planning, the experimenting, the risk-taking, the bonding, etc. It's not the end-result that counts. If I were to have a rich gaming experience twice, once winning and once losing. The difference in enjoyment between the two would be extremely tiny. But for others, winning and losing defines 'fun' for them.
Some people don't like when I let them win, but I don't care. If I feel a situation warrants me to ease up, then I will ease up. Sometimes, it happens unconsiously. Of course, I'm sure to make it unnoticeable to my opponent. I don't do it for them, I do it for myself, to improve my experience. I guess you could argue that I'm selfish in this way.
