I do martial arts at a gym, and there is this one guy named Dave who weighs 100 pounds more than me, has been training 7 years more than me, and who is a fast as a snake (even faster than me). I want to beat him, but I can't figure it out. Is there any way for me to win without getting slammed on the mat? Also, I train in a full contact (or almost full contact) martial art.
The simple answer is: No. You're gonna lose.
You may never win against a guy who is much heavier than you, much stronger than you, much faster than you, and much more skilled and experienced than you.
But, don't let that dissuade you from training with him. When you're up against someone like that, the best you can do is learn to relax, stop thinking so much (put your brain on auto-pilot and in the moment), and let your training kick in automatically.
Your goal here isn't to win. Instead, you want to be able to experience some progress, no matter how small it is.
But he's still going to win. What matters is how you perceive your progress. And you will know when you've made progress. It won't be obvious to everyone else sometimes. What matters is you remember you struggled with him before, unable to do anything, and then all of the sudden something in your head just clicks, and today you were able to keep him from doing the worst thing to you.
Most of it does come down to what I said above: relaxation and not over-thinking. Go into it with no plan. And, when you're rolling / sparring with the guy, don't try to strategize or think ahead. That hasn't worked for you in the past. Just be in the moment. Relax. Let things happen. If you catch yourself thinking things like, "I'm gonna step in to his side, slip around his back and get a rear-naked hold," then you're doing this the wrong way. Don't think ahead. Just wait. Relax. Let things happen. Be in the moment. Don't try to think ahead.
When you are paying attention to what’s going on right now instead of thinking about what you’re going to do, you can begin to see things that you weren’t able to before. That is when progress will happen.
But you won't win. Not for a long long time. And that should not matter at all right now. Right now, you just want to experience some progress. That's a goal you can achieve.
Hope that helps.
There's one strategy in particular that may optimise your chances of success against a more experienced, skilled and faster, stronger opponent. I make absolutely no claim that it will enable you to beat him, but only that it may enable you to significantly improve your ability to spar with him productively.
In the absence of any information as to what martial art you practice, there's one weakness that many of us have; even those of us who have trained for a considerable amount of time:
We often train exclusively against opponents who practice the same form of martial art.
Martial artists who have no experience against other styles are often bamboozled by unfamiliar techniques. I'm not suggesting you abandon your training in search of another style just to beat one person, but I do suggest there is value in identifying techniques typically employed by your style and in researching other techniques from other schools that might render your efforts less predictable.
Note: I'm not suggesting you should always do this. If your goal is to get better at a particular style, you clearly need to work hard at learning how to employ its techniques, but the element of surprise is a treasured strategic goal for good reason. It can be used to force your opponent into reacting in ways that aren't deeply drilled into their reactive system. Even if you are merely able to cause some confusion and force some adjustment from your opponent, you will have slowed them down and achieved something valuable.
Remember too that there are often techniques native to a martial art that are rarely utilised. Practicing these can be an excellent way to generate tactical initiative whilst remaining within the confines of your school's approach.
One of the obvious strengths of MMA is that it trains people in a variety of styles, so that it is much harder to surprise an opponent. If you are in an MMA school already, the advice here may still be of use, for even MMA can be prone to creating combat expectations which can be subverted by creativity and analytic strategy.
Watch him spar other people who are as good or better than him. What methods do they use?
If you ask nicely, he might honestly reveal what he thinks his weaknesses are.
You asked a good question. Many simply avoid sparring those who are far more advanced than them. You may well learn a lot from your efforts.
Realistically speaking, short of smuggling a shank into the gym, no, there is no way to win a match. So just look at what you can learn - break it down into "How do I deal with A?", "How do I deal with B?", etc. Learning martial arts is a slow process, and learning how to adapt to the other person takes longer than, say, learning how to throw a correct, powerful round kick.