The votes on what you would do if you knew your opponent was using an engine were pretty evenly divided. Six people would also use an engine just to level the playing field. Six would report them and presumably continue playing. One person voted that they would simply resign in disgust.
I understand resigning. Back in the early 1980’s when Chessmaster was rated about 2000-2100, I was playing in a couple of USCF postal tournaments and became suspicious that some of my opponent’s were using the program. I ran all the games through Chessmaster and discovered that out of 12 opponents at least 8 were using because their moves were identical to those suggested by Chessmaster. After over 20 years of postal chess I was disappointed that that was what it had come down to so I simply resigned all the games and lost over 300 rating points. I resumed CC back in 2004 and found things had not improved any.
For the most part my opponents are over 2000. If I play a lower rated player, I play on my own and actually I prefer players in the 1600-2000 range because they usually are not using engines and are good enough to make the game interesting. Over that and it’s a tough call because somewhere between 2000-2200, maybe they are, maybe they aren’t. If I suspect an opponent is using an engine, I’ll run the game through Fritz and see what moves it’s recommending and if I find a significant number of matchups I will also use one. I didn't always feel that way. There was a time I'd try to see if I could beat the engine, but nowadays that's impossible and I got tired of beating my head against the wall. What usually makes me suspicious is when I start seeing moves that don’t make any sense to me. I figure I should have some idea of what my opponent is trying to do if we are about the same rating but if his moves make no sense, then something’s up.
Recently though it’s becoming harder to detect engine use. Or, rather I should say, which one is being used. That's because there are so many good ones available and I’ve noticed Fritz rarely chooses the same move as the stronger Houdini. Add to that the fact that sometimes you have to let the engine run a long time get a decent evaluation. However, I’ve noticed most engine users will play whatever Fritz suggests within the first 30 seconds or so. That’s probably because many of them are playing lots of games and don’t have the time to let an engine run overnight. For opponent’s over 2400 there isn’t much to think about…they’re using…trust me. One point I should make here is that there ARE a lot of good players out there. When I started playing chess “good” players were few and far between. It’s a function of numbers; with millions and millions of players a LOT of them are going to be good. That wasn’t the case back when the USCF had 5000 or 6000 members and there were 100 GM’s in the world and you knew all their names!
The problem with reporting engine users is that many sites simply do not have the staff to check hundreds or thousands of players and games. Most sites will require substantial proof and to get the ball rolling, you will probably have to provide some evidence yourself and that means analyzing 15 or 20 of your opponent’s games on your own for submission to the proper authorities. Another reason most sites are loath to kick off engine users is because if they examined the games of their top players most of them would be gone.
One site I’m aware of recently kicked off some people but I think that was probably a token. Another has what they claim is a foolproof method of catching them but I’ve seen 1200’s banned for engine use so I’m a little skeptical. Another major site had a couple of their top players, in a moment of weakness, confess that they used engines, but they promised not to do it anymore so no action was taken.
Final analysis…engine use is here to stay and not much can be done about it. But unless you are playing consistently at around the 2200 level they should not be a problem unless you meet someone on their way up through the ranks. Even then I wouldn’t worry about them because at some point they are going to run into a whole gaggle of other engine users and if they are not really good players who are able to break through the ranks of other engine users they’ll get stuck and go no higher.