I'm a big fan of the Call of Cthulhu/Basic Role-Playing resistance roll chart, whereby you compare two 3-18 type stats and get a percentage to roll. So my 10 Power versus a spell with a hex cast by an 11 Power witch gives me a 45% chance to resist. You can use that for all sorts of thing. You can do Strength versus Strength for wrestling. Poisons can be rated 3-18 versus the Con of the victim. Hazards can be rated for ninja-ing past them with Dex. All sorts of good stuff can be resolved this way.
The only thing I don't dig about the RR chart is its binary output: You win or I win. Sometimes I want a third option where people are still wrestling on the ground and neither has quite reached the gun or the poison is ravaging their body but they can still get off one last action. 2 dice rolls are the easy way to get these results. The players roll, the GM rolls, and a tie is interpreted as some sort of standoff or incomplete resolution. But if you want to keep the basic RR chart methodology, here's an alternative I whipped up. Click to make it legible.
The basic thought at work here is that the closer the two stats are to each other, the more likely an unresolved result.
Random Animal Table - 1E DMG
1 hour ago