What is the exact chance that my attack roll beats the defender's roll?

Two players each roll a handful of dice and the higher total wins. Guessing the fairness from a few test rounds is slow and often wrong. This entry gives the exact winning, tying and losing chances, and shows how a flat bonus shifts them.

Why this works

Every possible total can be reached in a countable number of ways, so the whole spread of results can be built up one die at a time, with no guessing. Counting beats sampling, since it is exact and the same every time you ask.

When not to use it

Skip it when dice can explode, be re-rolled or be picked after seeing them, or when pools are so large that counting every total gets slow. Use a bounded depth for those rules, or a long simulation for huge pools.

In the full entry

• What to build, step by step
• Starting values and the reason for each
• 3 common mistakes and the fix
• 30 lines of example code with 4 checks that pass
• How your AI shows you that it works

Say this to your AI

Use the Spielerando entry "What is the exact chance that my attack roll beats the defender's roll?" (read_entry dice-pool-versus-dice-pool-exact-win-chance) in my game. Build it step by step, and show me how you checked that it works.

Or skip this and connect the MCP: your AI then finds all of this by itself.Connect the MCP