# An Optimal Mastermind (4,7) Strategy and More Results in the Expected Case

arXiv: https://arxiv.org/abs/1305.1010 · HTML: https://mlsanity.com/paper/1305.1010/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2013.

## Built on by (most cited first, 1 of 1)

- [On Optimal Strategies for Wordle and General Guessing Games](https://mlsanity.com/paper/2305.09111/) (2023)

## Abstract (arXiv)

This paper presents an optimal strategy for solving the 4 peg-7 color Mastermind MM(4,7) in the expected case (4.676) along with optimal strategies or upper bounds for other values. The program developed is using a depth-first branch and bound algorithm relying on tight upper bound, dynamic lower bound evaluation and guess equivalence to prune symmetric tree branches.