The Uphill Drunk
A walker on the integer line starts at 0. Each step he moves +1 with probability 2/3 or −1 with probability 1/3, independently. What is the expected number of steps until he first reaches +10? Give an exact number.
Related problems & prerequisites
Worth solving first
- First Heads Wins 3.0/10
- Roll Until Six 3.0/10
- Seven Before Eight 2.0/10
Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.