| Summary: | We consider a discrete-time random walk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> which, at random times, is reset to the starting position and performs a deterministic motion between them. We show that the quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">Pr</mo><mfenced separators="" open="(" close=")"><msub><mi>x</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>|</mo></mrow><msub><mi>x</mi><mi>t</mi></msub><mo>=</mo><mi>n</mi></mfenced><mo>,</mo><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined.
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