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Objective . Fractionated radiotherapy typically delivers the same dose in each fraction. Adaptive fractionation (AF) is an approach to exploit inter-fraction motion by increasing the dose on days when the distance of tumor and dose-limiting organs at risk (OAR) is large and decreasing the dose on unfavorable days. We develop an AF algorithm and evaluate the concept for patients with abdominal tumors previously treated at the MR-linac in 5 fractions. Approach . Given daily adapted treatment plans, inter-fractional changes are quantified by sparing factors δ t defined as the OAR-to-tumor dose ratio. The key problem of AF is to decide on the dose to deliver in fraction t , given δ t and the dose delivered in previous fractions, but not knowing future δ t s. Optimal doses that maximize the expected biologically effective dose in the tumor (BED 10 ) while staying below a maximum OAR BED 3 constraint are computed using dynamic programming, assuming a normal distribution over δ with mean and variance estimated from previously observed patient-specific δ t s. The algorithm is evaluated for 16 MR-linac patients in whom tumor dose was compromised due to proximity of bowel, stomach, or duodenum. Main Results . In 14 out of the 16 patients, AF increased the tumor BED 10 compared to the reference treatment that delivers the same OAR dose in each fraction. However, in 11 of these 14 patients, the increase in BED 10 was below 1 Gy. Two patients with large sparing factor variation had a benefit of more than 10 Gy BED 10 increase. For one patient, AF led to a 5 Gy BED 10 decrease due to an unfavorable order of sparing factors. Significance . On average, AF provided only a small increase in tumor BED. However, AF may yield substantial benefits for individual patients with large variations in the geometry., (Creative Commons Attribution license.)