This paper presents a finite length analysis of multi-slot type frameless ALOHA based on a dynamic programming approach. The analysis is exact, but its evaluation is only feasible for moderate number of users due to the computational complexity. The analysis is then extended to derive continuous approximations of its key parameters, which, apart from providing an insight into the decoding process, make it possible to estimate the packet error rate with very low computational complexity. Finally, a feedback scheme is presented in which the slot access scheme is dynamically adapted according to the approximate analysis in order to minimize the packet error rate. The results indicate that the introduction of feedback can substantially improve the performance of frameless ALOHA.