The growing significance of mobile ad-hoc networks (MANETs) in mobile communications has drawn a lot of focus on efficient routing techniques. Position-based routing methods rely on nodes’ location data to make routing decisions. The route environment in the majority of today's Position-Based routing algorithms is typically considered in two dimensions. But in reality, a node may be found in three dimensions. In this research study, we define two randomized routing algorithms that combine the high delivery rate of random selection techniques with the minimal cost of progress-based routing algorithms. The first algorithm, GRandom, operates by choosing a route based on progress toward the destination, in case of the failure of delivery, the algorithm extracts a subgraph and then it uses the random algorithm. The second algorithm, GRandomPlus, is similar to GRandom but with a higher probability of selecting a neighbor nearer the source-destination line. Both algorithms aim to optimize routing efficiency by leveraging the benefits of position-based routing and random selection methods. These approaches offer a promising solution for improving delivery rates while maintaining minimal overhead.