In this work we introduce a novel approach to the problem of cardinality estimation over multijoin queries. Our approach leveraging randomized hashing and data sketching to tighten these bounds beyond the current state of the art. We demonstrate that the bounds can be injected directly into the cost based query optimizer framework enabling it to avoid expensive physical join plans. We outline our base data structures and methodology, and how these bounds may be introduced to the optimizer's parameterized cost function as a new statistic for physical join plan selection. We demonstrate a complex tradeoff space between the tightness of our bounds and the size and complexity of our data structures. This space is not always monotonic as one might expect. In order combat this non-monotonicity, we introduce a partition budgeting scheme that guarantees monotonic behavior. We evaluate ourmethods on GooglePlus community graphs~citegoogleplus, and the Join Order Benchmark (JOB)~citeLeis:2015:GQO:2850583.2850594. In the presence of foreign key indexes, we demonstrate a 1.7times improvement in aggregate (time summed over all queries in benchmark) physical query plan runtime compared to plans chosen by Postgres using the default cardinality estimation methods. When foreign key indexes are absent, this advantage improves to over 10times.