Out-of-Bag Sampling in Random Forests

Every tree in a bagged ensemble — random forests included — is trained on its own bootstrap resample: N rows drawn with replacement from N original training rows. This simulator draws that bootstrap sample in 3D, one pick at a time, so you can watch which training points land in-bag (drawn at least once, brightened, with a bar tracking how many times) and which are left out-of-bag (never drawn, dimmed). Grow trees one by one or let the forest auto-grow, and watch the cumulative out-of-bag fraction settle onto its theoretical limit — (1 − 1/N)^N, which approaches 1/e ≈ 36.8% as the dataset grows — the same statistic random forests use internally to score every tree on data it never saw.