In　this　paper,　we　modify　the　proof　methods　of　some　previously　weakly　consistent　variants　of　random　forest　into　strongly　consistent　proof　methods,　and　improve　the　data　utilization　of　these　variants　in　order　to　obtain　better　theoretical　properties　and　experimental　performance.　In　addition,　we　propose　the Data-driven　Multinomial　Random　Forest　(DMRF) algorithm,　which　has　the　same　complexity　with　BreimanRF　(proposed　by　Breiman)　while　satisfying　strong　consistency　with　probability　1.　It　has　better　performance　in　classification　and　regression　tasks　than　previous　RF　variants　that　only　satisfy　weak　consistency,　and　in　most　cases　even　surpasses　BreimanRF　in　classification　tasks.　To　the　best　of　our　knowledge,　DMRF　is　currently　a　low-complexity　and　high-performing　variation　of　random　forest　that　achieves　strong　consistency　with　probability　1.　©　The　Author(s)　2024.