Chametz and Chumros

Enterprising thieves, in the times of the Gemara, seemed to always be able to catch up to the latest anti-theft trend. The Gemara goes through various measures a watchman was supposed to undertake to safeguard cash. (Bava Metzia 42a) The Gemara proceeds to explain how creative burglars ultimately defeated every technique. At one point in time, the only safe way to safeguard money was to bury it in the ground. There was some question as to how deep a watchman must dig to bury the cash. The Gemara points out that if chametz is buried under a pile of rubble, it may be left there over Pesach. However, if the chametz is buried under less than three tefachim of debris, the owner must remove it. Is the same true for cash? Is three tefachim the magic depth? Ultimately, the Gemara concludes that even one tefach suffices to bury money. Three tefachim is required for chametz so that a dog doesn’t dig it up over Pesach.
It is clear that under certain situations a person can be aware of definite chametz, yet he will have no obligation to remove it before Pesach. One component of bedikas chametz is declaring that all of one’s chametz is worthless and ownerless. However, one can’t simply make that declaration and be absolved from all Pesach cleaning. Chazal mandated that one cannot rely on bitul chametz alone. One reason is that if a person finds chametz over Pesach, he may come to eat it. Therefore, practically, we remove chametz from our houses and declare that any chametz we own is ownerless.