最近，三位數學家將這項理論擴展到更不精確的日常洗牌方式，他們透過為每張牌分配由零與一組成的條碼來追蹤牌組中難以混合的「冷點」，證明了即使切牌不均勻，截斷現象依然存在。
根據這項最新的數學證明，如果在每次洗牌時都隨機切牌，大約需要十四次不精確的日常洗牌才能將一副五十二張的標準撲克牌徹底混合均勻。
In 1992, mathematicians proved that seven perfect riffle shuffles are enough to completely randomize a deck of cards through a cutoff phenomenon, but this proof relied on strict conditions requiring the deck to be cut exactly in half and interleaved evenly.
Recently, three mathematicians extended this theory to less precise, everyday shuffling methods by assigning barcodes of ones and zeros to each card to track unmixed "cold spots," proving that the cutoff phenomenon still occurs even with uneven cuts.
According to this latest mathematical proof, if the deck is cut at a random place during each shuffle, it takes roughly fourteen sloppy shuffles to thoroughly mix a standard deck of fifty-two cards.