重复牌的处理方法比较
Comparing dealing methods with repeating cards
摘要：
在最近的工作康格和霍华德推导出渐近公式的随机性，洗牌后，甲板与重复卡或所有不同的甲板处理到手中。在后一种情况下，这副牌不需要完全随机化：玩家收到的牌的顺序是无关紧要的。他们分别将这些情况称为“固定来源”和“固定目标”情况，并将其分开处理。我们建立在他们的结果和混合这两种情况下：我们获得的随机性的一副重复的卡是洗牌，然后处理到手中的球员的渐近公式。我们确认，从有序的循环处理，或从循环到来回处理的切换，以类似的方式比在非重复的“固定目标”的情况下，提高了随机性。我们的公式允许改进甚至来回处理时，甲板上只包含两种类型的卡。
英文摘要：
In a recent work Conger and Howald derived asymptotic formulas for the randomness, after shuffling, of decks with repeating cards or all-distinct decks dealt into hands. In the latter case the deck does not need to be fully randomized: the order of cards received by a player is indifferent. They called these cases the "fixed source" and the "fixed target" case, respectively, and treated them separately. We build on their results and mix these two cases: we obtain asymptotic formulas for the randomness of a deck of repeating cards which is shuffled and then dealt into hands of players. We confirm that switching from ordered to cyclic dealing, or from cyclic to back-and-forth dealing improves randomness in a similar fashion than in the non-repeating "fixed target" case. Our formulas allow to improve even the back-and-forth dealing when the deck only contains two types of cards.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
