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New results for the Coupon Collector's problem with swapp...
2015-04-02 · via math.PR updates on arXiv.org

This paper focuses on the Coupon Collector's Problem with replacement (limited purchasing of missing stickers) and swapping. We have simulated combined strategies and found new results, which we were able to prove for a particular case. The ratio of the average number of stickers needed to fill the album by the album size (number of different stickers needed) and the number of collectors as well as the ratio of the variance and the album size depend approximately only on the percentage of replacement stickers (the limited number of stickers that can be bought directly from the vendor) and the number of collectors, but not on the total album size. Thus collectors can estimate the average cost of completion of an album and its standard deviation just based on basic calculations and a table lookup. Additionally we could show that asymptotocally the effect of replacement is stronger than swapping. ----- In diesem Artikel wird das Sammelbilderproblem mit Nachkaufen und Tauschen untersucht. Wir haben mit Hilfe von Simulationen neue Ergebnisse gefunden und sie auch in einem Spezialfall bewiesen. Das Verhältnis der mittleren Anzahl zu kaufender Karten pro Sammler als auch das Verhältnis der Varianz zur Albumgröße hängt in sehr guter Näherung nur vom Anteil der nachkaufbaren Karten ab, aber nicht von der Albumgröße. Damit können Sammler anhand des Prozentsatzes der Nachkaufkarten die mittleren Kosten eines Albums sowie deren Standardabweichung nur mit einer Tabelle und Grundrechenarten bestimmen. Ausserdem konnten wir belegen, dass asymptotisch der Effekt des Nachkaufens stärker ist als der des Tauschens.