in the first two rounds a player gets 12355 after each roll. This would happen if a 12355 is thrown on the first roll and then, whatever dice are re-thrown, getting the same combination again; for instance, keeping 55, rethrowing the 123, and still getting 12355. The optimal strategy uses the 1s box in the first round, scoring 1, and the 2s box in the second round, scoring 2. Now suppose that for the next 3 rounds 11226 results after each roll. Once again, this is possible because 11226 may be thrown on the first roll and the same may be gotten when some of dice are re-thrown. The optimal strategy uses the four-of-a-kind and Yahtzees boxes in the third and fourth rounds and then the 3s box in the fifth round, scoring 0 each time. For the last 8 rounds, suppose 11223 is rolled each time. 0 is scored in all the remaining categories—except chance, where 9 is scored—giving a total of 12. Commercial versions Deluxe and collector editions Deluxe edition games have been sold alongside the regular issue games since the early 1960s. They all contain components that are more luxurious than standard game parts. In recent years, a number of collector issue Yahtzees have been sold as well. Some of these collector issues have dice that replace the pips with certain symbols connected to a theme, but still correspond to the numbers one to six. Travel Yahtzee Since the 1970s, Travel Yahtzee has been sold in various forms as part of Milton Bradley's line of travel games. In the past, the travel form of Yahtzee was composed of the five dice contained in a special apparatus (see image at the right). "Rolling" the dice is initiated by turning the apparatus over, running it on one hand and turning it upright to see the faces of the dice. Dice to be saved for the next roll are locked by snapping the reverse of the apparatus. Currently, a zip-up cloth deluxe folio edition is sold. It consists of the set of dice, the cup, the scorecards and a tray for the dice to roll on, which includes a holder for the dice to be saved for the next roll. The cup has an oblong lip for easy storage. In addition to the game folio, Hasbro also released Yahtzee to Go. It comes with a dice cup that stores the