    Rules of Shut-the-Box The rules of the game are quite simple, and here I will exhaustively explain them to the best of my ability. As you probably know, the game involves two dice and a wooden box constructed with shutters or sliders that can be moved to reveal or conceal each of the numerals from one to nine. The player begins by rolling the two dice. The sum of the dice becomes the target value for that particular round. For example, if the dice are as they look below, the target value for that round is eight.  The player then proceeds to close any number of sliders such that the final sum of the sliders that have been shut during that particular round is exactly equal to the target. In the instance above, a player could close sliders 8; 1 & 7; 1,2 & 5; 1,3 & 4; 2 & 6; or 3 & 5 since 8 = 8 = 1 + 7 = 1 + 2 + 5 = 1 + 3 + 4 = 2 + 6 = 3 + 5. Before the player arrives at the target sum, the player has the option to "take back" their last move. Continuing with our example, if the target is eight and the player starts by shutting the 2, and then decides that shutting the 3 and 5 would be a better play, then the player is allowed to open the 2 and shut the 3 and 5, provided that the player has not yet shut the 6 (as 2 + 6 = 8, the target). Once a slider is shut, it stays shut for the whole game. Shut-the-Box does not involve subtraction from a slider total (though such a rule could add another level of complexity to the game). As the game reaches its completion, their exists another possible situation. For example, if a player successfully closes every number save 5 (that is, if 5 is the only number still open), the subsequent roll will be of a single die (die = singular of dice). The reason for this is straight-forward. If the total of open numbers is six or less, the probability of rolling that total increases if the player rolls only one die. For instance, the odds of rolling a 5 on two dice are 1/9 or roughly 11% (meaning with two dice, you will roll 5 11% of the time). Using one die, the odds of rolling a 5 are 1/6 or roughly 16.6% (meaning you roll 5 16.6% of the time). In some versions of the rules, players are allowed to decide if they would rather roll 1 or 2 dice if the remaining total is 6 or less; however, it is always better to roll one die, so that is how I've implemented the rules. Play continues until all of the sliders are shut or until an impossible roll occurs. If all of the sliders are shut, the player cries out "ShutBox!" indicating that the player has accomplished the goal of the game, and in a multi-player situation, is likely to be the winner. An impossible roll occurs if the sum of the dice cannot be "shut out" by closing sliders. As mentioned before, the sum of the sliders shut must exactly equal the target sum. If this is not possible given the remaining open numbers, then the game ends. Again, if one rolls an eight, but only the five is left open, the game is over and the score is 5. It would be impossible to close off the remaining open sliders to equal the target number in this case. Though the player in this case may be dissapointed that ShutBox was not accomplisher, 5 is a pretty good score. In the worst case scenario, a player could roll "snake eyes" (double ones, or sum of two) twice in a row. Since the two would have been closed on the first roll, on the second roll of 2, the game would end, leaving the player with a score of 1 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 43. This scenario happens 1 of 1296 games or 0.077% of the time.

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