Category: dice games

Recall that the Baron's latest game involved he and Sir R----- each casting four four sided dice. For each pair of dice formed from one of the Baron's and one of Sir R-----'s with matching faces, Sir R----- should have received thirteen coins having given twenty eight to play.

The Baron's most recent wager set Sir R----- the task of placing tokens upon spaces numbered from zero to nine according to the outcome of a twenty sided die upon which was inscribed two of each of those numbers. At a cost of one coin per roll of the die, Sir R-----'s goal was to place a token upon every space for which he should receive twenty nine coins and twenty nine cents from the Baron.

In their most recent wager Sir R-----'s goal was to guess the outcome of the Baron's roll of four four sided dice at a cost of four coins and a prize, if successful, of forty four. On the face of it this seems a rather meagre prize since there are two hundred and fifty six possible outcomes of the Baron's throw. Crucially, however, the fact that the order of the matching dice was not a matter of consequence meant that Sir R-----'s chances were significantly improved.

The Baron's latest wager set Sir R----- the task of surpassing his score before he reached eight points as they each cast an eight sided die, each adding one point to their score should the roll of their die be less than or equal to it. The cost to play for Sir R------ was one coin and he should have had a prize of five coins had he succeeded.

A key observation when figuring the fairness of this wager is that if both Sir R----- and the Baron cast greater than their present score then the state of play remains unchanged. We may therefore ignore such outcomes, provided that we adjust the probabilities of those that we have not to reflect the fact that we have done so.

The Baron's latest wager set Sir R----- the task of rolling a higher score with two dice than the Baron should with one twelve sided die, giving him a prize of the difference between them should he have done so. Sir R-----'s first roll of the dice would cost him two coins and twelve cents and he could elect to roll them again as many times as he desired for a further cost of one coin and twelve cents each time, after which the Baron would roll his.
The simplest way to reckon the fairness of this wager is to re-frame its terms; to wit, that Sir R----- should pay the Baron one coin to play and thereafter one coin and twelve cents for each roll of his dice, including the first. The consequence of this is that before each roll of the dice Sir R----- could have expected to receive the same bounty, provided that he wrote off any losses that he had made beforehand.