play on a given round by re-rolling up to twice if he or she isn’t satisfied with their initial result. On the other hand, if any subsequent player is satisfied with a particular roll, that player is not forced to roll as many times as the leading roller. Thus, any player can stop after the first roll if they like (or anytime before the maximum roll allotment), even if his or her result isn’t the highest yet rolled, which follows from the fact that in this game one is only concerned to avoid rolling lowest in a given turn. Accordingly, the worst thing someone can do as lead roller is roll three times, only to end up with a mediocre result. Therefore, unless one has rolled something very easy to beat, and unless the field of opponents is extremely narrow (particularly in the case in which only one opponent remains) it is best to satisfy oneself with an average or even slightly below-average single result. The odds against any particular non-double result are 17 to 1, and the odds against each double are 35 to 1. However, because of the game’s open rolling structure and idiosyncratic adding system, determining what is a good roll is somewhat counterintuitive, and the most important thing to know is the median result for a given roll (i.e., the result such that it is an even proposition whether the next roll is likely to beat it). The median first roll result, in terms of the likelihood of some other result beating it, is 54—not 62, although there are ten possible results above and below the latter—one of the game’s oddities. Thus, the main thing to be kept in mind on the first roll is where one stands in relation to 54. However, a good result on the first roll is entirely different from a good result on the second or third, with the median result becoming more and more difficult to attain on each reiteration: The median results for the second and third rolls are, respectively, 64 and 1-1 (double ones). Naturally, if one knows the likelihood that they will beat their own last roll by rolling again, they also know the likelihood that someone following them will do the same. For example, if a player were to roll a 52 and then stop, that player would be looking at approximately a 61% probability that