can result in a deduction of 500 or 1000 points from the player's score. Another variation is using five dice instead of six. In this version, players cannot score three pair, and this variation often couples an "instant" win option, where on the first roll of the five dice on any turn, if the player rolls five of a kind, that player instantly wins the game, regardless of the scores to that point. An end-of-game variation described as "welfare" requires the winner to score exactly 10,000 points. If a player scores more than 10,000 points, then all points scored in that turn are given to the player with the lowest score. Probabilities Following are the probabilities of scoring combinations in the initial throw of six dice. For the most part, less probable combinations are scored higher than more probable combinations (see Scoring Variations). Following are the probabilities of scoring combinations in subsequent throws of the dice. Following are the probabilities of farkling if all variant scoring combinations are allowed, depending on the number of dice thrown. Three-pair is the only scoring variation that alters the likelihood of farkling, and only on the initial throw of six dice. If three pairs are not scored, the probability of farkling on the initial throw increases to 1 in 32.4 (5 in 162). Following are the probabilities of making hot dice in a single throw if all variant scoring combinations are allowed, depending on the number of dice thrown. If no variant scoring combinations are allowed, the probabilities of making hot dice are decreased only slightly for 4–6 dice thrown, and unchanged for 1–3 dice thrown. Odds for these and other die combinations with explanations and simulation results can be found elsewhere. Effects of scoring variations Scoring additional combinations such as straights and three pairs increases the speed of play by awarding high scores for low probability events that otherwise would score little or nothing (for example, a straight with standard scoring is worth only 150 for the single 1 and single 5). To assess the impact of scoring variations, the following table shows the average score on the initial throw of six dice, assuming that all scoring dice are banked and ignoring any additional scores that would be made on a re-roll of hot dice. The first row shows the average score with standard scoring, and the other rows show the increment in