![]() But just knowing the total number of rolls won’t help me when it comes to the game itself I need to know the actual rolls themselves and which ones actually score versus which one are “farkles” (no scoring dice). Mathematically, you can calculate the total number of possible rolls of n six-sided dice as 6^n. My initial analysis was just to look at the basic dice combinatorics. We have four choices for the roll above: should you aggressively score all the dice you can and reroll the fewest, or even just stop rolling and keep your turn’s score? Do you only score the fewest dice you can so that you can reroll more dice and have a chance at getting a bigger score on that next roll? Or do something in between like score the higher scoring dice like the 1’s but not score the 5 so it can be rerolled? In essence, what is the choice that optimizes the risk versus reward? Score just the single 5 for 50 points and reroll the remaining 5 dice.Īnd this is where the player’s choice affects their likelihood of scoring lots of points.Score just one of the single 1’s for 100 points and reroll the remaining 5 dice.Score one of the single 1’s for 100 points and the single 5 for 50 which is a total of 150 points, and I can choose to reroll the remaining four dice.Score both single 1’s for 200 points and the single 5 for 50 points which is a total of 250 points, and I can choose to reroll the remaining three dice.I could score this roll in any one of four ways: For example, say I were to roll a 1, 1, 2, 4, 5, and 6 on my initial roll. With scoring, the important thing to understand is that it is the player’s decision what dice to score and what dice to re-roll if they want to continue rolling on that turn. Over the years, we have refined our variation to the following scoring table: There are many variations to the scoring rules for Farkle. This is the basic game for more details, you can read about the game here. Those players keep rolling until they either beat that score or they farkle. At that point, all remaining players have one final to turn to see if they can beat the first player’s score. This is repeated until the first player reaches 10,000 points. If the player stops rolling before they farkle, they add their turn’s score to their total score and play continues to the next player. If the player is lucky enough to score all six dice, they may continue rerolling with all six of the dice. ![]() The player may continue to keep rolling as long as they do not farkle and elect not to stop. If no dice score points, the player has “farkled” and they forfeit their score for that turn. The scored dice are set aside, and the player then rerolls the remaining dice if they would like to. On a player’s turn, they start by rolling all six dice and selecting which ones to score and which ones to reroll (if any). Today, in part one, I’m going to cover the basics of the game, some of the basic roll statistics, and how I modeled player behavior so that it could be optimized using a genetic algorithm.įarkle is played in turns with each player taking their turn before passing the dice on to the next player. I will also show how to use the KNIME recursive loop nodes to perform open ended processing where the end state cannot be predetermined. Along the way, I will present some interesting modelling techniques. In this series of articles, I’m going to guide you through my explorations of the game which led me to come up with a way to use genetic algorithms to evolve the best Farkle player algorithm I could. It let me quickly and interactively explore the combinatorics of the game and try out approaches for testing various methods for modeling play behavior. The open source KNIME data science platform was the ideal tool for tackling this problem. In short, could I build the optimal Farkle player algorithm? Our frequent strategy debates led me to start thinking about how I would model the game to see if I could come up with the optimal behavior for each situation in the game. And even though we both consider ourselves scientists, we often find ourselves joking about runs of bad luck and hot streaks. We’ve had spirited debates as to what the best choice is in many of those situations. She and I love this game because even though the odds are governed by the basic combinatorics of six-sided dice, the player can make many choices which affect the odds throughout their turn. My wife has a PhD in Global Public Health and has often taught epidemiology to master’s level students which means she has a great appreciation for statistics and data science too. Don’t be offended Farkle is a dice game played with six dice for two or more players. My wife and I love to Farkle and it drives our kids crazy.
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