Make a Game: FArkle
Introduction
For this unit we were given several different options to pursue this project, we could make a game and describe the mathematics of it, we could solve a pre-determined problem, or we could look through a book of open-ended problems and choose a problem that interested us. My group decided, after confirming that we could with the teacher, to find the mathematic properties of the game Farkle.
You Will Need:
Instructions:
After all players have agreed on a rotation as to when each player goes when, hand off all six dice to the person rolling first. To get on the 'board', or record, the points you had rolled, you had to have gotten a minimum of 500 points. The player currently rolling has the option to put the dice in a cup to and roll them from there, and if a die falls our of the play area, re-roll it. Falling out of the play area would be the die rolling underneath items or off a table. From the die that were rolled, take out a minimum of one dice to stay in play. The player rolling decides which die to keep, and continues to roll the die not chosen to play. This is how players collect points in the game, rolling the die, removing die of points, and adding them to the players total score. If a player uses all six die, they have the opportunity to roll again, however if you are unable to set aside any die (the dice rolled are worth no points), the player rolling loses all points accumulated the round, which is Farkle. Each player is trying to achieve the most points in each round, and the first player to meet or exceed 10,000 points to start the end game sequence. The remaining players have one round to try and beat the score set, and the player with the highest points in the end is declared the winner.
Points:
Strategies
For this unit we were given several different options to pursue this project, we could make a game and describe the mathematics of it, we could solve a pre-determined problem, or we could look through a book of open-ended problems and choose a problem that interested us. My group decided, after confirming that we could with the teacher, to find the mathematic properties of the game Farkle.
You Will Need:
- Minimum of 2 people
- 6 six-sided dice
- Writing Utensil
- Something to write on
- A cup to roll dice in (not necessary)
Instructions:
After all players have agreed on a rotation as to when each player goes when, hand off all six dice to the person rolling first. To get on the 'board', or record, the points you had rolled, you had to have gotten a minimum of 500 points. The player currently rolling has the option to put the dice in a cup to and roll them from there, and if a die falls our of the play area, re-roll it. Falling out of the play area would be the die rolling underneath items or off a table. From the die that were rolled, take out a minimum of one dice to stay in play. The player rolling decides which die to keep, and continues to roll the die not chosen to play. This is how players collect points in the game, rolling the die, removing die of points, and adding them to the players total score. If a player uses all six die, they have the opportunity to roll again, however if you are unable to set aside any die (the dice rolled are worth no points), the player rolling loses all points accumulated the round, which is Farkle. Each player is trying to achieve the most points in each round, and the first player to meet or exceed 10,000 points to start the end game sequence. The remaining players have one round to try and beat the score set, and the player with the highest points in the end is declared the winner.
Points:
- 5’s = 50 points
- 1’s = 100 points
- Three of a kind = The number rolled multiplied by 100 (i.e. 5, 5, 5 = 500), the only exception is 1, 1, 1 which equals 1,000
- Four of a kind = Similar to three of a kind, except that product is multiplied by two
- Five of a kind = Same as four of a kind, but doubled
- Six of a kind = Five of a kind, doubled points
- A straight of 1 - 6 = 1,000 points
- Three pairs = 1,000 points
Strategies
- SAVE - Even if you have one dice with a one on it and two die with a five on each, doesn't mean you need to keep all three. It is more efficient to the single one to have a solid 100 points in the game, there's a larger chance to roll a three of a kind.
- TWO FOR FIVE? - Similar to the rule before, if you have two die with a five on each, only take one! More die for different combinations.
- THIRD TIMES THE CHARM - Rolling a three of a kind usually mean high points, but if there is a dice with a five or a one, take that instead and roll again. Rolling three dice with a two on each only give 200 points, two die with a one on each guarantee the same amount of points in less. More die give more options.
- CAUTION HELPS - Always be cautious and know your limits. Even if your the closest to 10,000 know, Farkle is a game of luck, so don't always try to aim high with each round, sometimes settle for the small points. They add up in the end.
- WHAT ARE THE CHANCES? - When you are done to one or two die left, quit while your ahead. The chances of getting a five or one in those two die are much slimmer than if there were three or four die left. Also, there is a zero percent chance of rolling three of a kind with only two die, so be cautious and roll again (if you think it's best) if there are three die left, and definitely roll again if there's more. But not when there's one or two die left.
Reflection
I've used ideas about probability and strategy in analyzing this game by the charts shown above and the strategic rules I've told. With the scoring that is used in this Farkle game, there are many different scoring when playing Farkle, and the probability of acquiring the highest score is shown in the graphs above. With the probability of getting a Farkle on the last chart, the different chances of getting three of a kind or better with the number of die left on the middle chart, and the chances of getting different types of point combinations on the first chart.
+ Write-Up
- Problem Statement
- Process: Include a description of exactly what you did to carry out the experiments for part a.
- Results: Describe each strategy you tried. For each, tell what you found as the probability of predicting correctly. If possible, describe your results in terms of both your experimental results and your theoretical analysis.
- State what strategy you think gives the highest probability of predicting success. Justify your answer.
- Self-assessment
I've used ideas about probability and strategy in analyzing this game by the charts shown above and the strategic rules I've told. With the scoring that is used in this Farkle game, there are many different scoring when playing Farkle, and the probability of acquiring the highest score is shown in the graphs above. With the probability of getting a Farkle on the last chart, the different chances of getting three of a kind or better with the number of die left on the middle chart, and the chances of getting different types of point combinations on the first chart.
+ Write-Up
- Problem Statement
- Process: Include a description of exactly what you did to carry out the experiments for part a.
- Results: Describe each strategy you tried. For each, tell what you found as the probability of predicting correctly. If possible, describe your results in terms of both your experimental results and your theoretical analysis.
- State what strategy you think gives the highest probability of predicting success. Justify your answer.
- Self-assessment