- Haywire Group Kerfuffle Dice Game (Product Packaging May Vary), (Model: 5512407) Merchant Video. Videos for related products. Click to play video.
- Sevens, elevens, and doubles (also referred to as ' 7s, 11s, and doubles ', ' 7/11/2x ', sloppy dice or hero.) is a drinking game played with two dice. The game can be played with as few as two people, but is usually played in a group of five or more. The object of the games is to roll a 7, 11 or any double.
If the second player can’t finish his glass before a 7, 11 or double is played, the game starts again until the drinker beats the roller. Once the drinker wins or loses 5 consecutive times, the dice are passed clockwise to the next player who tries a hand at rolling a 7, 11 or a double to nominate another drinker.
In front of you are two fair dice.
One is a 7-sided dice with faces -3, -2, -1, 0, 1, 2, 3.
The other is an 11-sided dice with faces -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5.
You pick a dice, and I will get the other one. We will roll together, and the person with the larger number wins. If the two dice show the same number, we roll again until someone wins.
Which dice should you pick, if you want to maximize your chance of winning?
Bonus: solve the game for the generalized case: one dice has integer sides from –n to n and the other dice has integer sides from –m to m, where n < m.
Watch the video for a solution.
Or keep reading.
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'All will be well if you use your mind for your decisions, and mind only your decisions.' Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
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Answer To 7 Vs 11 Sided Dice Game Riddle: Who Wins?
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
I saw this puzzle at Puzzling StackExchange and the answer initially surprised me until I read the excellent solution from hexomino.
First let’s solve the 7 vs 11 case directly. There are 7 equally likely ways to roll the 7 sided dice, and 11 equally likely ways to roll the 11 sided dice, for a total of 7 x 11 = 77 equally likely events.
We can visualize the sample space as an ordered pair (i, j) for rolling (7 sided dice, 11 sided dice).
There are 7 possible ways both dice show the same number:
(-3, -3), (-2, -2), (-1, -1), (0, 0), (1, 1), (2, 2), (3, 3)
For any other roll, the game ends with a win for some player. Thus there are 77 – 7 = 70 equally likely rolls in which the game ends.
Out of these, exactly 35 will be a win for the person rolling the 7-sided dice, which we can enumerate:
(-3, -5), (-3, -4)
(-2, -5), (-2, -4), (-2, -3)
(-1, -5), (-1, -4), (-1, -3), (-1, -2)
(0, -5), (0, -4), (0, -3), (0, -2), (0, -1)
(1, -5), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0)
(2, -5), (2, -4), (2, -3), (2, -2), (2, -1), (2, 0), (2, 1)
(3, -5), (3, -4), (3, -3), (3, -2), (3, -1), (3, 0), (3, 1), (3, 2)
(-2, -5), (-2, -4), (-2, -3)
(-1, -5), (-1, -4), (-1, -3), (-1, -2)
(0, -5), (0, -4), (0, -3), (0, -2), (0, -1)
(1, -5), (1, -4), (1, -3), (1, -2), (1, -1), (1, 0)
(2, -5), (2, -4), (2, -3), (2, -2), (2, -1), (2, 0), (2, 1)
(3, -5), (3, -4), (3, -3), (3, -2), (3, -1), (3, 0), (3, 1), (3, 2)
How To Play 7 11
Lord of the rings free online slot game. We can also use a table to represent the outcomes:
So the 7-sided dice wins with a 35/70 = 50 percent probability. And since the other game-ending outcomes are a win for the other dice, this means the 11-sided dice also wins with a 35/70 = 50 percent probability.
In other words, it doesn’t matter which dice you pick: the game is fair! There is a 50 percent chance of either player winning, and this is true even for the general case of an n dice versus an m dice for n < m.
General proof
There’s a neat trick to see why each dice has the same chance of winning.
Consider the roll (i, j) = (player 1 rolls n dice, player 2 rolls the m dice).
Player 1 wins if and only if i > j.
But for every such winning pair, there will also be a roll (-i, –j) because if a dice has a face labeled x it also has the face labeled –x. And this roll is a win for player 2 since i > j implies –i < –j.
And we can make the same argument for player 2 as well! Player 2 wins on a roll (i, j) if and only if i < j. But for every such winning pair, we can find the paired outcome (-i, –j) which is a win for player 1. Lightning slots on facebook.
Thus, the mapping (i, j) to (-i, –j) is a bijection between the winning rolls between the two players. Player 1 and 2 have exactly the same number of winning outcomes, and the game ends in a win for some player, implying each person has a 50 percent chance of winning.
The game is fair, and it doesn’t matter which dice you pick, even in the general case!
Source
7-11 Dice Game Gift
Problem adapted from Puzzling StackExchange. Post by athin, 11 sided vs 41 sided dice. Solution from hexomino.
https://puzzling.stackexchange.com/questions/77557/a-short-dice-puzzle
https://puzzling.stackexchange.com/questions/77557/a-short-dice-puzzle
Seven Eleven, or “rolling dice for money,” has become increasingly popular amongst the Leesville male population and has taken over as a way to win money from friends.
The goal of the game is to roll a sum of seven or eleven. Seemingly simple, the game is highly addictive because of its unpredictability.
To start the game, the players throw the same amount of money into a betting pool. Each player has one die; both players roll the dice at the same time and whoever rolls the higher number goes first. The player that rolled the higher number then takes both dice and rolls; if the player rolls doubles, the player rolls again; if each die rolls a one (snake eyes) then that player loses.
Whichever player rolls the seven or eleven first earns possession of whatever money was originally placed into the pool. This amount can be anywhere from a couple dollars to a couple hundred.
“My friends taught me to play at school, and it’s just a fun way to earn money. Yeah, you lose occasionally, but that’s just all the more reason to keep playing and win your money back,” said an anonymous dice-rolling junior.
Because the game involves betting money on something with an uncontrollable outcome, it is considered gambling, which is illegal in the state of North Carolina.
How To Play 7-11 Dice Game
“I’ve been hearing about this game recently,” said Officer Faust, Student Resource Officer at LRHS. “To me it’s just like placing money on the NCAA tournament; they’re going to do it. It’s just one of those issues that won’t be addressed until it starts affecting other students.”
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However, that may be soon because students have recently been playing the game in class.
“It’s a great game,” said another junior gambler. “It’s a fun thing to do at parties, sometimes we’ll have parties where you’ll see twenty or thirty games going on at once. My teacher took my dice away the other day because I had them out during class, but she gave them back after school. It was no big deal.”
Dice could soon be joining cell phones and iPods on the list of “Nuisance Items” that are banned inside school walls. Be careful with where you play the game or take the safest choice–don’t play at all.
7 11 Doubles
Katy has been on staff since her sophomore year, starting as a staff writer. With hard work and diligence, she earned a junior editor position and ultimately became Editor-in-Chief her senior year. She will pursue a degree in journalism in college.