# 7 11 Dice

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If the Roller does not roll a 7, a 11 or doubles then they have to take a drink from their own beer and hand the dice to the player on the left. This player now becomes the new Roller. Annette obrestad hot. One average is takes about four rolls to get either a 7, a 11 or doubles and a fast Roller can roll once a second. Seven Eleven Dice - Set Of 2; Seven Eleven Dice - Set Of 2. Set of 2 dice that can only roll seven or eleven! A winner every time! Not for actual gambling use. Each die is 1/2 inch square, smaller than standard. Add to Wish List.

1. The number seven is often thought to be a lucky number. But in this dice game, rolling seven is considered a bad thing. You'll need three or more players and six 6-sided dice. How do you play Sevens? The game is played in an agreed-upon number of rounds. In each round, all players take a turn rolling the dice.
2. 7-14-21 Game Type: Dice - # Supplies: 3 or more players; Alcohol; Dice cup with 5 dice; Instructions. Play begins with a die for each player to roll off to see who shakes first. First player shakes all the dice looking for 1's (aces). If a player doesn't shake any dice, the cup is passed on to the player to his left.
(Redirected from Natural (Gambling))

A natural is a term in several gambling games; in each case it refers to one or two specific good outcomes, usually for the player, and often involves achieving a particular score in the shortest and fastest manner possible.[1]

## Examples

In blackjack, the best possible hand for the player is to reach a score of 21 with exactly two cards, which necessarily involves an Ace and a ten-valued card (a 10, jack, queen, or king).[2] This hand, which usually defeats any other hand of 21 and carries a higher payout of winnings, is referred to as a 'blackjack' or a 'natural'.[3][4] A natural in blackjack pays 3:2, however in recent years some casinos have changed the payout ratio to 6:5 for a larger house edge.[5]

In craps, a natural is a roll of two dice with a score of 7 or 11 on the come out roll. This will lead to a win for the players who wagered money on the Pass or Come bet, but a loss for players betting Don't Pass or Don't Come.[6]

In baccarat, a natural is a two-card hand totaling 8 or 9, for either the player or the banker. Natural 9 beats natural 8.[7]

## References

1. ^Mark Bollman (13 June 2014). Basic Gambling Mathematics: The Numbers Behind The Neon. CRC Press. pp. 216–. ISBN978-1-4822-0893-1.
2. ^'Casino Online'. Archived from the original on 11 August 2017. Retrieved 11 August 2017.
3. ^Thorp, Beat the Dealer, 1st edition, New York 1962.
4. ^Beat Multiple Deck Blackjack. Cardoza Publishing. pp. 13–. ISBN978-1-58042-421-9.
5. ^William N. Thompson Ph.D. (10 February 2015). Gambling in America: An Encyclopedia of History, Issues, and Society, 2nd Edition. ABC-CLIO. pp. 25–. ISBN978-1-61069-980-8.
6. ^Craps A Smart Shooters Guide. Cardoza Publishing. pp. 25–. ISBN978-1-58042-576-6.
7. ^'How To Gamble: Baccarat'. VEGAS.com. Retrieved 2016-03-29.

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.

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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.

## 7 11 Dice Game

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)

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.

## 7 11 Dice Drinking Game Rules

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.

## 7 11 Dice Tattoo

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 Rules

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