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Post by slacker 🐨 on Jun 1, 2021 12:18:38 GMT -5
TL;DR:
What are the odds of rolling a pair of dice 150 times and never rolling a 9?
Here's a question for you. I played a game yesterday called Settlers of Catan...fun game. Long story short, you roll a pair of dice and people get resources if they are built next to a region with that number assigned. So, built next to a forest with the number 9 on it, when a 9 is rolled you get one wood resource card.
So, here's the question. We played a game yesterday with 5 players (expansion pack, if you know the game and are wondering how we had 5 players). I had a settlement on a spot that touched three regions, two of which had the number 9. The game lasted an hour with 5 people each rolling the pair of dice each time around, and we probably had roughly 30 times around (very rough estimate). That means the pair of dice were rolled approximately 30 x 5 = 150 times.
What are the odds of rolling a pair of dice 150 times and never rolling a 9?
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Post by rickyguitar on Jun 1, 2021 12:45:40 GMT -5
Slim and none
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Post by Larry Madsen on Jun 1, 2021 13:35:31 GMT -5
Not a final answer by any stretch ... but if one of the two dice have a 1 or 2 showing then the chance is zero.
Basic averages say one third of the time it’s zero chance.
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Post by modbus on Jun 1, 2021 13:38:02 GMT -5
Chance of rolling a 9 on a pair of dice: 1/9 = 0.11111111
so,
Chance of not rolling a nine on a pair of dice: 8/9 = 0.88888888889
Chance of not rolling a 9 on a pair of throws = (0.88888888889)^2 = 0.79
Chance of not rolling a 9 on 5 throws = (0.88888888889)^5 = 0.555
Chance of not rolling a 9 on 150 throws = (0.88888888889)^150 = 0.0000000212 ==> 1 in 47 million
Dice loaded?
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Post by gato on Jun 2, 2021 5:38:58 GMT -5
And the odds of that stannus prang nut rolling under the car to the exact center, where you can't reach it? (Even with that piece of buttered toast that landed face down?)
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Post by Pinetree on Jun 2, 2021 6:22:45 GMT -5
50/50
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Post by LVF on Jun 2, 2021 10:35:32 GMT -5
I was curious about this so, I pulled out a pair of dice that was carried by my grandpa during the attack on Pearl Harbor and rolled them to find out how many rolls it would take to hit a nine. I hit on 10 twice and 11 once before I hit on a nine which took 20 rolls.  |
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Post by slacker 🐨 on Jun 2, 2021 11:38:15 GMT -5
We've been using the same dice that came with the game. I know there have been games where 9 was rolled way more often than you'd expect too. In fact, we usually consider 9 to be a good number to build next to because it is usually rolled pretty often.
What a strange deal.
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Post by Vibroluxer on Jun 3, 2021 11:04:45 GMT -5
Might be wrong but isnt rolling a nine with 2 dice 1/12 rather than 1/9?
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Post by modbus on Jun 3, 2021 11:23:35 GMT -5
Might be wrong but isnt rolling a nine with 2 dice 1/12 rather than 1/9? No, it's 1/9.
There are 36 possible outcomes from a roll of 2 six-sided dice. (1,1), (1,2),...,(1,6), (2,1),(2,2),...,(2,6),...,(6,1),...,(6,5),(6,6). You see the pattern.
Of those 36 outcomes, four end up being a 9: (3,6), (6,3), (4,5), and (5,4). Four out of 36 is 1/9.
There's only one way to roll a 2 or 12, so they both have probabilities of 1/36. 2 ways to roll a 3 or 11, so 1/18. 3 ways to roll a 4 or 10, so 1/12. So on and so forth until 7, which can be rolled 6 different ways, for a probability of 1/6, the most common roll. That's why 7 figures so prominently in Craps.
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Post by Vibroluxer on Jun 3, 2021 20:47:36 GMT -5
Doh!! I hate to be wrong about such things.
Thanks for the excellent explanation.
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Post by slacker 🐨 on Jun 4, 2021 6:49:16 GMT -5
Might be wrong but isnt rolling a nine with 2 dice 1/12 rather than 1/9? No, it's 1/9.
There are 36 possible outcomes from a roll of 2 six-sided dice. (1,1), (1,2),...,(1,6), (2,1),(2,2),...,(2,6),...,(6,1),...,(6,5),(6,6). You see the pattern.
Of those 36 outcomes, four end up being a 9: (3,6), (6,3), (4,5), and (5,4). Four out of 36 is 1/9.
There's only one way to roll a 2 or 12, so they both have probabilities of 1/36. 2 ways to roll a 3 or 11, so 1/18. 3 ways to roll a 4 or 10, so 1/12. So on and so forth until 7, which can be rolled 6 different ways, for a probability of 1/6, the most common roll. That's why 7 figures so prominently in Craps.
Yep, the Catan game has the tokens with the numbers on them that you put on the resource regions and, underneath the number on each token are pips indicating the number of ways that number can be rolled with a pair of dice. |
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Post by HenryJ on Jun 6, 2021 7:27:04 GMT -5
Might be wrong but isnt rolling a nine with 2 dice 1/12 rather than 1/9? No, it's 1/9.
There are 36 possible outcomes from a roll of 2 six-sided dice. (1,1), (1,2),...,(1,6), (2,1),(2,2),...,(2,6),...,(6,1),...,(6,5),(6,6). You see the pattern.
Of those 36 outcomes, four end up being a 9: (3,6), (6,3), (4,5), and (5,4). Four out of 36 is 1/9.
There's only one way to roll a 2 or 12, so they both have probabilities of 1/36. 2 ways to roll a 3 or 11, so 1/18. 3 ways to roll a 4 or 10, so 1/12. So on and so forth until 7, which can be rolled 6 different ways, for a probability of 1/6, the most common roll. That's why 7 figures so prominently in Craps.
OK, I'm not as experienced as the rest of y'all (although I did play Monopoly with grandkids a couple of times this past week), but I would think there are only 21 combinations, with 6 and 3 being the same as 3 and 6. 5 and 4 or 6 and 3 would be two chances in 21, the way I see it. 9.5% chance of rolling a 9. |
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Post by modbus on Jun 6, 2021 10:02:31 GMT -5
No, it's 1/9.
There are 36 possible outcomes from a roll of 2 six-sided dice. (1,1), (1,2),...,(1,6), (2,1),(2,2),...,(2,6),...,(6,1),...,(6,5),(6,6). You see the pattern.
Of those 36 outcomes, four end up being a 9: (3,6), (6,3), (4,5), and (5,4). Four out of 36 is 1/9.
There's only one way to roll a 2 or 12, so they both have probabilities of 1/36. 2 ways to roll a 3 or 11, so 1/18. 3 ways to roll a 4 or 10, so 1/12. So on and so forth until 7, which can be rolled 6 different ways, for a probability of 1/6, the most common roll. That's why 7 figures so prominently in Craps.
OK, I'm not as experienced as the rest of y'all (although I did play Monopoly with grandkids a couple of times this past week), but I would think there are only 21 combinations, with 6 and 3 being the same as 3 and 6. 5 and 4 or 6 and 3 would be two chances in 21, the way I see it. 9.5% chance of rolling a 9.
Even though (3,6) and (6,3) give the same result, they are totally different rolls, just like (3,6) and (5,4) are totally different rolls but give the same result.
Imagine throwing two dice, but instead of being identical, one is a standard die with dots and and the other has a number from 1 to 6 on each side. A roll of 3 dots and a '6' is definitely a different roll than 6 dots and a '3'. Now, if you just add the dots to the numeral, you get the usual result and both rolls are a '9'. However, if you were playing some hypothetical game where the dot die was for the number of spaces you move in a turn, and the numeral die was the amount of money you get for a turn, then the two different rolls give two very different results. They are clearly two different rolls.
When you roll two 6-sided dice, there are 36 possible outcomes, all with equal probability. How you choose to group the results, like for instance adding the two die faces together, will lump certain results together increasing the probability for the lumped results.
Here's a nice picture:
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Post by modbus on Jun 6, 2021 10:04:56 GMT -5
Here's another nice picture:
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Post by Pinetree on Jun 6, 2021 18:22:35 GMT -5
I stand by 50/50.
It either does or it doesn't.
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