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Started By
Message
Help me figure out a dice/math question
Posted on 10/31/16 at 11:39 am
Posted on 10/31/16 at 11:39 am
While at the bar waiting for a Badger game to start the other week, some friends and I were playing a dice game called Farkel, which requires you to take rolls of the dice and score points. As long as you're scoring points you keep going.
In order to score points and keep going you need to roll either a 1 or a 5 on one of the dice rolled. Where we got stuck was when we were determining if it made sense to roll when you only had two left (or catalogue your points and end your turn). You would only need one of the dice to be a 1 or a 5 to stay alive. Our thinking was that the odds of getting a 1 or 5 on a single dice was 33%. And since you're rolling two the odds would be 66%. But that logic doesn't work, because if you continue that thinking, you'd have a 99% chance of a 1 or 5 if you rolled 3 dice...which can't be right.
There is something in there we weren't adjusting for, but we couldn't figure it out while drinking and focused on other football games. All the formulas I found online deal with craps totals, and I haven't taken a math class since college.
tl;dr: What are the odds of rolling two dice and having one of the two be either a 1 or a 5?
In order to score points and keep going you need to roll either a 1 or a 5 on one of the dice rolled. Where we got stuck was when we were determining if it made sense to roll when you only had two left (or catalogue your points and end your turn). You would only need one of the dice to be a 1 or a 5 to stay alive. Our thinking was that the odds of getting a 1 or 5 on a single dice was 33%. And since you're rolling two the odds would be 66%. But that logic doesn't work, because if you continue that thinking, you'd have a 99% chance of a 1 or 5 if you rolled 3 dice...which can't be right.
There is something in there we weren't adjusting for, but we couldn't figure it out while drinking and focused on other football games. All the formulas I found online deal with craps totals, and I haven't taken a math class since college.
tl;dr: What are the odds of rolling two dice and having one of the two be either a 1 or a 5?
16
Posted on 10/31/16 at 11:42 am to Chucktown_Badger
quote:
Our thinking was that the odds of getting a 1 or 5 on a single dice was 33%. And since you're rolling two the odds would be 66%.
Try again amigo
Posted on 10/31/16 at 11:42 am to LSU_Saints_Hornets
quote:
Try again amigo
Did you stop reading at that point? I acknowledged in the very next sentence
quote:
But that logic doesn't work, because if you continue that thinking, you'd have a 99% chance of a 1 or 5 if you rolled 3 dice...which can't be right.
Posted on 10/31/16 at 11:43 am to Chucktown_Badger
I'm pretty sure it's still 1/3.
4 chances of 12 to get one of those numbers.
4 chances of 12 to get one of those numbers.
Posted on 10/31/16 at 11:43 am to Chucktown_Badger
Sounds like a Yankee game
Posted on 10/31/16 at 11:43 am to Chucktown_Badger
2/6 on one
2/6 on another
4/12 total. same odds. but then again i haven't taken math in a long time either.
2/6 on another
4/12 total. same odds. but then again i haven't taken math in a long time either.
Posted on 10/31/16 at 11:43 am to Chucktown_Badger
I believe it's 1 - (1 - p)^n. Where p = 0.333 and n = 2.
So 1 - (1 - 0.333)^2 = 55.6%
So 1 - (1 - 0.333)^2 = 55.6%
Posted on 10/31/16 at 11:45 am to Chucktown_Badger
quote:
Did you stop reading at that point? I acknowledged in the very next sentence
quote:
But that logic doesn't work, because if you continue that thinking, you'd have a 99% chance of a 1 or 5 if you rolled 3 dice...which can't be right.
What is 4/12? That will show you that the probability has not increased since you added a second die. It is still 33%.
ETA I haven't done this in a long time but I believe there is a probability formula that will better explain this.
This post was edited on 10/31/16 at 11:46 am
Posted on 10/31/16 at 11:45 am to Chucktown_Badger
quote:
Our thinking was that the odds of getting a 1 or 5 on a single dice was 33%. And since you're rolling two the odds would be 66%. But that logic doesn't work
No, it doesn't.
To get the odds that it will happen, you have to calculate the odds that it won't happen, and subtract that from 100%.
2/3 x 2/3 = 4/9 chance that you won't roll a 1 or 5 on either, or a 5/9 chance that you will.
Unless, of course, you are me playing backgammon and need a 1 or a 5 to get out of jail, in which case the probability of rolling a 1 or a 5 is precisely zero.
This post was edited on 10/31/16 at 11:53 am
Posted on 10/31/16 at 11:46 am to Chucktown_Badger
Each roll is mutually exclusive so the odds won't change.
It's still a 4/12 chance with 2 dice.
It's still a 4/12 chance with 2 dice.
Posted on 10/31/16 at 11:46 am to Chucktown_Badger
quote:
tl;dr: What are the odds of rolling two dice and having one of the two be either a 1 or a 5?
55.555%
Posted on 10/31/16 at 11:47 am to Chucktown_Badger
It's around 55%
Posted on 10/31/16 at 11:48 am to Winston Cup
quote:
2/6 on one 2/6 on another 4/12 total. same odds. but then again i haven't taken math in a long time either.
By this logic, even rolling 100 dice you still on only have a 1/3 chance of getting a 1 or 5 on one of them.
This post was edited on 10/31/16 at 11:49 am
Posted on 10/31/16 at 11:48 am to RJL2
quote:
Each roll is mutually exclusive so the odds won't change.
It's still a 4/12 chance with 2 dice.
Yeah, but you're rolling two dice and you only need to get the number on one of them.
If I rolled 10 dice, are you saying there's still only a 1/3 chance that 1 of the 10 will have a 1 or a 5?
Posted on 10/31/16 at 11:48 am to LSU_Saints_Hornets
quote:
That will show you that the probability has not increased since you added a second die. It is still 33%.
Of course rolling more dice adds to the probability that ONE of them will turn up a 1 or a 5. Do you seriously think you could roll 1000 dice and there'd be a 66% chance that NONE of them would come up either 1 or 5?
The probability is the same for each die, but the more dice you roll, the better your chances that ONE of them will be what you need (in this case, 1 or 5).
Posted on 10/31/16 at 11:49 am to FutureMikeVIII
quote:
I believe it's 1 - (1 - p)^n. Where p = 0.333 and n = 2.
So 1 - (1 - 0.333)^2 = 55.6%
Who downvoted this? It seems to be the smartest answer in here.
Posted on 10/31/16 at 11:50 am to FutureMikeVIII
quote:
I believe it's 1 - (1 - p)^n. Where p = 0.333 and n = 2.
So 1 - (1 - 0.333)^2 = 55.6%
Correct.
Posted on 10/31/16 at 11:51 am to Chucktown_Badger
quote:
Who downvoted this? It seems to be the smartest answer in here.
It is the correct answer.
Posted on 10/31/16 at 11:51 am to Chucktown_Badger
quote:
If I rolled 10 dice, are you saying there's still only a 1/3 chance that 1 of the 10 will have a 1 or a 5?
This sounds like the kind of problem that would never get figured out after a few beers.
Posted on 10/31/16 at 11:51 am to Chucktown_Badger
Nuts4LSU explained it better, but it's correct.
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