# Probability of throwing three sixes in a row? **URL:** \ **Category:** Factual Questions\ **Created:** [July 29, 2021, 5:37am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574 "2021-07-29T05:37:28Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [July 29, 2021, 5:37am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/1 "2021-07-29T05:37:28Z")
(There was a time I knew this, sigh) A basic probability calculation would yield 1/216, or (1/6)_(1/6)_(1/6), But, surely that’s the probability of throwing just three identical numbers not just three 6’s. Throwing three 2’s will have the same probability. But, I think the probability of throwing three consecutive of one particular number would be different from throwing three consecutive of any number. ---
**Author:** ![lisiate](https://avatars.discourse-cdn.com/v4/letter/l/f05b48/32.png) [@lisiate](https://boards.straightdope.com/u/lisiate)\ **Post date:** [July 29, 2021, 5:52am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/2 "2021-07-29T05:52:55Z")
But the probability of throwing three 2s should be the same as throwing 3 6s? Otherwise there would be something wrong with your die. The probability three of any number will be the sum of those - 6/216 which reduces to 1/36 which makes sense as the first roll sets the target and the next two just have to match it. So its effectively the same as the probability of throwing that particular pair. ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [July 29, 2021, 6:05am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/3 "2021-07-29T06:05:16Z")
The odds of throwing three consecutive of one particular number is one in 216 (6x6x6). That is the same for any particular number whether it be three 3’s or three 6’s. I think what is tripping you up is that you are comparing that to the odds of throwing three consecutive _of any_ number. The odds of that are one in 36 (1x6x6). On your first throw you will roll a number (doesn’t matter which, so that is a 1/1 chance), on your second there is a 1/6 chance of throwing the same number and on the third there is another 1/6 of throwing the same number. Which is exactly what you would expect given that there are six numbers so there are six ways to roll one particular number three times consecutively, so that’s 216/6 = 36. ---
**Author:** ![Velocity](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/velocity/32/18006_2.png) [@Velocity](https://boards.straightdope.com/u/Velocity)\ **Post date:** [July 29, 2021, 6:16am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/4 "2021-07-29T06:16:01Z")
Yes, the odds of throwing three straight (any 1-5 number) in a row are the same for three 6’s in a row. Unless the thrower were somehow trying to manipulate the toss to make it land a certain way (as I would as a kid, to little avail.) ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [July 29, 2021, 7:11am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/5 "2021-07-29T07:11:16Z")
> [@Princhester](#): > > I think what is tripping you up is that you are comparing that to the odds of throwing three consecutive _of any_ number. The odds of that are one in 36 (1x6x6). This is where I should say I failed Statistics, unfortunately, 😲 I actually got very good grades in Stats in College… it was 20 years ago though. ---
**Author:** ![Princhester](https://avatars.discourse-cdn.com/v4/letter/p/3e96dc/32.png) [@Princhester](https://boards.straightdope.com/u/Princhester)\ **Post date:** [July 29, 2021, 8:52am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/6 "2021-07-29T08:52:55Z")
34 years ago for me! ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [July 30, 2021, 5:50pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/7 "2021-07-30T17:50:34Z")
Not to be confused (which I did momentarily) with calculating the probability of getting a six at least once in three tries. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [July 30, 2021, 7:25pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/8 "2021-07-30T19:25:16Z")
Over 50 years for me. It was a tough course; we were still using Roman numerals. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [July 30, 2021, 7:27pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/9 "2021-07-30T19:27:20Z")
I remember the uproar amongst my classmates when they discovered zero. ---
**Author:** ![Frodo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frodo/32/302_2.png) [@Frodo](https://boards.straightdope.com/u/Frodo)\ **Post date:** [July 30, 2021, 7:31pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/10 "2021-07-30T19:31:11Z")
A whole lot of uproar, and for what? nothing!. ---
**Author:** ![kayaker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kayaker/32/441_2.png) [@kayaker](https://boards.straightdope.com/u/kayaker)\ **Post date:** [July 30, 2021, 8:00pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/11 "2021-07-30T20:00:28Z")
Heh, wherever I go today I’ve been playing the straight man. 😊 ---
**Author:** ![Keeve](https://avatars.discourse-cdn.com/v4/letter/k/f07891/32.png) [@Keeve](https://boards.straightdope.com/u/Keeve)\ **Post date:** [July 30, 2021, 9:16pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/12 "2021-07-30T21:16:45Z")
> [@Princhester](#): > > The odds of throwing three consecutive of one particular number is one in 216 (6x6x6). That is the same for any particular number whether it be three 3’s or three 6’s. Or _any other specific combination of three rolls_. Examples: 1/216 that the first will be 2, the second will be 5, and third will be 1. 1/216 that the first will be 6, the second will be 2, and third will be 4. 1/216 that the first will be 6, the second will be 2, and third will be 6. 1/216 that the first will be 3, the second will be 3, and third will be 2. (I bet I could make that list 216 lines long with no repeats!) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 30, 2021, 10:19pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/13 "2021-07-30T22:19:53Z")
> [@Keeve](#): > > (I bet I could make that list 216 lines long with no repeats!) You could, but you’d be well-served to do it systematically. ---
**Author:** ![Somethingwitty1](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/somethingwitty1/32/8899_2.png) [@Somethingwitty1](https://boards.straightdope.com/u/Somethingwitty1)\ **Post date:** [July 30, 2021, 11:52pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/14 "2021-07-30T23:52:39Z")
What is it called when gamblers try use these odds? on single rolls of the dice? or roulette? for example, what are the odds of roulette hitting black 20 times in a row? must be astronomical. So of course I bet on red. It hits black again and I lose. each roll of the dice is independent of the previous roll of the dice. it is a 1/6 chance of rolling a six each time. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 31, 2021, 1:29am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/15 "2021-07-31T01:29:17Z")
Assuming that a particular result is “due” is usually called the Gambler’s Fallacy. Of course, if a roulette wheel has actually hit black 19 times in a row already, then you probably actually want to bet on black. If it’s a fair wheel, it won’t hurt, but at 19 black in a row, you should be seriously considering the possibility that it’s not fair, and is actually biased towards black. ---
**Author:** ![Somethingwitty1](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/somethingwitty1/32/8899_2.png) [@Somethingwitty1](https://boards.straightdope.com/u/Somethingwitty1)\ **Post date:** [July 31, 2021, 2:41am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/16 "2021-07-31T02:41:05Z")
I am coming from this question as a gambler. Not a math guy. First time you throw the die. 1 in 6 chance of throwing a six. Second time you throw, still a 1 in 6 chance of throwing a six. Third time, 1 in 6 chance. The probability of throwing 3 sixes in a row goes up exponentially, if that is what you are betting on. But every time you throw the die, you have a 1 in 6 chance of throwing a 6 ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [July 31, 2021, 1:11pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/17 "2021-07-31T13:11:42Z")
Which is 1/2. Actually, its 91/216. ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [July 31, 2021, 4:12pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/18 "2021-07-31T16:12:46Z")
> [@Somethingwitty1](#): > > for example, what are the odds of roulette hitting black 20 times in a row? must be astronomical. So of course I bet on red. It hits black again and I lose. I decided to take a bomb on a plane to make sure there wouldn’t be a terrorist attack. My wife said, “How is that going to avoid a terrorist attack?” “Well, what are the odds there would be two bombs on the same plane?” ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [July 31, 2021, 4:32pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/19 "2021-07-31T16:32:28Z")
The odds that you have been added to half a dozen watchlists as a result of that post is about 1. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [July 31, 2021, 7:15pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/20 "2021-07-31T19:15:14Z")
I don’t understand what it is you’re trying to ask. As far as I understand it, you cannot bet that roulette will his black 20 times in a row. You can wait until it hits black 19 times in a row (better bring a book), and then bet on the next spin. **This is not the same as betting it will hit black 20 times in a row!** It’s betting it will hit black 20 times in a row, given the information it has already hit 19 times in a row. Not remotely the same thing. [Next page](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574.md?page=2)