# 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:** 16\ **Page:** 2
**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, 7:40pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/21 "2021-07-31T19:40:58Z")
> [@Snarky\_Kong](#): > > **This is not the same as betting it will hit black 20 times in a row!** That is the point I am trying to make. the odds of roulette hitting black 20x in a row are astronomically against it. But the gamblers fallacy (thanks @Chronos) leads some people to believe red must be the next spin, based on the previous 19 spins. The odds of the 20th spin are 50/50 (ignoring 0 00 green). The odds of the 20th spin aren’t 5 billion to one. The displays they have at the roulette table, listing all the previous winning numbers, prey upon this fallacy. Likewise for throwing three sixes in a row. I understand the mathematical explanation of probability, and the above posters are mathematically correct. ---
**Author:** ![Northern\_Piper](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/northern_piper/32/5304_2.png) [@Northern\_Piper](https://boards.straightdope.com/u/Northern_Piper)\ **Post date:** [August 1, 2021, 12:31am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/22 "2021-08-01T00:31:33Z")
I think one of the things that confuses people is that the chance of throwing a particular number on a die is the same, regardless fo the number and the sequence, but the chance of throwing a particular _total_ varies tremendously. In craps, for instance the chance of snake eyes is 1 in 36, since there is only one combination out of the 36 possible throws that adds up to 1. Same odds for box cars. But the chance of throwing 7 is 1 in 6, because there are six ways to throw a 7. The individual chance for each die throw is the same, but the chance for the total varies. ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [August 1, 2021, 4:33am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/23 "2021-08-01T04:33:45Z")
I remember that, but I failed. I’ll never understand the new number system if I live to be C! (h/t frantic times) ---
**Author:** ![Tripler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripler/32/21807_2.png) [@Tripler](https://boards.straightdope.com/u/Tripler)\ **Post date:** [August 1, 2021, 5:52am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/24 "2021-08-01T05:52:43Z")
[True Story] I was once in Las Vegas for a convention, and _after hours_ went down to the floor to play a little craps. The dice passed to me after a bit, so I laid out a few bets, and set a point. After that roll, with a pair of chips in my hand, called out to the dealer, “Two-way yo!” I hit an eleven to everyone’s amazement. Dealers were happy, I was happy, so on a whim, I threw out another two-way yo. I hit it again. Got paid, threw out another two-way yo. . . lather rinse repeat two more times after that. I hit eleven _four times in a row_, and then crapped out. Bottom line, and even the dealer was amazed, that I rolled an eleven four times in a row, which I admit is a wildly impossible statistic anomaly–but it happened. [/True story] Tripler T’was my best (and only time) downtown in Vegas. ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [August 1, 2021, 10:53am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/25 "2021-08-01T10:53:07Z")
> [@Tripler](#): > > T’was my best (and only time) downtown in Vegas. Only BS in that story is this 😜 Zilch chance you didn’t try again after that. ---
**Author:** ![Tripler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripler/32/21807_2.png) [@Tripler](https://boards.straightdope.com/u/Tripler)\ **Post date:** [August 6, 2021, 12:57am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/26 "2021-08-06T00:57:07Z")
Nope. . . I cannot say that I’ve been to “Vegas\*” with the exceptions of overnight outlying hotel stays waiting for flights the next day. I have played two-way yo bets since then, but they always lose. “Vegas\*” meaning _‘The Strip’_. Tripler There’s lots of other nuclear nonsense to do in Nevada. ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [August 6, 2021, 1:17am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/27 "2021-08-06T01:17:43Z")
> [@Tripler](#): > > Bottom line, and even the dealer was amazed, that I rolled an eleven four times in a row, which I admit is a wildly impossible statistic anomaly–but it happened. If I understand craps play, your odds of this chain are 1/18^4, or 1/104,976. Pretty crazy rare. But how many sets of four rolls in a row happen in Las Vegas craps games every night? If it’s at least 10,000, you’d expect this sequence to show up a few times a month. ---
**Author:** ![Tripler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripler/32/21807_2.png) [@Tripler](https://boards.straightdope.com/u/Tripler)\ **Post date:** [August 6, 2021, 1:30am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/28 "2021-08-06T01:30:33Z")
I would expect a 2d6 roll of 6, 7, or 8 to come up often, _maybe_ four times in a row. But of the 36 possible combinations with a 2d6, a roll of 11 is only possible twice (2/18, or 5.56% chance). Four times in a row (5.56%^4)? That’s a ((2/18)^4 or 1/6561) 0.000952% chance of that happening on any given sequence of four rolls in a row. Hell, it made me and the dealers an extra $300 each that night, IIRC. Tripler Five dollar table. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [August 6, 2021, 1:34am UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/29 "2021-08-06T01:34:15Z")
> [@kayaker](#): > > Heh, wherever I go today I’ve been playing the straight man. 😊 Not true. I’m pretty sure I’ve set you up a few times. Thought maybe that was @kaylasdad99. You kay posters used to all look alike to me—until we got avatars. ---
**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:** [August 6, 2021, 1:33pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/30 "2021-08-06T13:33:23Z")
> [@Left\_Hand\_of\_Dorkness](#): > > But how many sets of four rolls in a row happen in Las Vegas craps games every night? If it’s at least 10,000, you’d expect this sequence to show up a few times a month. Or to look at it from the other point of view, how many things in @Tripler’s (or any other individual’s) life have had quantifiable odds? Plenty. ---
**Author:** ![zimaane](https://avatars.discourse-cdn.com/v4/letter/z/a3d4f5/32.png) [@zimaane](https://boards.straightdope.com/u/zimaane)\ **Post date:** [August 6, 2021, 2:28pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/31 "2021-08-06T14:28:39Z")
> [@Tripler](#): > > Hell, it made me and the dealers an extra $300 each that night, IIRC. How did the dealers make an extra $300 on your dice throws? ( I admit I know nothing of dice games, so forgive me if it’s obvious) ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [August 6, 2021, 2:46pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/32 "2021-08-06T14:46:56Z")
This is not a question about statistics; it is a question about probability a very different discipline. I never had a course in stats and actually know essentially 0 about it, but I do understand probability pretty well. ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [August 6, 2021, 4:10pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/33 "2021-08-06T16:10:48Z")
Probability was taught as part of Statistics in our college classes. We needed to clear 4 modules, of which at least 1 had to be Statistics and 1 mechanics. For the record I took two Pure Maths courses and the basic modules for stats and mechanics (known to us as Stats1 and Mech1), and the modules together were known as “Mathematics”. I am sure they are different but this was how the course was named and taught. I wasn’t very good at it, though amazingly I actually got very good marks in all. Go figure. (Replying to @Hari_Seldon ). ---
**Author:** ![AK84](https://avatars.discourse-cdn.com/v4/letter/a/85e7bf/32.png) [@AK84](https://boards.straightdope.com/u/AK84)\ **Post date:** [August 6, 2021, 4:17pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/34 "2021-08-06T16:17:58Z")
Well this is embarrassing. Looked up my college course list and the full name of the Statistic 1 module (S1) is errrr “Probability and Statistics”), 🤦🏻‍♂️ The question paper. > **[9709\_s03\_qp\_6.pdf](https://www.cienotes.com/wp-content/uploads/2018/06/9709_s03_qp_6.pdf)** > > 83.02 KB ---
**Author:** ![Left\_Hand\_of\_Dorkness](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/left_hand_of_dorkness/32/7156_2.png) [@Left\_Hand\_of\_Dorkness](https://boards.straightdope.com/u/Left_Hand_of_Dorkness)\ **Post date:** [August 6, 2021, 4:20pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/35 "2021-08-06T16:20:48Z")
> [@AK84](#): > > I wasn’t very good at it, though amazingly I actually got very good marks in all. Man, what are the chances? ---
**Author:** ![Tripler](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripler/32/21807_2.png) [@Tripler](https://boards.straightdope.com/u/Tripler)\ **Post date:** [August 6, 2021, 10:09pm UTC](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574/36 "2021-08-06T22:09:30Z")
It’s all good! A “two way” bet (a bet for me ‘one way’, and a mirrored bet for the dealers ‘the other way’), in craps, is a way of tipping the dealer with a wager. So if a number comes up to pay out the wager, I win my bet, and so does the other bet, which I immediately surrender as my tip to the dealers. In my case, I had $10 left over in my hand, so I played my ‘two-way yo" bet: $5 on my behalf, and $5 on the dealers’ behalf that an 11 would come up on the next roll. When that 11 came up, the payout was $75 to me, and $75 to the dealers. Lather, rinse, repeat four times. Tripler I find it’s a good way of rounding out my chips-in-hand for a few rolls. [Previous page](https://boards.straightdope.com/t/probability-of-throwing-three-sixes-in-a-row/947574.md?page=1)