Special Roll

From a viewer named Patti...

My class has been studying probability and yesterday we calculated the probability of rolling a Yahtzee on the first roll.  
So, today, we watched your video.  
The students were intrigued and waited for that Yahtzee with close attention.  After the video, I told them, like you said, in the game Yahtzee, you get three tries.  
So I rolled five dice...and got a Yahtzee!  
The class and I were stunned.  Utter silence and disbelieve.  
The look of "did that really happen"  on 30 7th grade faces.  
Thank you for showing the students your perseverence of waiting through 600 some trials.  
And thank you for making my roll look so special!!

Well done Andrew

Huge congratulations to eight-year-old Andrew who managed a one-roll Yahtzee in just NINE rolls.

Unfortunately it wasn't filmed because everyone thought it would take him an eternity (remembering the odds of five matching dice are 1 in 1296).

Not only a Yahtzee, but my personal favourite of five sixes (it's 1 in 11,664 if you specify the number!!!!)

FYI Andrew: My Christmas cracker this year contained three dice and I did not allow myself to eat dinner until I rolled three matching numbers… It took me about 30 rolls but I also managed matching sixes!)

Here's the Numberphile video which started the die rolling:



And here are some viewer Yahtzees (and some classic reactions).

Walk Away from a Yahtzee

So this week I uploaded another video to my Yahtzee collection.

I've been amazed by the number of people who have contributed their own videos.

And I've also been intrigued to note the disproportionate number of viewers who seem to have rolled all 5s.

One viewer produced the following tally of which number has been most common.

1s - 7 times
2s - 11 times
3s - 11 times
4s - 9 times
5s - 19 times
6s - 9 times

(Reminder: A Yahtzee is five matching dice of any number - so on 19 occasions the five dice all came up as a 5)

Anyway, onto the real reason for today's blog post.

It is simply to share another nice Yahtzee related email from the Numberphile inbox.

This one is from a chap named Simon and it goes as follows:

Hey Brady,

I just have to tell you a story. 

During the last three weeks I was on a cycling trip with two friends of mine.

To kill some time in the evenings we played Yahtzee almost every day. On one day we invented the rule that if someone throws a yahtzee in a single roll, they would have to stand up not saying a word and just walk away... then they would win the game.

We invented this rule pretty much for fun as we were pretty sure this was never going to happen.

On the last day of the trip when we were at the airport we decided to play some final rounds.

In total we played three rounds and in the second round one friend of mine actually threw a Yahtzee in one roll.

Unfortunately we wasn't aware of the rule anymore and forgot to walk away in silence. So we finished the round to play the final third on

Two throws into the third round I jokingly said to my friend how unnecessary it is to throw a Yahtzee in one roll when I lifted up the cup to see Yahtzee of 6's.

I stood up not saying a word and just walked off to win the game. I left a photo in the attachment that my friends took while I was walking away in triumph ;)

I think it's just unbelievable that not only we got a one roll Yahtzee during our trip but also got a second one just a few throws later.

And to crown it all this all happened on the two last rounds we played during our entire trip. Crazy, right?

Keep it rolling,
Simon

Girlfriend says no!

Regular viewers of Numberphile will know we've been featuring viewers who roll a "one-roll Yahtzee" - odds of 1 in 1296.

This evening I have been sorting through the next batch, which include some rather exceptional and quirky contributions.

Stay tuned for those ones!!!

But amoung the submissions was a message that made me smile. And I could relate to it.

Here it is, from a chap named Gareth:

"Just like to say that I stumble on your site a couple of months ago and I religiously keep checking your site for new videos. 

"I'm close to watching all your videos and I love them. 

"I was thinking of entering some Yahtzee videos, however I was watching the video with my girlfriend and before I could say anything she said no and walked away."

Amazing Yahtzees

The amazing one-roll Yahtzees continue from viewers of Numberphile.

One viewer names Seth (right) not only sent in a Yahtzee - he also included a remarkable moment when one dice came to rest on top of another (links directly to the moment).

Some viewers seemed unimpressed - but I think it's far rarer than rolling five matching dice.

Brady gets lucky?

Numberphile viewers are brilliant. One of them, Alan Stewart, has very promptly (*) emailed me about the latest video.

In the film, I attempt to throw a one-roll Yahtzee.

The odds of accomplishing such a feat (five matching dice showing any number) are 1 in 1,296.

I achieved the feat on the 627th roll. According to Alan's spreadsheet and graph (below), there was a 38% probability I would have reached my goal so early.

To reach a 95% chance of success, I'd have needed 3,881 rolls.

So 627 doesn't seem such an ordeal after all.

Here's the video:



(*) Alan's email arrived in the numberphile inbox at 10am - exactly one hour after the video was published!