When I was in high school, my brother and I got into one of those arguments that only teenaged boys get into, and I grabbed one of his coin-collecting books and tossed it out the back door. He made a fuss and my mother came running. He told her what I had done and she went to slap my face. Of course, I put my elbow up to deflect the blow, and Mom hit it, hard. With her hand in pain, she then tried to kick me. She was wearing deck shoes, which didn’t have much substance, and almost broke her toe. She spent the next week limping around with a big bruise on her hand. My brother and I thought it was hilarious.

One of the first examples they use in a Probability and Statistics class is tossing, or flipping, a coin. If the coin is a fair one, the odds of getting “heads” are 1 in 2, or 0.5. We then progress to rolling a standard six-sided die, for which the probability of rolling any one of the numbers (assuming it’s a fair die and not “loaded”) is 1 in 6 (or 0.1666666…). It gets a little trickier when you move to two dice, or three, or five (I once tried to figure out the probability of a Yahtzee on a single roll of the dice and about drove myself crazy). And don’t get me started on the dice used in many role-playing games.

But anyway, back to the coins. I picked up a book on the I Ching when I was in high school, thinking that it might unlock the secrets of the universe or something. They said that it was possible to use a handful of coins to create the hexagrams, after which you look it up in the book and it tells you something you can’t understand. I decided to have a whack at it, and used fifty pennies to do my divining with. Of course, tossing that many coins over and over makes a racket, and it drew my mother’s attention.

“What are you doing?”

“Casting the I Ching, Mom.”

“The what?”

“The I Ching. See?” I showed her the book.

“Oh, for God’s sake. Clean your room.”

So much for figuring out the secrets of the universe.

By the way, I have been listening to the sound of a laundromat, also known as a coin-op laundry, while I’ve been writing this. I use the site MyNoise.net, which has a million sounds (or at least fifty). Check them out.

Stream of Consciousness Saturday is sponsored by Linda Hill.

My mother has only smacked me once, and that was before I even knew what was happening. I can’t imagine having blocked her. She probably woulda chased me down and beaten me senseless! lol

Loved that. Sounds exactly like me, my brother and my mum when I was a kid.
A Yahtzee is 5 of a kind. So that is a probability of 1 in 6 to the power of 5, although because there are 6 ways you can do it (because there are 6 numbers in a dice) that reduces the odds by a factor of 6. Works out as a 1 in 1,296 chance.

That’s what I thought, too, but then I got thinking about it, and it got much more complicated. For example, if one of the dice comes up a 1, another can’t be a 6, and vice versa. Likewise, whatever number shows up on one die can’t show up on another…. and that’s where I gave up.

It gets more complicated in the classic version where you get three goes in a turn. So the probability of getting at least one Yahtzee is 1 minus the probability of getting none. So you do 1295 to the power of three which is 2,171,747,375 and take that away from 1296 to the power of three which is 2,716,782,336. That leaves you 5,034,961 out of 2,716,782,375 which works out at about 0.02 or a 1 in 50 chance.

You know, what I thought was a Yahtzee is actually a long straight. This page (http://datagenetics.com/blog/january42012/index.html) goes through the calculations of getting a Yahtzee (five of a kind). You were right about the chances in one roll, but then it gets crazy.

Think I’ll play with the odds of a long and short straight. That’ll drive me nuts for a whilre.

Thanks for posting the link. I’ve had a look and it makes sense. I didn’t realise you could hold some dice and just roll the others. That is what introduces the most complications. It’s an interesting problem. I might give it to some of my sixth formers (= 17/18 yr olds) to see if they can work it out.

I remember incidents of mom trying to be tough and ending on the wrong end of a funny situation. Ours would look to dad for support (which never ended well).

Was the probability of Yatzee on off roll or the cumulative result of all three? It’s making my head spin just thinking about it.

I was thinking on the initial throw, because after that it gets much more complicated. For example, say you roll a 1, 2, 4, 5, 6 on the first roll. You could choose either the 1 or 6 and try to roll a 3, or you could choose both and try to roll a 3 and either a 1 or 6. And so on…

I could see this scenario being a good one for a teenage dating story. The boys are flipping coins working out probability while the girl wonders when he’s going to hold her hand. Be romantic. I’ve known a few people like that back in the day.

Excellent trio of tales 🙂

My mother has only smacked me once, and that was before I even knew what was happening. I can’t imagine having blocked her. She probably woulda chased me down and beaten me senseless! lol

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See, I had been smacked a number of times, so I knew what was coming…

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No reason to. I didn’t…

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Oh my…it sounds like I have luck just like your mom’s! Love it.

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I don’t think it was because of luck that she almost broke her hand and toe. 😉

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Loved that. Sounds exactly like me, my brother and my mum when I was a kid.

A Yahtzee is 5 of a kind. So that is a probability of 1 in 6 to the power of 5, although because there are 6 ways you can do it (because there are 6 numbers in a dice) that reduces the odds by a factor of 6. Works out as a 1 in 1,296 chance.

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That’s what I thought, too, but then I got thinking about it, and it got much more complicated. For example, if one of the dice comes up a 1, another can’t be a 6, and vice versa. Likewise, whatever number shows up on one die can’t show up on another…. and that’s where I gave up.

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It gets more complicated in the classic version where you get three goes in a turn. So the probability of getting at least one Yahtzee is 1 minus the probability of getting none. So you do 1295 to the power of three which is 2,171,747,375 and take that away from 1296 to the power of three which is 2,716,782,336. That leaves you 5,034,961 out of 2,716,782,375 which works out at about 0.02 or a 1 in 50 chance.

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Tell you what… I’ll look for an answer…

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What I don’t know is if you stop if you get a Yahtzee. That would make it more complex still.

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You know, what I thought was a Yahtzee is actually a long straight. This page (http://datagenetics.com/blog/january42012/index.html) goes through the calculations of getting a Yahtzee (five of a kind). You were right about the chances in one roll, but then it gets crazy.

Think I’ll play with the odds of a long and short straight. That’ll drive me nuts for a whilre.

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Thanks for posting the link. I’ve had a look and it makes sense. I didn’t realise you could hold some dice and just roll the others. That is what introduces the most complications. It’s an interesting problem. I might give it to some of my sixth formers (= 17/18 yr olds) to see if they can work it out.

Great post

M

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I remember incidents of mom trying to be tough and ending on the wrong end of a funny situation. Ours would look to dad for support (which never ended well).

Was the probability of Yatzee on off roll or the cumulative result of all three? It’s making my head spin just thinking about it.

Good job on the prompt, John.

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I was thinking on the initial throw, because after that it gets much more complicated. For example, say you roll a 1, 2, 4, 5, 6 on the first roll. You could choose either the 1 or 6 and try to roll a 3, or you could choose both and try to roll a 3 and either a 1 or 6. And so on…

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This might require some programming 🙂

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Or some Internet searches to see if someone else has already worked it out…

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I could see this scenario being a good one for a teenage dating story. The boys are flipping coins working out probability while the girl wonders when he’s going to hold her hand. Be romantic. I’ve known a few people like that back in the day.

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That could work…. 🙂

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