Math Is Fun Forum

Here's mud in your eye!

Sticks and stones may break my bones, but jokes will never harm me.

Hi GreatSandy

It's a pun on the word "deep". It can be used to mean that it's very philosophical, but also to refer to "deep" as in "deep under the earth".

You can see the rest of us followed by even more puns with words related to dirt and mud.

Ah, okay. I will try getting something out of the chain.

It seems right for infinite throws. I think it's different for finite.

So, you cannot do it by Markov chain?

Fixed my matrix above, forgot that 654321 is not an absorbing state.

{{5/6,1/6,0,0,0,0,0},{2/3,1/6,1/6,0,0,0,0},{2/3,1/6,0,1/6,0,0,0},{2/3,1/6,0,0,1/6,0,0},{2/3,1/6,0,0,0,1/6,0},{2/3,1/6,0,0,0,0,1/6},{5/6,1/6,0,0,0,0,0}}

Hm, let's try the second option. I put my hands together and say the magic words.

Yes, but I do not know how.

Which method?

I used the independence of expectation trick.

Thanks. I have miscounted something, that's why I got the first answer.

I wouldn't have been so sure of either answer if it wasn't for the simulation.

Hm, actually, I think I know what I did wrong.