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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

I will take and put it into my notes and work with it.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Ok, thank you,

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

How did you label your rows and columns?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Here is the state diagram with probabilities.

B6 means second player with 6 bullets, A3 means first player with 3 bullets, DA means A is dead, BA means both are alive etc.

*Last edited by gAr (2011-04-07 01:56:57)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Check the above image.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

I am labeling it like that too! That is sort of like a check.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Yes, it would be easier to check for mistakes, if any.

And the software which I used to draw is JFLAP. It's a mighty software for dealing with automata theory!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

I need a little break to rest, I will see you later.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Ok, see you later.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

I have not been able to find anything wrong with your Markov chain. Could be because it is correct.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Thanks for checking.

What confuses me is this: Take E.g. the state A5. A gets B with probability 5/12, or transitions to B5 with probability 7/12, which includes the chance of not firing also.

If A didn't fire, then there should be a possible transition to A5. Don't know how the chain takes care of that!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

I am not sure I am understanding what you are asking. In your problem there is no option of not firing. If you wanted to have that then you could put the probability into the intersection of row a5 and column a5. That would mean there is a chance of A5 -> A5.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I mean A pulls the trigger, but the cylinder slot is empty.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

I see what you are saying. Right now it looks like that is being combined to he aims fires and misses. Maybe you could create more choices?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

One way may be to name the states as A6B6, A5B6,A5B5, ... , A3B4, ... A1B1. That would be too many states.

You get what I mean?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

I think it is easier to reword the problem. Or, increase the choices, right now A5 has two choices. Make a third choice of when the cylinder is empty. At least the matrix does not get bigger.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

I tried that too.

If choices are increased, then from A5 there would be a possibility to go to B5,B4,B3,B2 or B1 and similarly for the others.

Then calculating those probabilities would be a bigger task.

I'll take a little break, see you later.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Okay, gAr. See you later.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I couldn't get any further with this.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

Well look, let's not tell anybody about it. That way we can keep my series solution and your markov chain up there.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I did not get what you implied!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi gAr;

Just joking about hiding it.

I was thinking that if I understand what you are saying those solutions are flawed.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"We will pretend to be right"?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Ya, got it reading again...

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Absolutely! Since I put the wrong answer up there first I will expect my name to go first when we name it the bobbym gAr solution.

Kidding aside, I was thinking that the problem could me modelled like this

1) A5 fires and kills B, game over.

2) A5 fires and misses so control passes to B5.

3) A5 has an empty chamber so he stays in A5. He spins the cylinder and repeats 3) until 1 or 2 occurs.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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