Math game...

[Michael74]

Scenario 3 would make the odds 100% of eventually finding a chambered round for player 2, regardless of whether he spun or not on any given turn. However, the odds would remain 1 out of 3 on any given turn, regardless of whether Chuck's opponent spun or not. Palming the rounds would remove any informational content from Chuck's turn.

Now how do we model the effects of coriolis force from the earth's 24 hour rotation on this scenario?

 

[TOG]

Here's how I figured it out. The leftmost digit represents the one shot by Manson and the others represent, in order, the other shots. A "1" represents a bullet and a "0" represents an empty chamber. Here are all the possibilities.

0-0-0-0-1-1
0-0-0-1-1-0
0-0-1-1-0-0
0-1-1-0-0-0
1-1-0-0-0-0
1-0-0-0-0-1

Since we know that the first chamber was empty, we can rule out the last two, leaving 4 possibilities, one of which has a bullet in the next chamber. Without spinning the chamber, you would have a 1/4 chance of losing and a 3/4 chance of living until the next shot. But if you spin, then nothing is ruled out an you have all 6 possibilities again, 2 of which have a bullet in the chamber. That gives you a 2/6 or 1/3 chance of losing. 1/4 is better than 1/3, so it would be best not to spin the chamber.

The TOG​

 

[agua.]

I don't know this particular problem or the math but in Gaming Theory there is a principle that basically states, "Stay with the known."

So no, don't spin the chamber.

The instinct of a mathematician eh .

This leaves 3 empty chambers plus one full chamber as possibilities. One out of 4 chance of an empty with no spin, versus a 2 out of 6 chance with a spin?

In real life though, the weight of the rounds may prevent a completely random spin. Gravity acts on the rounds, potentially moving them toward the bottom, or maybe just beyond. I am not quite sure how to account for this possibility via modeling.

Of course, a clever prestidigitator might simply palm the rounds before spinning, and then reinsert them before passing over the revolver. So we must then ask if Chuck has any skills in that area. ;)

Almost Michael but opposite ie. after the first shot you have a 3/4 chance of an empty chamber but return to the 4/6 if you spin.

Here's how I figured it out. The leftmost digit represents the one shot by Manson and the others represent, in order, the other shots. A "1" represents a bullet and a "0" represents an empty chamber. Here are all the possibilities.

0-0-0-0-1-1
0-0-0-1-1-0
0-0-1-1-0-0
0-1-1-0-0-0
1-1-0-0-0-0
1-0-0-0-0-1

Since we know that the first chamber was empty, we can rule out the last two, leaving 4 possibilities, one of which has a bullet in the next chamber. Without spinning the chamber, you would have a 1/4 chance of losing and a 3/4 chance of living until the next shot. But if you spin, then nothing is ruled out an you have all 6 possibilities again, 2 of which have a bullet in the chamber. That gives you a 2/6 or 1/3 chance of losing. 1/4 is better than 1/3, so it would be best not to spin the chamber.

The TOG​

Cool well done TOG I like the way you used the chamber sets.

Here's the chamber EEEEBB.

The odds that you get a bullet after spinning the barrel are 1/3 ie. 2 bullets out of 6.

The odds that you get a bullet after taking one shot and not dying are 1/4 because you learned after Chuck didn't blow his head off that there are 3 empty chambers left and the chance the next one is a slug is 1/4.



Ok so what happens next ? Should Chuck pull or spin if you get a click ?

 

[Michael74]

2/3 versus 4/6. Doesn't matter.

 

[TOG]

. A "1" represents a bullet and a "0" represents an empty chamber. Here are all the possibilities.

0-0-0-0-1-1
0-0-0-1-1-0
0-0-1-1-0-0
0-1-1-0-0-0
1-1-0-0-0-0
1-0-0-0-0-1

Cool well done TOG I like the way you used the chamber sets.

Here's the chamber EEEEBB.

I realized something after comparing your representation of the chambers (E vs. B) to min (0 vs. 1). I've been working with computers for way, way, waaaayyyy too long. I'm starting to think in binary.

Ok so what happens next ? Should Chuck pull or spin if you get a click ?

The possibilities that are left (in binary, of course) are:

0-0-0-0-1-1
0-0-0-1-1-0
0-0-1-1-0-0

Only 1 of those has a bullet in the third chamber, so you have a 1/3 chance of getting that one, but if you spin, you have a 2/6 chance. The probability is the same either way.

The TOG​

 

[agua.]

I realized something after comparing your representation of the chambers (E vs. B) to min (0 vs. 1). I've been working with computers for way, way, waaaayyyy too long. I'm starting to think in binary.



The possibilities that are left (in binary, of course) are:

0-0-0-0-1-1
0-0-0-1-1-0
0-0-1-1-0-0

Only 1 of those has a bullet in the third chamber, so you have a 1/3 chance of getting that one, but if you spin, you have a 2/6 chance. The probability is the same either way.

The TOG​

Umm ok

Aren't the remaining possibilities

0-0-1-1-0-0
0-1-1-0-0-0
1-1-0-0-0-0

?

Yeah TOG you def have binary disease :biggrin

Oh angon yeah that's the same thing but different ( exactly the same but completely different : D _)

 

[TOG]

Umm ok

Aren't the remaining possibilities

0-0-1-1-0-0
0-1-1-0-0-0
1-1-0-0-0-0

?

It depends on your starting point. I forgot to say, but I used the same starting point as before. The leftmost digit represents the first shot by Manson. In your version, the leftmost digit represents the next shot. Taking that into consideration, we have the same possibilities.

[/quote]Yeah TOG you def have binary disease :biggrin[/quote]

I'm afraid I do.

01010100 01101000 01100101 00100000 01010100 01001111 01000111

 

[agua.]

It depends on your starting point. I forgot to say, but I used the same starting point as before. The leftmost digit represents the first shot by Manson. In your version, the leftmost digit represents the next shot. Taking that into consideration, we have the same possibilities.

Ah ok !

Yeah TOG you def have binary disease :biggrin

I'm afraid I do.

01010100 01101000 01100101 00100000 01010100 01001111 01000111

TOG = Flight of the Conchords Binary solo :biggrin

01100001 01100111 01110101 01100001

 

[Sparkey]

Wanna try another sequence?

1
11
21
1211
111221
312211
13112221

What comes next? (Don't Google it, cheater!)

_________________
@ No extra charge: “An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says, ‘Give me a break!’, and pours two beers.”

 

[TOG]

Wanna try another sequence?

1
11
21
1211
111221
312211
13112221

What comes next? (Don't Google it, cheater!)

At first I thought it was some part of the Fibonacci series, but then I took a closer look and see that that's not it. I think it may be something related though. Does the next line start with a 4?

_________________

@ No extra charge: “An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says, ‘Give me a break!’, and pours two beers.”

I understand the logic, but what's the question?

The TOG​

 

[reba]

you guys are NUTS

 

[Sparkey]

Does the next line start with a 4?

No, the next does not start with a 4 (sorry). SPOILER ALERT: It starts with a '1'.

I understand the logic, but what's the question?

The TOG​

It was @ no extra charge. Like this one:

"Three mathematicians walk into a bar. You'd think the third one would have ducked."

 

[Sparkey]

This is one of my favorites.
Each line (after the first) describes the line above it like so:

1
11 -- describes the line above: "One 1."
21 -- describes the line above: "Two 1's."
1211 -- describes the line above: "One 2, one 1."
111221 -- describes the line above: "One 1, one 2, two 1's."
312211 -- describes the line above: "Three 1's, two 2's, one 1."
13112221 -- describes the line above: "One 3, one 1, two 2's, two 1's."

Next in sequence would also describe the line above it:
1113213211

 

[Sparkey]

A physicist, a biologist, and a mathematician are sitting on a bench across from a house. They watch as two people go into the house, and then a little later, three people walk out.

The physicist says, "The initial measurement was incorrect."

The biologist says, "They must have reproduced."

And the mathematician says, "If exactly one person enters that house, it will be empty."

____________________________________________

The 'B.' in Benoît B. Mandelbrot stands for Benoît B. Mandelbrot.

Hint: The Mandelbrot set is a fractal.​

 

[TOG]

Can I try one? Assuming the answer is "yes", here's a simple problem.

You have two identical jars. In jar #1 you have one amoeba. In jar #2 there are 2 amoebas. Amoebas reproduce by splitting in two. Each amoeba splits in two exactly 3 minutes after the last split. Jar #2 is completely full after exactly 1 hour. How long will it take to fill jar #1?

The TOG​

 

[Sparkey]

63 minutes?

______________________

One thought that goes back to the Russian Roulette problem. Use a well-oiled gun and hold it parallel to the ground as you spin. Gravity will help to increase the chance of an empty chamber coming to rest at the top.

DISCLAIMER: Treat every firearm as if it is loaded. Always point firearm in a safe direction. Know your target and what is behind it. Never put your finger on the trigger until you’re ready to fire. Never use a firearm while under the influence of alcohol or drugs.

 

[TOG]

63 minutes?

______________________

One thought that goes back to the Russian Roulette problem. Use a well-oiled gun and hold it parallel to the ground as you spin. Gravity will help to increase the chance of an empty chamber coming to rest at the top.

DISCLAIMER: Treat every firearm as if it is loaded. Always point firearm in a safe direction. Know your target and what is behind it. Never put your finger on the trigger until you’re ready to fire. Never use a firearm while under the influence of alcohol or drugs.

That's correct. After 3 minutes, the first jar has the same number as the second jar had originally. After that, it takes 1 hour to fill the jar. What you said about firearms is also correct.

The TOG​

 

[agua.]

In Binyawanyawanya ( an undiscovered Island nation ) 1/2 of 5 clams gets you 3 clams . What does 1/3 of 10 clams get you ?

 

[Michael74]

6 and 2/3 clams.

 

[Michael74]

The above is based on (3.3333/2.5) * 5.

Unless they don't use fractions, and just average change up to the next number (4), or closest number (3).