1. ## Shoot to survive

Without searching the Internet....

Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?

glhf
Maud

2. I know what I'd do, so I looked up the answer. We do not agree.

cheers, Paul

3. Very interesting! Now my creativity is flowing !!!

4. The answer may not be clear as Black or White but rather a Gray area........

5. Paul,

That was my conclusion exactly; I did not agree with the answer........until I did some analysis. What I discovered is not what I expected at all!

I am assuming that each hit is a fatal shot and not a wound.

Maud

6. When I did a stats course (HNC Maths Stats and Computing in 1980 for UK readers), about the only thing I learned was that you can use stats to prove anything; it takes an expert statistician to spot where the wrong formulae are used. So the question I ask Maud, is: as Mr Black, would you put your faith in these stats when you shot first?

7. And that's the paradox, it seems logical from both sides to me now. Answer me this, what scenario will give you a second turn to shoot at the last man standing without yet being shot at? Are they the better odds?

From my statistics course, I believe my calculations are correct except on scenario 5 when Mr. Black shots at Mr. White for the second time, I mistakenly placed 66% instead of 33% which would have yielded a 7% outcome.

PobalityTotal(Pt) equals the product of its factors. The probability of rolling a 5 then a 3 then a 2 in that order with a die (dice singular) is =1/6 x 1/6 x 1/6 OR ~0.5%

The same rules apply to calculating the combination of a hit, miss, miss, and then a hit.

Maud

8. Sorry Maud, I wasn't questioning your stats (my course was so long ago I've forgotten most of it - Two way anova with replication has stuck - not the stats just the name!). I was just wondering if as Mr Black you could calmly take a decision to miss the first shot!

9. Originally Posted by Maudibe
I am assuming that each hit is a fatal shot and not a wound.
Also, that a miss doesn't kill one of the other shooters inadvertently.

10. Also, that a miss doesn't kill one of the other shooters inadvertently.
Good morning Mr. Phelps! I totally missed that possibility. Good thinking. Just wondering, how many other shooters do you think there would be?

access- Impulsively, I'd take the shot at Mr. White. Calmly, I'd die of a heart attack! Retrospectively from the grave, I'd be thinking of what the heck I did to piss these guys off!

Maud

11. This reminds me a bit of a story from WW2. The RAF were losing bombers to icing when bombing Germany, so they developed a mechanical anti icing device on the wings to stop icing. But because the device was relatively heavy, each bomber had to load fewer bombs, so more aircraft were needed to deliver the same amount.

Statistics showed that more bombers would result in even more losses from AA, night fighters et al, so it was decided not to fit the device. I wonder what crews thought as their aircraft plunged out of the sky with icing, knowing an anti icing device existed but wasn't fitted....

This story may be apocryphal.

12. Originally Posted by Maudibe
Good morning Mr. Phelps! I totally missed that possibility. Good thinking. Just wondering, how many other shooters do you think there would be?
Certainly Mr. Jim Phelps would have been one of the shooters. But they rarely hit him, and so that would bring in a whole new calculation.

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