Highlander #16 - Last Starship Trooper Standing

[Mustang]

A squad of 19 Starship Troopers is pinned down on Klendathu and they are making their last stand as the bugs advance in on their position.

Working as a team, each trooper remaining gives a 5% chance to kill a bug but, if the group misses, a trooper is killed. (19 troopers = 95%, 18 troopers = 90%, etc, etc...)

The Starship Troopers know they will all die. How many bugs will they end up killing?


Highlander winners to date:
BrianD #12, #14
Chas in Cinti #4
digamma #9
Mustang #8, #15
Passacaglia #11
Pumpy Tudors #2, #6, #13
Raiders Army #10
Toddzilla #5
wbatl #1
Wolfpack #3, #7

[Wolfpack]

Neat! I'm in. :)

[Barkeep49]

Yeah this was a cool one. I sent my response in.

[BrianD]

Much more fun than the ideas I came up with. I'll have to ponder this one for a bit...

[Mustang]

Afternoon bump.

I'll let this run til around 5:00 PM EST.

[Mustang]

Closed.

Will post results in a few...

[Mustang]

Huddled together, the Troopers started firing at the oncoming hoard of bugs approaching their position. Hopes were high that the initial bug death count would be significant but, after only 5 bugs were killed the first trooper was dropped. By the time the next 5 troopers were killed, the bug death toll only stood at a total of 34 and then the fight really went south for the troopers as they only dropped a total of another 9 bugs. Total kills - 43. No one guessed the exact total and the closest was St Cronin with 47.

Breakdown by # of soldiers and bugs killed before they missed

19 - 5
18 - 8
17 - 8
16 - 4
15 - 9
14 - 2
13 - 1
12 - 1
11 - 0
10 - 3
9 - 0
8 - 0
7 - 0
6 - 0
5 - 1
4 - 0
3 - 1
2 - 0
1 - 0


I was expecting the number to be much higher. If I would have submitted a score for myself it would have been around 250 but, didn't work out that way as the troopers completely sucked in the early going. (95% chance to kill and only 5 dropped? yeesh... In the second one I did just to compare the 1st round was 30 dead).

[Barkeep49]

What was the range of guesses here? Because I had 52 so I was in the same neighborhood as cronin.

[Eaglesfan27]

I'm embarassed to state my guess, but it was MUCH higher. I figured by probability, 95 bugs should have been killed before a trooper died. I thought they might be unlucky and therefore only estimated 75 before the first one died. Obviously, my answer was way off.

[digamma]

My guess was actually much lower. I completely misread the question, and my math suffered as a result.

[Barkeep49]

In retrospect, I do feel by guess was a little low, despite it being higher then the winner. But I figured just one bad hit in the early going would make for very low results. I also figured that 19 was towards the upper end of realisitic expectations for the first round. The key here is that only 1 piece of "bad" luck dooms the series.

[st.cronin]

woot I rock like Tom Brady

[Mustang]

The range was 11 - 866. The bulk of the answers were in the range of the end result though...

[st.cronin]

So should I do one tomorrow, or wait til monday?

[BrianD]

I came close again. My guess of 37 was nearly there.

[Toddzilla]

Wow - I ran this simulation 20 times and never got a score over 30. Mathematics wouls dictate that with 19 soldiers each with a 5% chance for success, you are not guaranteed to get a hit even with that group, and the odds go south real fast after that. To get as high as 43 seems reasonable though unlikely, but anything over that, esprcially into the 100s, is suspect at best and damned near impossible. I've got to call shenanigans on the math used in this Highlander unless someone can explain this a little better.

[Vince]

I believe that each contributes a 5% chance -- so with 19 soldiers there is a 95% chance of killing a bug. Rather than 19 5% chances.

[st.cronin]

I believe that each contributes a 5% chance -- so with 19 soldiers there is a 95% chance of killing a bug. Rather than 19 5% chances.

That was my understanding. First "roll" had a 95% chance of a kill, first miss made that a 90% chance, and so on.

[BrianD]

I believe that each contributes a 5% chance -- so with 19 soldiers there is a 95% chance of killing a bug. Rather than 19 5% chances.

Doesn't this amount to the same thing?

[Wolfpack]

Doesn't this amount to the same thing?

Actually, it doesn't. Think about something simpler, like a coin flip. Each toss is 50% heads, 50% tails. Two tosses, however, will not equate out to a 100% chance of getting at least one heads. Instead it's actually 75%. I can't think of what the correct math is for the situation for this game, but one 95% chance does not equal 19 separate 5% chances, I don't think.

[Passacaglia]

Actually, it doesn't. Think about something simpler, like a coin flip. Each toss is 50% heads, 50% tails. Two tosses, however, will not equate out to a 100% chance of getting at least one heads. Instead it's actually 75%. I can't think of what the correct math is for the situation for this game, but one 95% chance does not equal 19 separate 5% chances, I don't think.

I think it would be 1 - .95^19

But that's the probability of at least one hit.

[Mustang]

I believe that each contributes a 5% chance -- so with 19 soldiers there is a 95% chance of killing a bug. Rather than 19 5% chances.

This is correct.

[BrianD]

I think it would be 1 - .95^19

But that's the probability of at least one hit.

That makes sense. Rather than adding together the chances of each guy getting a hit, multiply the chances of each getting a miss. That will give the probability of all of them missing. Subtract that from one to get at least one hit.