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[mith]

Another gem from The Grey Labyrinth, credit to Zandor.

To join the game, post here and then send me a PM giving a point inside the square (±100,±100) - that is, send me an x-value and a y-value, each between -100 and +100. Your coordinates do not have to be integers. From the points submitted, the convex hull will be determined.

Anyone submitting a point on the boundary of the convex hull loses. If you are inside the boundary, your score is the distance between your point and the origin, (0, 0).

Example image of a convex hull (think of it like putting a big rubber band around the points so that all the points are either touching the band or inside):



Players:
Young Nick
yuma
SwitchedFromStarcraft
Tables
Jimmmmm
cayvie
Axxle
Schneau
Galzria
shraeye
Jorbles
Watno
Dsell
Kuildeous
Titandrake

[yuma]

in

[SwitchedFromStarcraft]

How many players, or what is deadline for submission (or other upper bound to participation)? I see 15 now (which is better than seeing dead people, I guess).

In. PM now sent.

[Tables]

Sure why not? /in

[Jimmmmm]

/in

[cayvie]

/in

[Axxle]

/in

[Schneau]

/in

[shraeye]

\in

[Galzria]

Pretty sure I /in'ed, even if I forgot to post here. Will double check.

[Galzria]

Pretty sure I /in'ed, even if I forgot to post here. Will double check.

Hey look, I did!

[Young Nick]

Yeah I entered coordinates, but I guess I should post in-thread, too, to say that I am participating.

[Jorbles]

In.

[Watno]

i'm in too.

[Dsell]

In.

These micro forum games are fun.

[SwitchedFromStarcraft]

If I've counted correctly, we need one more.

[Schneau]

I hope everyone ends up on the convex hull. Though, the chances of that seem slim.

[cayvie]

i just realized that there's no guarantee that the origin will be inside the hull

[SwitchedFromStarcraft]

i just realized that there's no guarantee that the origin will be inside the hull

Negative numbers are a beautiful thing.  Just sayin'.

-Psyduck

[Schneau]

i just realized that there's no guarantee that the origin will be inside the hull

I realized this the other day as well, but way after I had submitted my point.

I thought about submitting (100, 100) to give someone a lucky win, but decided to play competitively instead, since otherwise this game sort of falls apart.

[Galzria]

If I were to hazard a guess now, based on the personalities of the people of this forum, it would be that the majority of our Convex Hull will reside in they (-X, Y) quadrant. I'm willing to bet that we dip below the X-Axis though as well - but by how much I'm not sure.

Or we could have all simply picked the same point, in which case we'll all lose.

[Watno]

Im pretty sure noone else took my point

[Kuildeous]

Sure, why not?

/in

[Schneau]

Im pretty sure noone else took my point

Same. I'd like to say my submission has some interesting mathematical meaning, but hey, I just pushed a few number keys at random after the decimal point.

[mith]

Just need one more.

[Titandrake]

Oh sure, I need a minor distraction.

[Grujah]

Oh sure, I need a minor distraction.

Beat you to it I guess, just entered couple've minutes ago

[mith]

Convex Hull:
Watno (50-10^(1-10^137), 50-10^(1-10^137))   
Kuildeous (-73.4, 72.8)   
SwitchedFromStarcraft (-33, -33)   
yuma (0, -46)

Scores:
59.05: Schneau (-52.113, 27.77767)
55: shraeye (55/sqrt(2), 55/sqrt(2))
37.54: Axxle (28, 25)
35.33: Dsell (24.98, 24.98)
24.76: Young Nick (-18, 17)
16.97: Tables (12, 12)
6.28: Titandrake (0, 2pi)
6.08: cayvie (6, -1)
4.15: Jimmmmm (e, pi)
1.41: Jorbles (1, -1)
0: Galzria (0, 0)

Congrats, Schneau!

[Insomniac]

LOL Galz why did you pick 0,0 it's guaranteed to lose.

[Watno]

It's not.

At least i didnt kingmake^^

[mith]

It's guaranteed to not lose, but score 0. If every other point were on the convex hull, he would have won.

[Axxle]

LOL Galz why did you pick 0,0 it's guaranteed to lose.

Unless everyone else is on the hull.
edit: ninja'd!

[mith]

Challenge problem: What is the probability that 14 randomly selected points in the given range would be on the convex hull?

[eHalcyon]

It's not.

At least i didnt kingmake^^

When it was at 14/15 I contemplated submitting 99,99 or something ridiculous.  But I thought that wouldn't be fair to people actually trying.

[shraeye]

It's not.

At least i didnt kingmake^^

HAha, i LOOVE your coordinates!

Also, FoS to Kuildeous for picking such big numbers and letting Schneau win

[Galzria]

I also might've misread and thought the closest to origin won - which is why I thought people would end up with the same coordinates.

[Young Nick]

I figured it would be somewhat similar to the classic 2/3 of the average game. So I put something a bit less than that figuring people here would be smart/geeky/nerdy/mathematically-inclined enough to have heard of it.

Shucks.

[mith]

(Apparently the answer to the challenge problem is a little bit better than 1 in a hundred million. That's assuming a uniform random distribution of the points, which obviously isn't the case in this game, but I suspect a weighted distribution symmetrical about the origin would give a similar answer.)

[shraeye]

(Apparently the answer to the challenge problem is a little bit better than 1 in a hundred million. That's assuming a uniform random distribution of the points, which obviously isn't the case in this game, but I suspect a weighted distribution symmetrical about the origin would give a similar answer.)

I briefly thoght about this.  Not only is it really rare, but I think those calculations would be insane.  I couldn't do them, and I think about probability for a living.

[Grujah]

It's guaranteed to not lose, but score 0. If every other point were on the convex hull, he would have won.

but if 0,0 is on hull, it loses.

[Insomniac]

It's guaranteed to not lose, but score 0. If every other point were on the convex hull, he would have won.

but if 0,0 is on hull, it loses.

Everyone pick points in the same quadrant!

[SwitchedFromStarcraft]

The thing I am most surprised about is that no one else entered with two negative numbers.

[Jimmmmm]

I guess you're better off picking positive numbers because other people are more likely to pick positive numbers because other people are more likely to pick positive numbers.

[shraeye]

I realized that most people would pick positive coordinates (or at least assume that others would pick positive coordinates).  I figured that we might see one person max in each of the other quadrants.

Thus, I was trying to pick the winning score, and wanted to pick the point on the line x=y that has that magnitude.  I thought 55 would be tops.  Now i feel like calculating how far out I could have pushed that point on the same line and still been within Watno's point.

[Galzria]

If I were to hazard a guess now, based on the personalities of the people of this forum, it would be that the majority of our Convex Hull will reside in they (-X, Y) quadrant. I'm willing to bet that we dip below the X-Axis though as well - but by how much I'm not sure.

Or we could have all simply picked the same point, in which case we'll all lose.

[shraeye]

I guess you're better off picking positive numbers because other people are more likely to pick positive numbers because other people are more likely to pick positive numbers.

exactly

[Grujah]

I entered (late) 25,20. Wouldn't do much.

[Watno]

Watno (50-10^(1-10^137), 50-10^(1-10^137))   

You mean 50-10^137, dont you?

[Jimmmmm]

Thus, I was trying to pick the winning score, and wanted to pick the point on the line x=y that has that magnitude.  I thought 55 would be tops.  Now i feel like calculating how far out I could have pushed that point on the same line and still been within Watno's point.

Anywhere in the 60s would have done it I think.

[shraeye]

Thus, I was trying to pick the winning score, and wanted to pick the point on the line x=y that has that magnitude.  I thought 55 would be tops.  Now i feel like calculating how far out I could have pushed that point on the same line and still been within Watno's point.

Anywhere in the 60s would have done it I think.

Well only right up to watno's point, as his was also on that line.  As was Tables' and Galzria's.

[mith]

Watno (50-10^(1-10^137), 50-10^(1-10^137))   

You mean 50-10^137, dont you?

No, that would be well outside the range.

Watno submitted "50-10^-99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999" for each of his coordinates. (-9...[lotsmore9s]...9 = 1-10^137)

[mith]

(Apparently the answer to the challenge problem is a little bit better than 1 in a hundred million. That's assuming a uniform random distribution of the points, which obviously isn't the case in this game, but I suspect a weighted distribution symmetrical about the origin would give a similar answer.)

I briefly thoght about this.  Not only is it really rare, but I think those calculations would be insane.  I couldn't do them, and I think about probability for a living.

I have an idea how to approach this, but I cheated and googled the result: Valtr 1994

[Watno]

I meant 50-10^-137.  There's still one 10^too much in your version,  I think.

[Axxle]

I guess you're better off picking positive numbers because other people are more likely to pick positive numbers because other people are more likely to pick positive numbers.

That was my idea when picking my coordinates.

[Tables]

I had figured that the line (x,x) was the best chance of winning, as people were more likely to select positive numbers. I just underestimated how big some people would go. I hadn't expected them to be above 15,15.

[Axxle]

I realized that most people would pick positive coordinates (or at least assume that others would pick positive coordinates).  I figured that we might see one person max in each of the other quadrants.

Thus, I was trying to pick the winning score, and wanted to pick the point on the line x=y that has that magnitude.  I thought 55 would be tops.  Now i feel like calculating how far out I could have pushed that point on the same line and still been within Watno's point.

(50-10^(1-10^136), 50-10^(1-10^136))   would be close.  (watno's point is on the x=y line)

[Jorbles]

That was really interesting. I clearly didn't think it through very much when I entered, but I would totally play again.

[Schneau]

Wooo, I won! Total luck, especially considering there were only 2 other points in the II quadrant.

The thing I find most interesting is that almost all of the points besides yuma's were near y=x or y=-x.

Someone could have come close to winning by playing (0,58).

[mith]

I meant 50-10^-137.  There's still one 10^too much in your version,  I think.

What you meant and what you submitted are two different things, apparently. My shorter version is equivalent to what you submitted.