Tile Brawl or Nim^2 (Game 3 Sign Up)

[Lepton]

I looks to me like H' is the kingmaker.

[dethwing]

Bump

[Highest Prime]

It will obviously take more rounds of gameplay than we've logged to know for sure ... but I'm guessing that this scenario (the third-place contestant being able to decide the winner) will come up quite a bit in 3-4 player versions of this game.

Having said that ... I've got 24 hours left to make my move ... who's going to offer me the greater cut of their GL$ should they win?

H'

[casinopete]

[self_aggrandizement]
You'll notice it didn't arise in my game.
[/self_aggrandizement]

[Highest Prime]

Just a continuance of the above thought ...

This could make for a fascinating psychological study.* Assuming each of the other two players are perfectly rational, they should be willing to pay the "kingmaker" up to GL$9,999 to ensure their passage through to the championship (where they would presumably have a 1/2 chance of winning and thus collecting GL$20,000).

Yet the average expectation for each player at the beginning of the two semi-final matches is only $6,667 (6 equally matched contestants, one $20K prize). So it seems that it would actually pay to play in such a way that one finishes in third rather than first! This, of course, assumes that one find a method of play that allows one to consistently find himself in such a position at the endgame.

Anyway, where were we? Ah, yes. The first item up for bid ...

* -- I wonder if Zag has been reading this thread. He'd probably have something to say about this.

[casinopete]

The 9,999 figure is wrong. The person who paid would have a .5 chance at 10,001, or, 5000.5. That person would do better offering to let the third person win for a fee of only 9,998 (even though he's in first!). Then it would loop a bit. Hard to say where it would fall for certain, though 6,666 seems likely.

[Highest Prime]

You're confusing gross expectations with net.

Either CrystyB or dethy will play for $20K in the finals, which produces a gross expectation to the winner of $10K. A perfectly rational being would pay up to $9,999 for a $10K expectation, knowing that the alternative (not being the winning bidder) carries a $0 expectation.

Their net expectation in such a case would be [0.5*(10,001) + 0.5*(-9,999)], which is positive -- therefore advantageous.

Now, in reality, I would expect no one to pay more than $5K for the privilege -- both because (1) most people are naturally risk-averse, and (2) each could assume that, absent a solicitation of bids, I would choose the winner randomly -- which would mean they are currently sitting on a gross expectation of $5K ($20K * 0.5 * 0.5).

The same mentality applies to a "cut" of the profits. A perfectly rational being would offer me a 99% cut, as that still carries a positive net expectation (i.e. 1% of 20,000 is still better than nothing). But, as mentioned above, I would expect no one to offer more than a 50% cut (producing the same net expectation as they would enjoy from my random selection).

H'

[This message has been edited by Highest Prime (edited 06-12-2003 03:48 PM).]

[casinopete]

Ay, ay, ay.

What was I thinking?

Totally confuzzled for some reason. I beg your pardon.

[mathgrant]

Actually, you have closer to 47 hours. Also, keep in mind that the winner will be GUARANTEED GL$20,000, but might get GL$100,000. I'm not explaining how the top prize can be won until the finals start, so you'll have to just rely on your guts.

dethwing = GL$1,160,000
CrystyB = GL$25,000

[dethwing]

im a generous guy, i offer 100,000

[Lepton]

Having disregarded everything that has just been said...

[casinopete]

You should offer nothing, dethy, as your expected return is zero.
fnord.

[cuban smoker]

Did you hear that? That was the sound of pete laying the smack down.

[CrystyB]

i offer nothing. I would give up to 50%-$1 of the winnings, as you figured the average people would do, but i'm in no position to challenge dethy's offer. I've had a new idea: I'll solve your math homeworks for a year from now on.

Anyways, mg, i've spotted the unconscious reason that made me ask you if we could target an empty space: it would mean the closeness rule is broken since there'd be two explosion sites lying next to each other...

[mathgrant]

I don't see how that would flaw the game play. The targeted shot was meant to make your piece a corner of your shot.

[casinopete]

Aack. You bastard, HP. I wasn't totally confuzzled above, yet somehow you convinced me I was. My 10,001 number came from thinking you meant that the fee was contingent on overall victory.

And I still think you're wrong about the perfectly rational being. If he offers you a 99% cut of the winnings, hs expected gain is only $200. If, however, he instead goes behind your back to deal with the other player vying for the lead, he can charge a fee of his own to let that person win (or offer a lower fee for his victory). The competition should drive the price to $5000.

[mathgrant]

The deadline approacheth. . .

[mathgrant]

Bzzt. First random.org move ever. Sorry, HP. Your random move is A8.

CB, 72 hours.

[CrystyB]

g8 target f7

[mathgrant]

You used your targeted shot. Post a different move.

[CrystyB]

yeah, i did.

Sorry. b3. Though the previous winning move was prettier...

[dethwing]

F6, it's over.

[mathgrant]

HP's move is forced. There is no line of play that could save dethwing, so CB claims victory automatically. casinopete and CrystyB are the finalists.

The finals will not use any special shots. It will have ten $ squares on the board. You collect them by playing next to them. Two of them are real. If you win, you'll get a puzzle via e-mail for each real $ you found. Solve one of them for GL$50,000 instead of GL$20,000, and both for GL$100,000!

THERE IS WRAPAROUND! casinopete, you move first. 72 hours. Good luck!

code:

---

Finals


Starting board:


  ABCDEFGHIJ


1 55555115$5


2 111111$151


3 5$5515$511


4 51$5511$11


5 515$55$111


6 5111551555


7 1111515515


8 1111515111 1 - casinopete


9 55$55555$5 5 - CrystyB


Current Board:


  ABCDEFGHIJ


1      1    


2 S  E      


3      z i  


4  i 5     1


5         1 


6 h 1 g g   


7         h 


8    L z     1 - casinopete (has $ at B3, C4, G5)


9  S     E 5 5 - CrystyB (has $ at G2, G3, H4, I1, I9, C9, D5)


             Winner: casinopete!


Moves:


   casino Crysty


1.   B4     H3


2.   F8     F3


3.   D2     H9


4.   I7     A6


5.   A2     B9


6.   G6     E6


7.   D8


8.   WIN

---

[This message has been edited by mathgrant (edited 04-14-2004 02:41 PM).]

[casinopete]

B4

[mathgrant]

CrystyB, 72 hours.

BTW, the real $'s aren't being revealed until the end.

[This message has been edited by mathgrant (edited 06-16-2003 04:57 PM).]

[CrystyB]

i take it nobody could play in a $ square, right? I mean like it's not over one of my or his squares, it's an independent place.

[CrystyB]

if i'm right, i play in h3. If not, i want to see the answer b4 i play.

[casinopete]

f8

(I think the random setup was biased in my favor)

(not that I'm complaining)

(I mean, I am, a little, just not that much)

fnord.

[mathgrant]

No, you may not play in the $ squares. They are independent pieces. Both moves accepted.

CB, 72 hours.

[This message has been edited by mathgrant (edited 06-18-2003 11:30 AM).]

[CrystyB]

i noticed that too, pete. But being random, there was no reason i could really complain or something...

Gah i have 7 spots to gain a single square and only f3 to gain 2... And i'm already behind by 6.

[mathgrant]

casinopete, 72 hours.

*hides anti-CB randomization device*

[casinopete]

D2

Perhaps each player could veto one board if they wished? That certainly wouldn't guarantee even, but it would help a little.

(Definitely not suggesting this for >2 players, as the competition evens the board out naturally)

[mathgrant]

Interesting suggestion. Too late to implement it here, but maybe I should have.

CB, 72 hours.

[CrystyB]

H9

[This message has been edited by CrystyB (edited 06-20-2003 12:23 AM).]

[mathgrant]

casinopete, 72 hours.

[casinopete]

might as well i7

[mathgrant]

Back to CB, 72 hours.

[CrystyB]

A6

[casinopete]

A2

[CrystyB]

b9