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22 replies to this topic

### #11 unreality

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Posted 19 February 2008 - 10:20 PM

The king is 3x better than you, correct? (since you can beat him 1/4 of the times). So can the Jester only beat the King 1/3 of the times? <-- that's what you're asking, right? Yeah, that can get tricky cuz you're not sure how good the Jester is in relation to everyone else.

I should have clarified about the Prince and Jester: Everyone beats the Prince. And the Jester beats everybody (excpet the Peasant of course)

and you're welcome for the riddle I have yet to look at your spoilers and see what you did to beat 7/54 (which I'm sure as possible, I just didnt have enough time lol)

edit: I just checked, nice strategy of assigning "strength points"
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### #12 bonanova

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Posted 19 February 2008 - 10:39 PM

The king is 3x better than you, correct? (since you can beat him 1/4 of the times). So can the Jester only beat the King 1/3 of the times? <-- that's what you're asking, right? Yeah, that can get tricky cuz you're not sure how good the Jester is in relation to everyone else.

I should have clarified about the Prince and Jester: Everyone beats the Prince. And the Jester beats everybody (excpet the Peasant of course)

and you're welcome for the riddle I have yet to look at your spoilers and see what you did to beat 7/54 (which I'm sure as possible, I just didnt have enough time lol)

edit: I just checked, nice strategy of assigning "strength points"

Just as a quick response, Jester will survive, and beat you, if you don't eliminate him using Peasant.
And when, other than Round 1 can you ensure the two will play each other?

You used Jester to eliminate King in R1, but that leaves Jester and Duke probably still alive.
I put Duke against King, and Peasant against Jester, to eliminate 2 of the 3 dangers [Jester, King, Duke] in R1,
and achieved a better than 50% survival rate into the finals.

Thanks... I'll go back and give Jester some insane strength number and redo some calculations.

This is intriguing!
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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### #13 unreality

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Posted 19 February 2008 - 10:41 PM

What I did is I pitted the Jester against the King (guaranteed knockoff the hardest guy there, the King) and the Peasant against the Prince (ensuring that the Peasant moved on to play the Jester and beat him, before going up against me in the finals, giving me a 1/2 chance). Remember there are two absolutes- the Jester and the Prince (though the Prince has no exceptions, he just sucks at zarball )
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### #14 bonanova

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Posted 19 February 2008 - 10:49 PM

What I did is I pitted the Jester against the King (guaranteed knockoff the hardest guy there, the King) and the Peasant against the Prince (ensuring that the Peasant moved on to play the Jester and beat him, before going up against me in the finals, giving me a 1/2 chance). Remember there are two absolutes- the Jester and the Prince (though the Prince has no exceptions, he just sucks at zarball )

Yup .. I spoke before I thought. I'll run that simulation now.... thanks.

---------------------

Edit: I ran that simulation. It gives you a 0.130 winning chance.

The problem with that approach is that you have to fight through some strong opponents to reach the finals.
The good part is that you then have a 50% chance of winning the final match. IF you get there.

With You against Earl, you're in the semi's with a .667 probability.
But in the semi's you have a .667 probability of playing the Duke and a .333 probability of playing Queen.

That takes your odds of reaching the finals down to .259 so your winning chances are .130.

With my lineup:
----
Me - 100
Prince - 0
Queen - 100
Earl - 50
----
King - 300
Duke - 200
Peas - 100
Jest - 0 [loses to peas]
----
I get through Prince Queen and Earl - i.e. I make the finals with a .556 probability.

My opponent in the finals is:

King [against whom I have a .25 chance against his .450 probability of being there], or
Duke [against whom I have a .333 chance against his .267 probability of being there], or
Peasant [against whom I have a .5 chance against his .280 probability of being there], or

My championship chances are thus:

.556 x [.25 x .450 + .333 x .267 + .5 x .280] = .556 x .341 = 0.191.

So I only have only a .341 chance of winning the final match,
but my .556 chance of making the finals more than offsets that.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #15 unreality

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Posted 19 February 2008 - 10:55 PM

I have a new strategy which I think might work pretty good, I'm testing it out now
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### #16 unreality

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Posted 19 February 2008 - 11:09 PM

My strategy:

Spoiler for my newest answer (17.43% chance of winning the Royal Zarball Tournament!!!)

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### #17 bonanova

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Posted 19 February 2008 - 11:49 PM

Confirm - you get to the finals with a .500 probability.

Earl [.667 of beating him x.055 probability that he's in the finals] or
Queen [.5 x .189 prob] or
King [.25 x .471 prob] or
Duke [.333 x .284 prob]

Your chances of winning the final match is .3436 and being champ with half that - .171

We have differences in the 3rd decimal place, but I think we're getting the same result basically.

---------

It's still slightly better with Earl in your half of the bracket and make the finals with a .556 probability.
You than have a .341 chance of winning the final match and a .191 chance at the championship.

Which seems to make it advantageous to play weak opponents as long as possible
and then fight some statistical combination of the strong ones at the very end.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #18 unreality

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Posted 19 February 2008 - 11:52 PM

Oh yeah, I forgot that you had gotten that near-20%. woops lol. Yours is still the highest ;D it probably is the highest overall, though you never know
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### #19 unreality

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Posted 19 February 2008 - 11:57 PM

btw I'm working on another zarball riddle, that deals with the game itself
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### #20 Jkyle1980

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Posted 20 February 2008 - 12:35 AM

Can I at least get a little credit? I did post the same answer that Bonanova came up with long before the discussion between Unreality and Bonanova. Granted, I didn't do the math all the way out, but I was still right.
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