Dear Friends, I want your advice...
Yesterday, while roaming on the swanky streets of Mindabad, I
saw the glittering "Shakuni Mama's Casino". I got curious. What was a
mythological figure doing in modern times? To know further, I entered
the casino. First, there were usual games such as Roulette. After
moving further, I noticed a new game. It looked simple and I was
tempted to play it.
The game was "Get A Heads". A coin (certified to be fair,
that is unbiased, by the National Standards Organization) would
be tossed twice; if 'Heads' turns up even once, the player wins
100 bucks. The ticket for a game was 74 bucks. Wow! Is Shakuni
on charity business? Does he want to wash all his sins? I played
the game 100 times, won some, lost some. To be exact, I won 75
games, out of 100. I paid 7400 bucks for the tickets and earned
7500 as prize money. A net gain of 100 bucks! Yipee!
I wandered further and lo! I saw there, the 'Goro Sort Machine'.
The game was to sort N numbers in N table hits; if the numbers get
sorted,
you get 100 bucks. The ticket for a game was again 74 bucks.
Another Wow! Has the 'Guy from Gandhaar' lost all his evil
in 5000 years? I wanted to find! So, I played. I wanted to start
with small N, so I chose 2. Here also, I played 100 times,
won some, lost some; but again I made 100 bucks net.
Armed with great expectation theory from the ethereal world,
I got lured to play further; I tried then for N=3. I went on playing,
I played 216 games, won 151 (69.91 %) and lost 65 (30.09 %).
On ticket, I had spent 15984 bucks and got prize money of 15100.
A net loss of 884 bucks, which drowned my earlier gains! Shakuni
was known for his ability to influence the dice. Were his basic
instincts surfacing occasionally? No! I looked at the table; it
was written on it that it is made of "Bone Jaraasangh". So,
Shakuni was unable to influence! Then, this must be what Nassim
Nicholas Taleb calls as 'outlier' or 'black swan'. Don't get
disheartened, I said to myself.
Thus, I moved on to N=4. Here, I played a good 10368 matches.
I won 6966 (67.19 %) and lost 3402 (32.81 %). Moneywise, I spent
767232 bucks and got 696600 as prize. By this time, my appetite
to calculate loss had gone!
And here I remembered you, my dear friends! Should I continue
further with N=5, 6, etc to recoup my losses, or, run away from
here to avoid the fate of wilderness as Pandawas?
Eagle
On May 11, 12:31 am, Pedro Osório <[email protected]> wrote:
> Actually the proof has created a lot of confusion among some contestants.
> Specifically in the first Lemma, the statement:
>
> "x't = t for t ≤ N - 1. This is true by the inductive hypothesis."
>
> Includes the case x1, which doesn't make sense (it is impossible to have
> only 1 element out of order). Although the proof is correct, it should be
> made explicit that p1=0, so p1*x1 never appears in any formula and we can
> perform the induction from n(A) = 2, without ever needing to consider the
> case n(A)=1.
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