[ExI] 2/3 game, round 1

spike spike66 at att.net
Tue Jun 16 05:02:55 UTC 2009


> ...On Behalf Of Emlyn
> >> ...On Behalf Of Emlyn
> >> ...
> >>
> >> 99
> >>
> >> -->  I just wanted to grief the system a bit :-)
> --
> Emlyn

And so you did, and you gave me a terrific idea in the process, thanks!
Take a look at the final outcome of the game:

			time	play
spike		900		37
zelaron		945		25
damien		1055	34.8
jeff			1350	13
tom d		1514	57
david		1518	12.2
emlyn		1843	99

which resulted in:


...which is cool on several levels.  Firstly, Damien won by mistake!  After
he posted the 34.8, he realized he had forgotten to multiply his play by
2/3, and so he presumed he would be too far above.  However, had he
remembered to multiply, then the average would have been below Zelaron's 25,
and the Zel-meister would have taken the prize.  However, had not Emlyn
decided to grief the system on the high end, opting instead to go low, Jeff
might have been in the hunt.

So Damien accidentally won that round, altho he actually gains nothing, for
he already owns my everlasting admiration.  I came in second with my 37, and
Tom third with 57, so the consolation prizes shall be as follows: the second
prize is half of the first and the third prize a quarter of the first.
Since admiration is difficult to divide, I will instead divide the time
interval: I shall hold me in high esteem for half of forever, and Tom for a
quarter of that interval.

On to the idea which Emlyn gave me.

Anyone who wanted could have played 25.3, which would have driven the
average to 25.275.  Then that player would have been the winner, because a
subsequent player could not play 25.274; that play would drive 2/3 average
down to 24.33, which would pull Zelaron's 25 above the line and into the
winner's circle.  But a system-griever could come along after the 25.3 and
play another 99, which would again open the possibilities.

Imagine a game of 2/3 average, open like this round, except any person can
play as many times as she wishes.  For this idea, I need not even impose a
time limit.  Imagine some unit of play money, such as klargs, or Zimbabwe
dollars, and imagine that we start a round by posting some arbitrary number
like my 37.  Now anyone can play on that, but to do so requires that they
put into the pot some arbitrary sum of play money.  Then the next person can
play a 25 for instance, at the cost of matching the total already in the
pot.  For instance, if the original play is 37, then the 25 player might
choose to put in 1 klarg, and the 34 player would put in an additional
klarg, and the subsequent player would need to put in 2 klarg, and the next
player must put in 4 to play and so on.

We might end up with a blocked round, except for the fact that any player
who has already played can add a sum equal to that already in the pot, and
might use the opportunity to play a system-grieving 99, at which time she
can play again, and win on that play.  If a bid stands for some arbitrary
interval, say three days, the round is over.

Using play money (which one can mint for oneself in arbitrary quantities)
would not cause any problem, for the way one would keep score is to take the
ratio of winnings to losses.  It matters not what is the original bid, since
every score is actually a ratio.  To do the system-grieving 99, followed by
25.3 for instance, would require an investment of 384 klargs, and the total
winnings would be 512, for an earnings ratio of 4/3 or 1.333. 

We could imagine a set of simultaneous games, perhaps 20 or more, in which
any player can calculate a strategy and choose which game or games on which
to place their bets.

Oooooh this is cool.


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