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From: Leroy Quet on 10 Aug 2010 15:33
I am reposting this, since this post is probably lost among the many
replies I made to the original thread.

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Please ignore all else I have written about this game. I have
rewritten the rules to severely limit the types of definitions
allowed, plus made some other changes.

THE OFFICIAL NEW AND IMPROVED SUBSEQUENCE DEFINITION GAME
---------------------------------------------------------------------------
----------------------------
This is a game for any plural number of players.

In the first part of the game the players take turns, each player
picking any one nonnegative integer to be appended to the end of a
growing list of integers. The first part of the game is over when m
integers are picked, where m is a positive integer agreed upon before
the game by the players, and where m is a multiple of the number of
players.

Let the finite sequence of integers be {a(k)}, 1 <= k <= m.

The players, in the second part of the game, take turns each coming up
with a definition that describes some subsequence of {a(k)}. If the
last integer in the subsequence defined by the previous player is
a(j), then the currently moving player tries to find a definition
that
defines
(a(j+1), a(j+2), a(j+3),..., a(j+n)),
for some positive integer n. (j=0 when the first player first moves.)

The subsequence must be the first n consecutive terms of a sequence of
integers defined by "the definition". The definition must be of the
form "b(k) =..." (= an explicit function of k and/or of previous terms
of b). The definition may only contain:
any of the ten numerical digits
(
)
+
-
/ (divide, allowing fractional quotient)
\ (divide by expression following the \, then take the integer part)
* (multiply)
^ (that which follows the ^ is an exponent)
k (the index of the term), and/or
b (as in b(k-1), a previous terms of {b(k)}, for use in recursions).

Again, a(j+k) = b(k), for all k where 1 <= k <= n.
The currently moving player gets added to their score on a move:

r*n - (the number of characters that occur in their definition after
the =),
where r is some positive integer constant decided ahead of time by the
players, such as r = 10.

When all m integers have been described, then the game is over.

Largest score wins.

Any problems you can see with the game? (Of course there are.)

Thanks,
Leroy Quet

From: Leroy Quet on 11 Aug 2010 09:44
Leroy Quet wrote:
>...
> The currently moving player gets added to their score on a move:
>
> r*n - (the number of characters that occur in their definition after
> the =),
> where r is some positive integer constant decided ahead of time by the
> players, such as r = 10.
>...

It should be noted that r should be small enough such that a player
creating, say, a polynomial P(k) which outputs a(j+k), for all k where
1<=k <= m-j, would end up only losing points. If the first player to
move creates such a polynomial for all k, 1<= k <= m, then they should
receive a negative score, and all other players tie for first place
each with a score of 0.

Thanks,
Leroy Quet
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