Bag-o-trik's

The ability to create a game from a mechanic depends on whether that mechanic reminds you of a game. Your brain is wired to categorize information as efficiently as possible. Perhaps you've heard about experiments that have proven the following:
It takes your brain longer to respond to a request for a member of a set, if it is first told to think of a super-set of the requested set, rather than the reverse. For example, think of the letter "P". Now, think of of a fruit that begins with the letter "P". Your response takes longer than if you had been asked to think of fruits, then asked to think of a fruit beginning with the letter "P". I believe it has to do with the fact that you've already filtered out things-that-are-not-fruits from your short-term memory.

Anyway, while reading your post, since I knew I was supposed to come up with a game, my mind was already on games. As I continued reading, Solitaire and tableaux filtered through. But, pyramids made me think of Nim. This allowed me to start thinking of deterministic outcomes.
when you mentioned "values", I suppose the "9" and "3" in your text subliminally confined my thinking until I came up with the following:

Here is a simple game using this mechanic.
Let's call it Triskedecaphobia
The object of the game is to avoid holding three cards whose sum is 13.
The deck consists of 36 cards, with the following distribution:

four 1's five 2's
six 3's
five 4's
five 5's
four 6's
three 7's
two 8's
two 9's

The first round goes the way you stated (A from top, B from middle, C from bottom).
The cards are move down according to the mechanic.
The right to move first shifts clockwise.
After the third round, players compare cards. If a player has exactly 13, he loses. If a player has more than 13, he must swap his highest valued card and swap it with the lowest valued card on the bottom row. (This has the effect of eliminating any advantage to the person playing third - who otherwise would always have low cards from which to choose). If this swap causes his hand to equal 13, he loses.

After any swaps are completed, each player secretly discards one card from his hand.
From now on, each round is played like the third round.
Play continues until two players have lost or the deck is depleted.
If there is no clear winner, the winner is the player with the highest
total.

Having just made this up, I have no idea if it "breaks".

I was actually wondering if I understand the mechanic:

6 7 8 9
3 4 5
1 2

Player A chooses 7, Player B chooses 3 and player C chooses 2

Before sliding cards down, the pyramid looks like this:

6 - 8 9
- 4 5
1 -

Now, it seems like 4 must move down, and 6 must move down.
So before plucking random card, the pyramid looks like this:

- - 8 9
6 - 5
1 4

After plucking a card (say "9"), the pyramid ends up like this:

9 - 8 9
6 - 5
1 4

Is this what you intended?

Mitch

[/]

Here is a possible refinement:

Deal the 9-card pyramid, then deal out 3 cards face-down to each player.
The remaining 18 cards form the draw pile.
Arbitrarily decide who goes first. The right to move first shifts clockwise.
Each player is responsible for the welfare of their hand and one set of cards during the round. Whoever goes first is responsible for the middle row. The person going second is responsible for the bottom row. The person going third is responsible for the three chosen cards.
The responsibility is simple: At the end of the round, neither your hand nor your set can total 13. Since your pick dictates which cards ultimately make up your set and/or your hand, you should choose wisely.

First player chooses any card from the top row. Next he must discard any of the four cards from his hand, face-up in front of the third player.
Second player does the same thing, except she picks from the middle row.
The third player chooses a card from the bottom row and discards one of the four cards from his hand, face-up onto the other two discards.
Now, according to the mechanic, the lowest card from the second row slides down to the bottom row. The two lowest cards from the top row slide down to the middle row. Finally, two cards are taken from the top of the draw pile and placed on the top row.

Now, players must reveal their cards.
If there is a total of 13 in any hand or any set, except top row, the affected player receives one point. The cards are gathered, reshuffled and a new round begins.
If nobody has 13, the cards are not reshuffled. The third player tosses the three chosen cards into a face-down discard pile.

In either case, the right to go first passes clock-wise to the next player.

Play continues until one player accumulates 13 points. The winner is the person with the fewest points.

Mitch