game theory and design
Markgm
For those interested, Boardwalk games are very skilled single-player
and competition games with a twist. They are skilled, but swimming in
a sea of random possibilities. On the matter of game theory and
design, I have added the following article...
Any comments, suggestions or ideas are appreciated!
Sincerely,
Mark
From the Boardwalk Design Philosophy Page
http://bwsgames.org
The Complexity of the Game
There are four existing variations in Boardwalk Solitaire; Hopscotch,
Lucky Seven, Sqatsi and Cheshire. Hopscotch is the simplest and
hardest to win, and Cheshire is the most complex and easiest to win
(when played very carefully). In fact, the purpose of Cheshire is to
illustrate a point. Where it can be won every time, it is intended to
portray itself as mundane.
Boardwalk Solitaire introduces a genera of gaming, pitting skill
against random luck, each at its own height. From a design
perspective, this is the intended nature of the game. Ideally, it is
like golf. The range of all of human skill is to fill a boat that
swims in a sea of random possibilities. Recall that in these games
there is only one human player, and so a human opponent is not
available to implement the level of skill for the game.
The problem that appears to arise with attempts at incorporating an
opponent into a deck of cards is the narrowness of the opponent’s
range in potential skill, from its floor to its ceiling. To make a
simpler opponent for the human player, the skill floor is lower, but
the skill ceiling also tends to be badly reduced. When making a
variation that can match greater human skill, the skill floor also
tends to rise. As an example, Lucky Seven seems about half as
complicated to play as Sqatsi. Note that the rules of the two are not
greatly different, but that strategy in Sqatsi is significantly more
involving than in Lucky Seven.
In order to step up to Sqatsi, the player must face twice the
complexity. Any reward for doing so comes in the form of a game with a
higher skill ceiling. While it is worth noting that the skill floor
for Sqatsi still serves one who plays with lesser thought, there is
still the business of having to cope with the complexifying aspect of
Sqatsi over Lucky Seven, which is to have to cope with two ascending
walks in tandem.
Enter two categories of ideas for achieving greater complexity while
remaining within the constraints of the three existing entities; upper
walk, lower walk and hand, as well as within the three existing game
types; Hopscotch, Lucky Seven and Sqatsi . 1) A larger deck of cards
could be used, and 2) cards colored on both sides by suit could be
used to thrust the player into a significantly greater world of
“information”, or that which can be known by looking at the board.
In the first idea, 5 each of 20 face values could be dealt as "100-
card Boardwalk" (such as with a 9-column upper walk, a 10-column lower
walk and a 5-card hand). There would be 14 cards face-up on the deal
to carefully deliberate upon. Two 5-card row 1 stacks could be cleared
against a 10-column lower walk before having to file upon the upper. 5
upper walk stacks could be led from simultaneously against 10 lower
walk columns, giving rise to an exponential development in multiple-
lead-stack possibilities (off of a 9-column upper walk). The skill
floor for 100-card Boardwalk would (I would imagine) have to be higher
than for its 52-card counterpart, but I think its ceiling would rise
considerably more. The skill floor goes up because of the number of
ranks simultaneously involved.
With the second idea, the player would always be able to see all of
the instances of each suit in the deck, whether face up or face down.
The element of (deterministically) available information rises
drastically. In 52-card variations, each face down card is transformed
from 1 in 13 possible values to 1 in 52. With 100-card variations,
each face down card goes from 1 in 20 possible values to 1 in 100.
Conversely, possible values for face down cards can be narrowed based
upon how many of the same suit is already showing, for those who wish
to count them. The really fantastic thing about this “visible suits”
idea is that it would have a negligible effect upon the skill floor –
the additional information would not have to be used, whereas its
effect on the skill ceiling would be considerable. In the context of
this writing, it could be a design freebie.
The architectural vision of Boardwalk can be difficult to implement
against, such that the game will be both simple and skillful in its
range. While 52-card Boardwalk has been shown to be capable of pitting
significant skill against 52 cards worth of random possibilities, it
may also be too limiting when wanting to push the potential skill to
man’s height. 4 each of 13 ranks just isn’t enough. These new ideas,
such as a larger deck of cards and visible suits make great strides in
doing so. Of particular interest to me is the idea of visible suits,
since it would not affect the skill floor while greatly increasing its
ceiling. I am also very interested in the idea of 100-card variations,
as this would facilitate an exponential expansion in complex, upper
walk multi-stack lead possibilities, the likes of which novices would
not have to apply. Nevertheless, it would appear to increase the skill
floor to some degree, by way of a longer lower walk and a larger
number of face values to cope with simultaneously.
The goal of these genera of games is quite grand. It is to provide for
the entire ship of man’s skill to sail within an infinite sea of
possibilities. I know of no other game which attempts to do this,
except perhaps for any other game that may dream of doing so. In
solitaire, it is the finite man against infinite possibilities. In
competition, where the same arrangement is dealt to multiple players,
man may play against man, where each swims in the same sea.
Frederick Williams
>
> Hi,
> For those interested, Boardwalk games are very skilled single-player
> and competition games with a twist. They are skilled, but swimming in
A game is skilled? Do you mean that it requires skill to win it?
> [...]
> Boardwalk Solitaire introduces a genera of gaming, pitting skill
"a genera" makes no sense.
--
Needle, nardle, noo.
Odysseus
Frederick Williams <frederick...@tesco.net> wrote:
> Markgm wrote:
> > For those interested, Boardwalk games are very skilled single-player
> > and competition games with a twist. [...]
<snip>
> > [...]
> > Boardwalk Solitaire introduces a genera of gaming, pitting skill
>
> "a genera" makes no sense.
Agreed. Either "genre" or "genus" would do.
--
Odysseus
Markgm
wrote:
>
> A game is skilled? Do you mean that it requires skill to win it?
>
That's right. Perhaps more to the point, there are many options and
things to think about as a player.
> > [...]
> > Boardwalk Solitaire introduces a genera of gaming, pitting skill
>
> "a genera" makes no sense.
>
I mean to say "a category of gaming of its own".
I have looked at many existing kinds of solitaire, and I see them
falling into two kinds. One kind has many cards face down at the
start, giving such games an unknown, nondeterministic aspect, such as
Klondike, but none of them appear to give much in the way of options
to the player, or things the player can think about to alter the
course of the game. The other kind are like Freecell, where all of
the cards are face-up at the beginning, and which give the player
various options and where deep thought can be applied to alter the
course of the game. In this kind, there is no nondeterministic
aspect, such as cards which are both face down and important to the
outcome of the game.
As two-player games go, I think it is easier to find an increased
element of skill, as described above, but the opposing player embodies
the lion's share of that. Very challenging games, such as go or chess
or othello are purely deterministic, i.e. every element in the game is
visible at all times. Stratego would be one that is different in this
regard.
Boardwalk solitaire gives the player a good dose of options and things
to think about in altering the course of the game (towards winning),
in its deterministic aspect, i.e. visible, known values throughout the
playing area, and it combines this with an equally strong dose in its
non-deterministic aspect, e.g. 43 (important) cards face-down on the
deal. That is how I categorize Boardwalk solitaire - by it having
these two qualities in tandem. (and in a single-player game)
Does that make sense?
Cheers,
- Mark
Markgm
> In article <4C6C76FA.F15D7...@tesco.net>,
> Frederick Williams <frederick.willia...@tesco.net> wrote:
>
> > "a genera" makes no sense.
>
> Agreed. Either "genre" or "genus" would do.
>
Doh! Ok, I think now I see the error of my ways. "genre".
Thanks,
Mark