New Game: Torus
marks...@gmail.com
problem and for identifying the error in my first attempt at a
solution. Bill Taylor also deserves mention here. We've spent a lot
of time in the same neighborhood lately with him always arriving at
the intersections a step ahead of me - not necessarily with the ideal
solution in hand, but first nonetheless.
Torus rule sheet:
http://www.marksteeregames.com/Torus_rules.pdf
In Torus a filled board produces exactly one winner.
Bill Taylor
> First I have to thank Torben Mogensen for both posing the torus
> problem and for identifying the error in my first attempt at a
> solution. Bill Taylor also deserves mention here. We've spent a lot
> of time in the same neighborhood lately with him always arriving at
> the intersections a step ahead of me -
Too kind, too kind.
> not necessarily with the ideal solution in hand,
Alas, the same can be said about your "Torus".
It is a game I considered some while ago, but discarded
on the ground that the two players had noticeably different
goals, of unequal difficulty. The E/W direction paths
have a different (global & local) topology from the N/S paths.
If one wants a game that's as symmetric as possible
between the two players, this isn't it.
Mind you, that doesn't stop it being a good game!
I've already mentioned the matter of Unlur style games;
essentially "Chicken" games where both players play stones
for the weaker side, until someone cracks, (Chicken!),
and takes the weak side, suspecting it
to be strong enough by now.
OC the PIE rule is a special case of this "Chicken" style;
where the two sides are equal in all but 1st move.
No doubt with a suitable application of Chicken Pie
Marks' Torus game can be made properly equalised.
The NZ game remains the best attempt at full
player equivalence, though. IMHO.
-- Boardly Bill
marks...@gmail.com
>
> Alas, the same can be said about your "Torus".
>
> It is a game I considered some while ago, but discarded
> on the ground that the two players had noticeably different
> goals, of unequal difficulty.
>
You're wrong. The two goals are exactly equivalent. When viewed in
3D form, they "appear" to be different. One player is surrounding a
circular axis and the other a linear axis, but in the 2D form the game
clearly has equal goals. The 2D form is isomorphic to the 3D form.
The 2D form can be morphed into a rhombus with the left side matched
to the right side and likewise for the top and bottom, if that makes
you feel any better about it.
> The E/W direction paths
> have a different (global & local) topology from the N/S paths.
> If one wants a game that's as symmetric as possible
> between the two players, this isn't it.
>
In your game, as in mine, one player has a possible goal of forming an
N-S loop and the other player a W-E loop. So it's way beyond me how
you arrived at the conclusion that your game has equal goals and mine
doesn't.
>
> The NZ game remains the best attempt at full
> player equivalence, though. IMHO.
>
NZ has full player equivalence and so does Torus. I wouldn't release
an unequal goals game.
Bill Taylor
> > Alas, the same can be said about your "Torus".
>
> > It is a game I considered some while ago, but discarded
> > on the ground that the two players had noticeably different
> > goals, of unequal difficulty.
>
> You're wrong.
No, I'm right, and you're wrong.
And you're also far too quick off the mark with these posts.
You'd do a lot better to reflect for a while each time.
> The two goals are exactly equivalent.
They are not.
> When viewed in 3D form, they "appear" to be different.
That has nothing to do with it. They are clearly different in 2D.
> > The E/W direction paths
> > have a different (global & local) topology from the N/S paths.
You have totally overlooked the force of this comment.
You are making it very difficult to be polite to you.
> In your game, as in mine, one player has a possible goal of forming an
> N-S loop and the other player a W-E loop. So it's way beyond me how
> you arrived at the conclusion that your game has equal goals and mine
> doesn't.
Obviously! That is a great pity. I had previously formed the idea
that you were a logical and careful thinker and designer of games.
I see I was wrong!
Here is a simple explanation. I hope it is simple enough for you.
. . o .
. . . . Here is a 4x4 version of your "Torus"
. . o .
. . . .
Please note that the NS player can ensure a loop with just 2 stones!
The EW player has no such option.
.......................
Are we learning anything yet???
> I wouldn't release an unequal goals game.
You just did.
Please try and keep up!
-- Bill of Boardgames
marks...@gmail.com
>
> Here is a simple explanation. I hope it is simple enough for you.
>
> . . o .
> . . . . Here is a 4x4 version of your "Torus"
> . . o .
> . . . .
>
> Please note that the NS player can ensure a loop with just 2 stones!
> The EW player has no such option.
>
Well of course the NS player can ensure a loop with just 2 stones.
That's because there are already 2 stones oriented from N to S on the
board!! What the fuck does this prove??
Here:
. . . .
. o . o
. . . .
. . . .
Now, EW can ensure a loop with just two stones. Happy now?
Was this really your idea of an explanation? Good God!!
>
> Are we learning anything yet???
>
Yep. I'm learning that you're even more fat headed than I thought.
nicko...@gmail.com
pretending that a standard hex rhombus was a torus, and playing on
that?
Nick
marks...@gmail.com
Well, sorry to be the bearer of bad news, but you're wrong too.
>
> Could the problem be fixed by
> pretending that a standard hex rhombus was a torus, and playing on
> that?
>
Yes it could, and I already mentioned that in another post.
Here, let me play teacher here for a moment since Bill hasn't been
performing too well in that capacity.
Let's start with your ordinary, hexagonally tessellated rhombus:
. . . .
. . . .
. . . .
. . . .
Ok? Now, wrap this around a horizontal cylinder so that the top edge
meets the bottom edge. The two edges won't coincide completely, but
there will be a segment where the top edge and bottom edge coincide.
And there will be excess sticking out beyond that segment in both the
left and right directions.
Now, notice something really, really interesting. The right end of
the shape fits perfectly into the left end. Wow! A rhombus forms a
perfect torus!!
Now, moving on. Notice something else that's also fascinating. The
torus formed by the rhombus looks *exactly* like the torus formed by
the square. Amazing? You be the judge.
nicko...@gmail.com
together is the same (a torus) in either case, but it seems there is a
difference, specifically in which edge cells are considered adjacent
to cells on the opposite edge for the NS player. For example, using
an 11x11 rhombus and its standard notation, a1 and a11 can be
considered adjacent, but in the other system a1 would be considered
adjacent to, e.g. g11. Right?
So I'm wondering if this definitional change fixes the game.
Bill Taylor
>
> > . . o .
> > . . . . Here is a 4x4 version of your "Torus"
> > . . o .
> > . . . .
>
> > Please note that the NS player can ensure a loop with just 2 stones!
> > The EW player has no such option.
>
> Well of course the NS player can ensure a loop with just 2 stones.
> That's because there are already 2 stones oriented from N to S on the
> board!! What the fuck does this prove??
That you are too dimwitted to follow a simple explanation.
> > Are we learning anything yet???
>
> Yep. I'm learning that you're even more fat headed than I thought.
You are beyond help. People try to help you out and you bite
the hand that feeds you. Fine, if you want to live your life
like that, go ahead; but you'll have to do it without me.
I have recently learned by private email that Mark Steere has
in the past got into inumerable & unending flamewars,
that are chiefly due to his sociopathic nature.
Whatever his basic problem is, is not my problem.
Please go ahead and have the last word, Mark,
as I'm sure you will insist on. I shall be neither replying
to it nor reading it. I'm finished with you. You're hopeless!
Your obsessive compulsion with claiming standard games
as your own, and with priority generally, are a joke.
YOU, are a joke. Goodbye.
Bill Taylor.
** History will judge us all **
Harald Korneliussen
!
As far as I can see, Mark Steere is not familiar with the concept of
virtual connections - perhaps not so suprising considering he boasts
of not being a player himself. On the board Bill Taylor supplied:
> > . . o .
> > . . . .
> > . . o .
> > . . . .
... the two stones in questions have a connection already. You don't
need to play more stones, and connection game player can see that they
are connected into a loop - with the virtual connection known as
bridges. In Mark Steere's example,
. . . .
. o . o
. . . .
. . . .
they are not.
To appreciate the difference, play out the games (with x to move).
marks...@gmail.com
>
> As far as I can see, Mark Steere is not familiar with the concept of
>
> . . . .
> . o . o
> . . . .
> . . . .
>
> they are not.
>
> To appreciate the difference, play out the games (with x to move).
Ok.
. . . .
o o o o
. . . .
. . . .
How do so many otherwise intelligent people not understand that the
right side of the board merges seamlessly with the left side?
marks...@gmail.com
wrote:
>
> Please go ahead and have the last word, Mark,
> as I'm sure you will insist on. I shall be neither replying
> to it nor reading it. I'm finished with you. You're hopeless!
>
Ok, thank you. I will have the last word then. You made this post an
hour and a half after I posted my proof that Torus is an equal goals
game. You know? The proof that you conveniently ignored? The proof
that refuted your big claim to fame that your variant of my game has
equal goals and that my game doesn't?
Now you're embarrassed, rightfully so, and you're heading for the
hills. Fine. Don't come back.
> Your obsessive compulsion with claiming standard games
> as your own, and with priority generally, are a joke.
Ohhhh. So now it's a "standard game". If it's so standard then why
did you attempt to claim it as your own? And I quote:
"So there it is - the first (?) fully operational torus style
connection game. And named after New Zealand - YAY!"
That was you announcing a variant of my game an hour and a half (your
usual lag time) after I announced my game, and calling your variant
"the first".
So now that I've refuted your big claim to fame that your variant of
my game has equal goals and that my game doesn't, you're going to toss
a little stink bomb and run away. How dishonest and cowardly.
> ** History will judge us all **
Yes, it will. History will judge us by the games we designed. My
shadow isn't such a bad place to be, is it Bill?
nicko...@gmail.com
does anyone know if my proposal, repasted here, (ie redefining the
connection between the NS edges of the board), fixes the game? It
looks like it does to me. insight?
Harald Korneliussen
wrote:
> > To appreciate the difference, play out the games (with x to move).
>
> Ok.
>
> . . . .
> o o o o
> . . . .
> . . . .
>
You seem to misunderstand what "play out the game" means, and you
conveniently snipped Taylor's diagram (we're trying to show that these
positions aren't identical, remember.) Where are the moves of X in
your diagram?
Say x plays in the second row
> > . . o .
> > . . x .
> > . . o .
> > . . . .
Then o can just save the bridge
> > . . o .
> > . .o x .
> > . . o .
> > . . . .
on row 4 there is also a virtual connection, look what happens if x
tries to block
> > . . o .
> > . o x .
> > . . o .
> > . x . .
o just saves the bridge again, and wins.
> > . . o .
> > . o x .
> > . . o .
> > . x o .
Now can you show me how to do that in your diagram?
> > . . . .
> > . o . o
> > . . . .
> > . . . .
Observe that while there were two direct ways to connect the "o"s in
Taylor's example, in yours there is just one. If x blocks that:
> > . . . .
> > . o x o
> > . . . .
> > . . . .
... then o has to seek a different, more complex way of connecting
them.
marks...@gmail.com
>
> o just saves the bridge again, and wins.
>
> > > . . o .
> > > . o x .
> > > . . o .
> > > . x o .
>
Ok, that's fine. What you've demonstrated is that NS has an automatic
win when given a two point lead on a 16 point board. Whoop-de-doo.
The same could be said for EW.
Did you happen to notice my proof? It's been abundantly clear from
the outset that NS loops are not 90 degree rotations of EW loops.
That wouldn't even make sense.
What I demonstrated in my proof is that there are the same *number* of
winning permutations for NS as there are for EW. If the board is
randomly filled with 8 black stones (NS) and 8 white stones (EW), both
players have exactly 50% chance of winning.
Helices aside, Black has to form an NS loop and White has to form an
EW loop. Both players have *equal opportunities* to achieve their
*equal goals* of forming loops around the board in their given
directions. There's no need whatsoever for the pie rule. I can't
imagine any game being more fair than the game of Torus.
Now you want to make a big point out of the fact that the two players'
winning paths don't look exactly alike? I never said they did.
I think what matters here is that Torus is an extremely fair game. If
you want to get hung up on some little baby technicality, fine.
That's your prerogative.
marks...@gmail.com
rhombus with the assumption that the North and South edges match up
perfectly and that the East and West edges match up perfectly. Then
the two players would have identical loop paths.
Bill's big attempted point was that Torus is an unequal goals game and
*therefore an unfair game*. Whether played on a rhombus or a
hexagonally tessellated square, there couldn't possibly be a more fair
game than Torus.
Bill Taylor
(which is now obvious to everyone except Mark),
that in fact I strongly suspect that even on a 4x4
it is an easy win to NS, EVEN WHEN EW starts!
(It is clear that for large boards NS has such an overwhelming
advantage due to the topology, that EW can win against the start,
on sufficiently large boards.)
Thus I put out a general challenge to support my view.
I challenge all comers to take EW against me, and have first move.
All opening moves are equivalent, so I play my second...
. . . .
x o . . x: <insert yr name here>
. . . . o: Bill
. . . .
Anyone who wants to, just make yr move on the board,
and "reply" accordingly. May as well leave them here on the group.
Bill (kiwibill ob rognlie's pbem server)
marks...@gmail.com
wrote:
>
> I challenge all comers...
>
And your data sample of 1 is going to prove what?
marks...@gmail.com
wrote:
That you can overcome a zero first move advantage?
marks...@gmail.com
Even if you were to demonstrate a statistical advantage, I still have
the rhombus. Played on a rhombus, Torus has indisputably equal goals
(just like your game), it's indisputably fair (just like your game),
and a filled board produces exactly one winner (oops - unlike your
game).
nicko...@gmail.com
very imbalanced. But on a rhombus, it looks very nice.
nicko...@gmail.com
these two cases:
. b .
b . b
. b .
. w .
w . w
. w .
nick
marks...@gmail.com
> On the original board, I maintain with the others that the game is
> very imbalanced. But on a rhombus, it looks very nice.
I don't give a fuck what you maintain. If my proof is sound, then I'm
right. If I made an error, then I'm wrong. One thing that lends
credence to my proof is that if there were an error, Dishonest Bill
(the university math professor) would have found it by now and had a
fucking parade over it. The fact that he hasn't even acknowledged my
proof makes me even more confident than I already was. I'm a
designer, not a mathematician. But if Bill is pretending not to have
noticed my proof, what does that tell you?
The rhombus is perfect. That's not even an issue. Programmers will
most likely adopt the square since you can fit more cells into a
square window.
marks...@gmail.com
If the blank cells are filled in by the other player then White wins
in both cases. White's goal is to either form an EW loop or a
positive slope helix. In both of these examples, White has formed
positive slope helices.
nicko...@gmail.com
rhombus, because the geometry of the positively and negatively sloped
helices will be different.
If this turns out to be the case, then perhaps one could modify the
goal to say: if a helix forms, its an instantaneous win for whoever
owns the color of the helix.
N
marks...@gmail.com
Interesting. Your suggestion won't work but there is an asymmetry.
nicko...@gmail.com
> Interesting. Your suggestion won't work but there is an asymmetry.
It doesn't work because then a filled board doesn't produce exactly
one winner? Or is there another reason?
marks...@gmail.com
There could be two helices in a filled board. Doesn't have the
desired geometric property.
nicko...@gmail.com
nicko...@gmail.com
player's point of view, I rather like the solution, because it
introduces a race element. Don't know how much it would matter in
actual play though, since helix formation might be a rare occurence.
Mind if I claim this one as my own?
n
marks...@gmail.com
It's all yours. I wouldn't release a game for a hexagonally
tessellated board that didn't have the desired property.
nicko...@gmail.com
Bill Taylor
I don't know why I didn't see it straight off,
but there's a much simpler way to prove the point.
Just look at the 2x2 board!
Vertical has an obvious win, even when Horizontal moves first!
It doesn't even matter who owns the diagonal directions here!
| h v
| - -
Here are the first 2 moves, Vert just plays in
the same row as Horiz. Now whatEVER else happens,
Vert will win! Q.E.D
This simultaneously shows:
1: In "Torus" Vert and Horiz are unequally tasked;
2: Steere's alleged "proof" that they're equivalent is nonsense;
3: Steere is a complete idiot.
Bye all.
Bill Taylor
** Respect other people's belief systems.
** Never tell children there's no Santa!
steer...@yahoo.com
wrote:
>
> This simultaneously shows:
>
> 1: In "Torus" Vert and Horiz are unequally tasked;
> 2: Steere's alleged "proof" that they're equivalent is nonsense;
> 3: Steere is a complete idiot.
>
The two by two board is a special case in which there are six possible
permutations, three are wins for NS, two are wins for EW and one seems
to be undefined, strangely.
Bill, if I'm so fucking stupid, then why does your only decent game,
NZ, have to incorporate *my* game, Crossway, to resolve NZ's fucked up
"stymie" problem? You even quote my game in your rules, without
giving me credit of course. The only other way to resolve your game's
"stymie" (your word) problem is by using a hair brained, cumbersome,
awkward scheme of your own design which then makes the game of NZ
suck.
Bill, I could toss out Torus and I *still* shit all over you. Get the
fuck off my coattails you fat, bald fuck!