Super Tic Tac Toe

Hello,

recently some of my students were playing a
paper-and-pencil game called "Super Tic Tac Toe".
Jonah Scheinerman is not the inventor of this
clever variant of TTT, but there is a very nice
description of the game on his
website.
Does someone of you know about the origins of
Super Tic Tac Toe? Might Super Tic Tac Toe be an
interesting game for LittleGolem?

Cheers, Ingo.

The search space is so small that I believe the game must have been solved already.

> The search space is so small

???

There are more than 2^81 positions,
so many more than in the checkers game.
(In checkers it took an effort of more than 15
years to solve the game.)

Ingo.

That's a very loose upper bound. The average branching factor is only ~9, and the game seems to end quickly. My hunch is that the first player has a winning strategy.

> The average branching factor is only ~9

This no influence on the size of state space.

> and the game seems to end quickly

wrong.

Ingo.

Can someone make tic-tac-toe-ception on Khanacademy run with rule5b and monte-carlo? (https://www.khanacademy.org/cs/in-tic-tac-toe-ception-perfect/1681243068)

I can only make it run in random mode, not so much fun...

https://www.khanacademy.org/cs/spin-off-of-in-tic-tac-toe-ception-perfect-onlyno-extend-error-on-chromium/6311111886372864

With cooperating play, it's over in only 17 moves. And there are constraints that make plenty of piece distributions impossible. By the time the branching factor stops being 9 or less, it seems like you quickly enter the state where many of the moves are instawins. So vast proportions of the state space will never be reached. So one could say that size of state space is the irrelevant thing.

Size of state space in nim with 81 piles is huge too. That has no influence on how deep, complex, or interesting such a game is to play.

Size of the state space is just an upper bound, sometimes a very loose bound, of the search space size. Consider a contrived game played on an infinite grid where the first player to put a piece instantly wins. The state space is infinitely large, but the game is trivially solvable.

I suspect Ingo already has a good idea of whether it's interesting to play and whether it's easy to solve before recommending it here.

Hello,

> I suspect Ingo already has a good idea of whether it’s interesting
> to play and whether it’s easy to solve before recommending it here.

that is not the case.

My first question was/is really for the inventor of Super Tic Tac Toe.

Concerning complexity: I watched a single game of Super TTT,
played by two doctoral students. The length of the game was
about 50 moves. It was my impression that in almost all situations
there were several playable moves.

Concerning LittleGolem, the game would be interesting only if it's
complexity would not allow to find a solution by computer analysis.
So, I fully understand the question on solvability.

Ingo.

After ten minutes of googling, I believe the game was created by Brandon Middleton, branded as Tic Tac Toe Ten.

See http://tictactoeten.com/about/
http://vimeo.com/11841093

Thanks for the hint and the links,
Ingo.

I found one more bit of information on the history.
There has been a game named "Tic Tac Toe Times 10",
mentioned in boardgamegeek.com with year 1977:
TTTT 10

This game is still missing the rule that a move determines
in which other small board the next player has to move.

Ingo.

I found one more step in between.

In 2008 Tic-Tac-Ku was published, authored by
Mark Asperheim and Cris Van Oosterum.
It is played on nine TicTacToe boards. and each player,
by his move, is directing the next player in which
3x3-group to play. An now come the non-perfect part:
winner is who gets the majority of the 3x3 groups.
(Alternative rule: Winner is who is the first to win
a 3x3-group.)

So, the "final" design was reached via several intermediate steps.

Ingo.

It is interesting seeing so many variations on the theme of "meta" tic-tac-toe. I agree the "final" design mentioned in the original post seems better than those other versions.

For yet another (and rather different) take on the idea of "meta" tic-tac-toe, I recommend LOT by Nestor Romeral Andres:
http://boardgamegeek.com/boardgame/127989/lot
When you make 3 in a row, you must remove 2 of the 3 and turn the 3rd into a promoted/stacked piece. And the goal is to get 3 stacked pieces in a row.

And I've just invented a new one!

As super-TTT, but the restriction is inverted - but the *board* you play in decides the *position* that the opponent must follow up in.

@FatPhil: Very interesting variant! I think it deserves a name of its own.

@fatphil,
sounds interesting also for me.

What about calling it
Phil's Super Tic Tac Toe ?

Or when you want to use it to promote our server:
Golem's Super TTT ?!
Perhaps, with this name we might be able to convince
our boss Richard to introduce the game here.

It would be interesting to see, if from the viewpoint
of bot programming Super-TTT or your Super-TTT behave
differently or similarly.

Ingo.

Another game designed as a meta-Tic Tac Toe is Proteus. I think that was the first game I wrote a computer implementation of.

As I'd obviously not have come up with the idea without the Golem community having this very discussion, I have no problem with it being donated and dedicated to LG.

I like all of these simple extensions (proteus seems a bit remotely related) - it's amazing what a bit of creativity can do to a very simple game.

Sounds like fun :) I always love new game son lg.

hey, i have a new game idea, "Einstein Toe". Each player starts the game with nine einstein games laid out in a 3x3 grid. Say a player rolls a four, he can play that move in any grid. when a player wins one of the einstein games (best of one) then that player gets an X or O, first one three in a row wins

That sounds cool, Ray Garrison. I'd play that (at least once). Shall we play on this thread? (Using our own dice and the honor system)? Should the nine boards be set up as independent EWN positions, or via some other procedure.

I would suggest 180* symmetry, with the red position in the upper right board matching blue's position in the lower left, etc. The center board would be internally symmetric, with the same number on B5 as on D1.

I was thinking of another Super-Einstein variant with no dice and using 180° symmetry on a 5x5 grid with each 6 Einstein small grids disposed as usual Einstein starting boards.
In a small Einstein board a player chooses what number to advance, that tells by symmetry in which Einstein board the opponent must move.
Winning a small Einstein board gives you a big number (for example the same as the winning number of this cell, but that does not matter).
If opponent's move redirects you to a big number cell of yours, you can move it to any of the big cells like in normal Einstein, whether decided or not.
If symmetry rule yields an empty cell, you can play in any of the small Einstein cells.

Another game along these lines is Fire and Ice (http://boardgamegeek.com/boardgame/4643/fire-and-ice), which is a kind of meta-TTT. (It pre-dates Game of Thrones by several years and has nothing to do with those fantasy novels.) The movement rule is original and makes it into a very interesting game. BTW - I think we already have enough n-in-a-row games on LG.

William - still want to play Ray's variant?

I've got a very rough prototype running on my web server. Alas, it seems to lock up occasionally, so is very much pre-alpha, and so I don't want to publish the URL to it yet.

Lots of crappy bugs fixed - now testing with Anna - it's really fun!

If anyone wants a game against me, just let me know...

William and FP, Sorry, I am way too busy with work, life, etc and falling behind in my games as it is, but maybe someday I would like to play test Einstein Toe, meanwhile, if you two play a game, I would be interested in what you think....

I'm playing a game against FP right now, here are my first impressions.

It is an interesting game, with the tension building slowly.
It is much more demanding as far as EWN is concerned compared with the TTT skills you need if any.
It is quite complex, even if you have a good feeling on what are the good positions in EWN, to decide whether you should try to get a huge advantage in one of the boards or try to get e better mean advantage overall, anyone has a theory on that? I think it may be linked to the overall probability to win the TTT game depending on the probability to "get" the small boards, which is not obvious.
I think it leverages a bit the chance factor to be able to chose a small board as you should not be unlucky in each board.
But of course one some key moves, it is better to be lucky for the key board.
We did not rush to have an advantage on the central board, because I guess we did not have very good EWN moves in there.

And FP is ahead now having won a corner, but I hope I have some mean advantage over the rest of the board.

Feel free to kibbitz on Carroll and I:

http://87.119.183.129/perl/ninestein.pl?gameid=16;kibbitz=1

That address won't last forever. If the game reaches a state where people really want to play it I'll move it onto my real webserver, and start to keep the game state files somewhere other than /tmp ;-)

Looking for other volunteers who have plenty of patience when I make changes that cause the server to crash! (Yeah, I'm editing the live server - sue me!)

Really enjoying the game so far. Definitely more fun than EWN on its own.

Regarding what I'm dubbing NineStein: One feature that's becoming clear is that if you have the option of playing elsewhere, some of the zugzwang-like properties disappear, as you can just play on another board. So you end up with mexican standoffs, and thus a bit of a no-mans land that you don't want to draw your tic-tac-toe lines through.

Liking it more and more, the more I play.

glad you like the game...it is my first game design....I approve of the name change to "NineStein!"

It's definitely a fun playable game, thanks Phil for getting it up and running. The strategy is certainly different and the luck element is reduced, although still there

Awesome job, FatPhil!

Two suggestions:

1. Some kind of color coding on the captured squares. I can't figure out which color is "X".

2. Have you tried my setup idea? Here it is in more concrete form:

A. Place the red pieces as usual.
B. Place the blue pieces such that, if you rotate the whole board 180* you arrive at the same position (with colors reversed).

By chance I've managed to find an iPhone app called Ten which turns out to be exactly the same as Super Tic Tac Toe. My thoughts after a few games.

1. There is plenty of choice at the beginning, but play gets very forcing later on once players have started playing in all 9 grids.
2. The first player seems to have a significant advantage by playing in the centre grid, in all my games this led to the first player winning this grid.
3. I suspect the game isn't particularly deep, but it's certainly playable and quite interesting. I wouldn't recommend it for LG though, I'm guessing it would be solvable by somebody here if they put their mind to it given some of the strong bots in other games.

I think I'll be sticking to NineStein for now, it seems a much superior version!

I don't like reliance on colour (being colour-deficient), just a simple key would explain that player 1 is O and red. Right at the start I had the X and O in bold red and blue, and it was blindingly ugly and noisy so I removed that immediately. However, Anna had the great suggestion for using the same pale colours used to indicate last moves, and that works great (IMHO).

Symmetry can be implemented, I'll start a game against you with that set-up when it's done.

Yes, a simple key would be good enough.

I was picturing one bold square in the middle, though pale throughout would probably also look good.

I've been focussing on getting the Fano board running, which required reevaluating a lot of previous assumptions. I'm in a bug-bashing mode now, I'll add a key when that subsides.

I've wasted half a day just fighting how different rendering engines handle tables, it's been a nightmare! My conclusion is that browsers are buggier than my game!

Here's a Fano game in progress: http://87.119.183.129/perl/ninestein.pl?gameid=21;kibbitz=1

Maybe ninestein! is not an appropriate name for the fano version, since there are only seven boards....how about siebenstein? (sieben is german for seven). Or maybe fanostein! or Frankenstein!

The nomenclature did worry me, yes. All of your suggestions apart from the hilarious final one went through my head.

NineStein? Nein!

Hello,
I like all your ideas for meta-variants of Ewn.
And thanks to Phil for setting up a little server
for NineStein and FanoStein (that is my favorite name
for the version on the Fano graph).

One wish to Phil. Currently the graphic for FanoStein
looks too narrow. Could you double the breadth? Then it
might look like this:

Ingo.

PS. To better understand how to play meta-Ewn intelligently, one
might also try a version with three boards (Drei-Stein) where
the winner has to win two of the three boards.

Agree - FanoStein is a good name. There are many cosmetic issues, alas. I suspect much of the aspect ratio issue can be solved just by me finding a more appropriate font. (I need to get rid of the additional white blanking around the bottom corner boards too, for example, that's my biggest concern. That and the fact that some browsers don't support scaling, or background images at all.)

I can probably add DrieStein today. It's connect-2 on a triangular grid. I think it lacks some of the things that make NineStein so tense. In NineStein, there's the race aspect (which some think isn't "pure" in a game). FanoStein might be more reactive - as soon as there are 2 grids won by a single player, the other player has to win the third in that line at all costs.

For reference, anyone can start their own games on my server, maybe it's a bit of an intelligence test to work out how ;-) Note - PINs are *per-game*, as there's no concept of having an account on the server yet.

If people like the game, then I can move it onto my real website. This is purely prototyping and play-testing currently. However, I don't want to be seen as being in competition with LG. I'll happily help Richard implement these variants here on LG.

@Doctor_Strange - Anna thinks thinks that "FrankenStein" should be a variant played on a Klein Bottle rather than a planar grid!

DreiStein well on its way, will be alpha-testing RSN.
And there's another variant on its way after that ;-)

Fun, fun, fun!

Hi Phil,

> I can probably add DrieStein today.

thanks for doing so.

> It’s connect-2 on a triangular grid. I think it lacks some of the
> things that make NineStein so tense.

Agreed. My main intention when proposing it was to have a game
where newbies (like me) learn the difference between traidtional
Ewn (with full luck impact) and "chance-reduced" variants.

> In NineStein, there’s the race aspect (which some think isn’t “pure”
> in a game).

Yes. It feels a bit like in Havannah.

> FanoStein might be more reactive – as soon as there are 2 grids won
> by a single player, the other player has to win the third in that
> line at all costs.

Agreed.

In any case the current siutation with several different alpha-phases
will teach us quickly about most promosing alleys.

> Anna thinks thinks that “FrankenStein” should be a variant
> played on a Klein Bottle rather than a planar grid!

Funny comment, because of the following:
The Klein Bottle is named after mathematician Felix Klein.
Felix Klein was Professor at several German Universities, the
first one being that of ERLANGEN (1772-1775) in FRANKEN,
which is a part of Bavaria.

Ingo.

Hello,
now Phil and me have started a first game of DreiStein:
Ewn on three boards simultaneously. Winenr is who wins
at least two of the three boards.

The game (currently 37 moves have been played) is documented
with many diagrams here.

Ingo.

I like your ASCII-compatible representation of the most recent move.

IIRC, Phil had some metric applied to sequences of three or five die rolls in StreetSoccer that was more sophisticated than just sum-of-all-rolls to measure the role of luck in a game. Is there a metric in EWN to measure which player was luckier?

Hi Ghost,

in his doctoral dissertation Jakob Erdmann had defined and
tested an measure for the randomness of games, including
chance effects in single games.

You can download the pdf from

here.

PS. In my eyes Jakob's approach is a bit too academinc. You are
free to define (and compute) things in a more practical way.

\*\*\********************
By the way, I lost to FatPhil. My position was more or less
winning, but the end turned into a dice-driven tragedy.

Complete Protocol.

Ingo.

@Marley: Thanks - both Anna and I regularly use text-mode browsers, so being ASCII-friendly was an important feature for us.

To evaluate luck on one board only is relatively easy - evaluating moves (using RoRoRo's engine with a few tweaks), and seeing how far the expected value differs from the attained value, given the next roll. Anything on multiple boards is not so obvious.

For reference, 2 more variants are now active - QuadStein, which is a pure race, to get 2 boards out of 4, and HexStein, which is 3x3 Hex (P1 going across, P2 down). These are very much in early alpha testing phase, and as even DreiStein had bugs in win detection, more complicated boards could take a while to get just right.