Does the first player have an advantage?
That is my question. Here is the context. I spent a week in the hospital and got released Wednesday. During my stay to pass the time my fellow patients and I would pass the time playing games. UNO and Chess mostly, but I was corrupting my fellow patients and even the staff with Ultimate Tic-Tac-Toe.
To those not in the know. Ultimate Tic-Tac-Toe is a casual form of chess almost. All you need is something to write with and something to write on. Most people know how to play Tic-Tac-Toe, so there is a familiarity to it. How do you play? Make a big Tic-Tac-Toe board. The size of a page. Afterwards make small Tic-Tac-Toe boards inside of each of the squares of the big Tic-Tac-Toe e.g. Now there are two main rules for Ultimate Tic-Tac-Toe. I added another rule which adds a subtle layer to the game. I normally introduce these rules as they become relevant. First rule: Your move dictates where your opponent gets to move. I like to comment and tell new players that due to this rule: you win by forcing your opponent to let you win. That’s almost as cruel as screwing over people at UNO. When teaching new players, I tell them to start by selecting any square they want amoung the many mini Tic-Tac-Toe’s (I will also refer to these as boards). Whatever square you select on the mini Tic-Tac-Toe dictates where your opponent gets to play. If they picked the center bottom square on a board, then their opponent plays on the center bottom mini Tic-Tac-Toe and vice versa. Under the first rule we keep going, eventually a board will be won by either the x’s or the o’s. Second rule: If your opponent sends you to a board that is already won or full, then you get a free go onto any board you want. This quickly restricts your options, for typically you wouldn’t want your opponent to have a free go regardless if you are sending them to a board you won. As boards are won you win by making a three in a row by winning the boards in that series. Just like regular Tic-Tac-Toe. Unlike regular Tic-Tac-Toe I added a third rule. Third rule: In the event that the board is filled with either full mini Tic-Tac-Toe’s or won min Tic-Tac-Toe’s from the representative x’s or o’s, then whoever has the majority of boards won… wins. I added this third rule to curb the chances of a tie, and to allow another strategy where you focus on winning boards rather than getting a three in a row.
You can watch this video. This guy explains the rules pretty well sans including my third rule. He also makes a python program if you want to play on the command line. How I used the AlphaZero algorithm to play Ultimate tic-tac-toe. You can also play the game for free on Steam.
I guess you can make the game more complicated by adding extra dimensions or layers, but I think the point of the game is that it is accessible. I like to tell people I taught this game to my 6 year old cousin and that they are probably smarter than 6.
Does the first player have an advantage, or is it like chess that we just don’t know yet? Is the dominant strategy to go for the three in a row or getting a majority? Is it possible to get a tie with the third rule in affect? In normal play? On purpose?