Wednesday, August 20, 2014

Balanced diet

(Who ate all the pies?)

In the International General Game Playing Championship 2014, it struck me that many of the games that were played had significant bias for one player (usually, but not always, the first).  In an attempt to compensate, many games were played both ways round, often with the predictable outcome.  This was unfortunate because it increased the amount of time required to play games, reduced the excitement (by having predictable outcomes) and effectively reduced the best-of-3 rounds to a best-of-one (two matches of a game with a predictable outcome and then the decider - usually a game where the bias is unknown because it isn't played on Tiltyard and therefore statistics aren't available).

Whilst reading up on various abstract strategy games, I was introduced to the concept of the Pie rule.  Based on the traditional method for children to divide a cake ("you cut, I'll choose"), it aims to balance two player games by giving the second player the opportunity to swap places with the first player after the first move.  This way, the first player has an incentive to play the most balanced initial play the he possibly can.  (If he makes an opening move that is too strong, the second player will swap with him and get the strong position.  If he plays an opening move that is too weak, the second player will leave him with it.)

In the last few days, I have created Pie-rule variants of 9-board Tic-Tac-Toe and Hex.  (I've also created a visualization for regular Hex so that it can be played on Tiltyard.)  It's early days yet, but I notice that the pie rule seems to be doing the trick for 9BTTT.  In the first 16 matches played on the Tiltyard, 9 went with the first player and 7 with the second.  Whilst it's still a small sample size, that's looking substantially more balanced than the regular version.

So, for the GDL authors out there (by which I suppose I mean Alex!), consider the Pie rule for creating balance in your game.

For everybody else, what games would you like to see a Pie rule variant of?  Whilst I'm certainly not making any promises, if you post in the comments, I'll consider doing them.


  1. Replies
    1. Steve - as we discussed, there's no point in adding the Pie-rule to C4Suicide. It is already a strong win for the 2nd player - who would (or at least should) always choose to avoid the Pie.

      TicTacChess could probably benefit from a Pie-version though.

    2. Andrew - couldn't you extend the pie rule for strong 2nd player wins by making the pie choice occur on move 3 instead of move 2?

  2. I received the following comment about this post from someone by personal message. He is unable to post here (with an OpenId) for some reason, so I am copying he comment across for him:

    If the state that is reached by the move of the first player is more balanced, why not start with it in the first place?

    This could of course be extended to have one player play both sides for X turns and then the swap decision is made by the second player and the game continues as normal. That would be the challenge to find the most balanced game state that you can reach after X turns.
    Or, further extended, you could give the first player the decision when the swap decision is made. That would be the challenge to find the most balanced game state after any number of turns (with the winning conditions not active in that first phase).

    So in a way this is very interesting. It moves some of the challenge of game design from the designer to the player so a GGP can try to solve it.

    1. I guess that games are designed without some initial moves in place (a) for aesthetic reasons and (b) because the bias may have been unknown when the game was designed.

      Also "more balanced" is a slightly arbitrary concept in some cases. Technically, in Hex, the Pie-rule changes the game from a strong win for the first player into a strong win for the second player. However, with the current crop of GGP players (and human players for that matter) it's unlikely that they can analyse the game in sufficient depth to find the strong win paths.

      I can imagine that, as GGP players improve, they might be a useful tool in the game designer's toolbox for checking for bias and finding methods of correcting the bias (with the placement of some initial pieces being one example).

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