Thue-Morse (Fair Sharing) Sequence: A possible alternative to komi?

Could we maybe get more people interested in the simpler variant that I described in my previous post? I believe it plays quite similarly to TMG, but much easier to keep track of without using some sort of tool. I’m excited to play in any case, but I think the complexity of TMG might be a turnoff for most sane people :stuck_out_tongue:

I’m kind of trying to take a break from playing go games. I am finding hard to give up reading the odd thing on the forums though. I am also trying to keep the discussion going with my team in the team go game.

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It would be interesting, but I think it would defeat the appeal of TMG, which is the possibility of all but eliminating first move advantage, and using a cool mathematical sequence in the playing of it. :smiley:

I’d be interested in playing once or twice for the novelty, but I don’t see the benefit that is gained in exchange for the sacrifice of beauty. (parity of the 0-indexed move number tells you who gets to play)

Yesterday I cross-referenced all the people who are part of the TMG OGS group, who have posted at least once to this thread, and have responded in a positive or neutral fashion to at least one of my Tourney settings polls. I then used that info to get a list of 7 names who might be interested. I think you missed @xoxox, who is part of the group, has posted here, and voted positively in my polls, and @Haze_with_a_Z who is in the group and responded positively to the polls, but has not posted here. Other than your list also including Assai, HHG, and Kosh, we had very similar findings! How did you get your list?

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I don’t know, I just glanced through the topic a bit to see who played or wanted to play.

Also, Haze had already liked your announcement, so I didn’t think tagging was necessary.

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I figured it might be that since your list didn’t quite line up with any of my three metrics. :smiley:

Oh man, I can relate with the forums addiction, but, hey, why would we ever want to leave?

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I guess this comes down to me not really believing that Thue-Morse is significant in this context (there was some discussion about this in the beginning of this thread if I recall correctly). The value of getting the next move doesn’t follow a simple downwards trend except in the very beginning of the game, so most of the extra “fairness” gained from playing TMG is gained from the beginning of the turn order sequence being more fair. Therefore (and this is admittedly mostly based on gut feeling) I’m quite confident that the sequence
01101001 10010110 10010110 01101001 … (Thue-Morse)
is not significantly more fair than
01101001 01101001 01101001 01101001 … (simpler variant)
and if they are both equally fair, I prefer the latter since I like to be able to read sequences without using extra tools, and with Thue-Morse this proved too hard for me ^^

So my interest in this variant is almost entirely based around the novelty of double moves, and if that’s all you care about I believe the simpler sequence is better. But I don’t mind the extra complexity of the true TM-sequence if that’s what other people prefer, I just love playing variants, regardless of the rules :smiley:

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Yeah, to my knowledge it’s pure unsubstantiated conjecture that the best komi in TMG is 0.0, but it seems reasonable. I’d be interested in how fair the TM sequence is compared to AB and ABBA when, instead of picking numbers from highest to lowest. the two players pick numbers according to some other function. Like approximating a standard distribution. Or a right tail distribution. &c. This could provide some insight into whether or not TMG is more fair than regular go.

I’m not entirely convinced your variant is simpler. TMG is

if (parity(move) = 0) {
    // Black Plays
} else {
   // White Plays
}

Your variant is

while (TRUE) {
    // Black Plays
    // White Plays
    // White Plays
    // Black Plays
    // White Plays
    // Black Plays
    // Black Plays
    // White Plays
}
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Well I feel I need to play a game before I commit myself to a tournament. I am also kinda unsure about how the timing would work, and I don’t know if I can commit myself to a multi-week tournament.

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I definitely agree that TM is theoretically simpler and more beautiful, I meant simpler in the sense that its easier (at least for my human brain) to keep track of where I am in the sequence. I guess a quantative way of specifying the difference is:

TM is probably easier to define as a sequence, as it only requires a trivial base case and a simple extension rule, or something along those lines.

But a sequence with period of 8 requires less information to “remember where you are” compared to TM; a number from 0-7 rather than an arbitrary natural number.

Ah, I just saw that you edited your programmatic description of the two sequences and I think that explains it much better than I did above ^^ The first program is much nicer, but for a human brain the parity function is not that easy to compute, so I believe the uglier “while (TRUE)”-code will run quicker on most human hardware :wink:

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One thing that I like about the TM sequence, is the BWBBWWBBWB part (when playing black). This doesn’t appear when repeating only the first 8 bits.

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I guess I’m more optimistic about the capabilities of the human brain. There are people who add 4 or 5 digit decimal numbers incredibly quickly in their head by visualizing a soroban (Japanese Abacus). Most anyone can learn to memorize the order of a deck of cards using a 52-image system. Oral cultures memorize vast quantities of information for later retrieval and use. Strong go players are able to replay games from memory, or even to play blindfolded. I think remembering 2 hexadecimal digits isn’t that big a deal given that.

Still, remembering 1/2 of a hexadecimal digit (0-7) is still easier. I just don’t think either is scratching the surface of human potential, and so is not a major consideration.

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Maybe le_4TC would be open to repeating the first 16 moves of TM instead of 8? I would have the same objections to this as to 8, for the record, but maybe it would be better for people who are partial to le_4TC’s position?

I would then note that one interesting part of TMG is that a potential BBWWBB or WWBBWW sequence, will sometimes become BBWBWW or WWBWBB respectively, if the 16^1 hex digit changes parity in the middle. I think this is a very interesting texture which would be lost with a cylce of 16. I think you’d need to cycle the first 64 moves of the sequence to really capture this, and at that point is it even worth it anymore?

Let me once again emphasize that I am very much open to pure TM! Just wanted to put the other sequence out there as another option. I definitely agree that there is much more interesting stuff going on in TM than in a periodic sequence. However, although TM is globally non-periodic, it behaves rather tamely locally, i. e. there are never triple moves. This is probably a good thing, I think something like “progressive go” (cf. https://en.wikipedia.org/wiki/Progressive_chess) for instance is a bit too wild. But as a one-off I think trying other crazy sequences can be fun. You could guarantee fairness with a pie-rule:

  1. Player A specifies some infinite binary sequence (TM, a periodic sequence, binary digits of pi, or anything else that is easily computable).
  2. Player B chooses which side to play.

This is guaranteed to be at least as fair as everything else we just discussed :wink:
(Guaranteed fair only in a theoretical setting of course, where both players play perfectly. But I think even in practice it should turn out somewhat even)

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What about one player specifies a sequence, and then komi bidding commences beginning with the player who did not specify the sequence for the right to choose which side to play: in turn, each player bids at least .5 points more than the previous bid, or passes. Once a player has passed, the other player has won the bidding and gets to choose a side. The other side gets komi. So the players are essentially bidding as to how many points they can give the opponent in exchange for playing the better side (whether that be white or black). The first bidder can bid 0. If the opponent passes to that bid, then the player bidding 0 has won and can choose either side with no komi given. This would probably be a sensible bid in a TM sequence version of this. If the first player passes, the second player must make a bid of at least 0.

The advantage of this is that sequences which favor one side could still be played, instead of restricting it to fair sequences.

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Yes, that is of course a sensible extension, which also includes normal go with komi as a special case :slightly_smiling_face: You can continue generalizing until you arrive at “Player A chooses any game, player B chooses side” :stuck_out_tongue: Going too far in this direction is normally questionable game design, since you’re kind of putting the work of creating the game in the players hands (see Mind ninja, it’s a really interesting concept but almost more like a framework for creating games than a game itself). But in the context of proposing and trying different go variants, I actually think it works rather nicely! If there are more people like me who just wants to try lots of different variants, I could imagine a group/thread where players take turns posting variants they think are fun and fair, and then anyone who takes them up on the challenge gets to pick which side to play.

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Want to play a game of Mind Ninja on superdupergames.org?

Sure! I sent you (or at least someone who shares your username :wink:) a challenge

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My username is phi_618 there, sorry.