CORDIAL MINUET ENSEMBLE

Well, the reason that Hex is an interesting example is that we can prove White wins without actually being able to say how.  I.e., the players are on the same footing in practice, with the more skilled player winning more often.  All we know is that the extra move White gets to play can only help, not hurt, White in a game like Hex.  That's a simplified presentation of the strategy-stealing argument.

So, in theory, the coin flip would make the game subject to chance, if both players knew the perfect strategy that we know exists.  In that case, whoever played first would use that perfect strategy and win.

In practice, because the perfect strategy is unknown, the coin flip does not make the game subject to chance.

Ano, if it worked that way, I'd be making assumptions about what amulet was "better" to you.  Maybe you have the best chance at the copper you are holding, but you just played a game against gold and won.  Should I assume you want to keep working on the copper, or that you'd rather drop it for the gold?

I'd really need to ask before making that kind of choice for you, but asking is messy.

If I never let you play another amulet holder while you hold an amulet, the question does not need to be asked.

Also, it seems kinda insular and weird for two amulet holders to play each other.  There are likely hundreds of other players who would like a shot at an amulet, and we're going to let two amulet holders hog each other?

.., no, never heard of TheFirst bank, why do you ask?

Well, in this case, there is no second place prize for a given amulet contest.

I was aware of what you are describing for knock-out tournaments with multi-place prizes, though.  If I can't be Jere, ever, then I want to avoid playing him in a knock-out tournament as long as possible.  Having alt accounts will help me with this.  I will eventually face Jere, but having alt accounts will make it more likely that I face him for second place instead of for 5th place.

And yes, the problem we face here is essentially created by having no entry fee.  The normal tournament structure in the game (when I run a tournament) involves entry fees and limits on pair-wise rematches, which makes alt accounts not worth using.

Entry fees are out of the question here because they won't make sense for brand new players.

Your point-tier structure is better in terms of collusion, but it changes the feel too much.  I really like the idea of holding something that no one else holds at the moment... a hot potato, a golden ticket.

I'm fine with collusion lurking in there for a slight edge as long as there's no guaranteed win with it.

If people could play whoever they wanted while holding an amulet, the amulets WOULD be won by colluders, because they could easily rack more wins per amulet than any non-colluder.

But once that problem is solved, it becomes frustrating enough to collude, and colluding gives you no guarantee of winning.  I need to balance a cool, simple, exciting contest against preventing any kind of collusion edge.

HOLY CRAP I'VE GOT THE AMULET.

I need to preserve that moment.

Frank, I've thought about more complex mechanisms like that.... to allow players to vet the board somehow before actually playing on it.  I decided that this would be overkill, because the advantages to be had are so small for the player with the upper hand on a given board.  Especially for new players, you'd be sticking them with a necessary decision at the start of a round that they'd have very little understanding of.  I'm not sure advanced players really have a solid understanding of it either at this point.

Yeah, there's no proof that chess is a forced win for white.  That's my hunch, though.  We have non-constructive proofs for games like Hex through the strategy-stealing argument.  Of course, Hex cannot end in a draw.  That's sort of a fundamental flaw of Chess, though, eh?  But maybe that's part of its beauty...

But anyway, we'd have to chose player 1 in Hex through some mechanism, and that player can force a win.  If we flipped a coin to pick who plays first, I don't think that would make the game subject to chance.

I'm still not sure about your QED.  I buy the proof, but it doesn't feel intuitively right to me.

Say A and AA are colluding.  They each have 4 points on the amulet by beating weaker players.  Now they're at the point where both will lose against the stronger players at the 4-point level.

If we're randomly pairing them up, in a pool of N players, they do have 1/(N-2) chance of getting paired together.  Say there are 9 other players, so they have a 10% chance of getting paired together.

If they DON'T get paired together, assume they lose.  So each account, operating alone, has a 90% chance of losing.  If they get paired together, one will throw the match to the other.  Let's say AA is the one who will throw.  So AA has a 100% chance of never making it to 5 points (will lose to all others and throw to A), while A has a 10% chance of making it to 5 points.

If they weren't colluding, they'd still have a 10% chance of playing each other, in which case one would win, the better one,  let's say AA.  So then AA would have a 10% chance of getting to 5 points, and A would have a 100% chance of not getting to 5 points.

I see that colluding doesn't help them, in the case of friends who would both be playing anyway.

HOWEVER, compare the cases for player A where AA does and does not exist.  This isn't the friend case, but the case of whether or not to create an alt account.  If A has scored 4 points but has no chance of scoring 5, having a second account AA with 4 points would give A a 10% chance of getting to 5 points, where without the alt account, A will have a 0% chance of getting to 5 points.

Your horses example is a good one.

Hmm... this is exactly the kind of thought experiment that I love.  See:

http://monolith.sourceforge.net/

Anyway...

If you knew what your opponent was going to pick, you could easily win this word game every time.  You'd try various words and hash them with your opponent's known choice until you found a word that hashed with your opponent's word to make 1.

If your opponent could pick any word in the dictionary, could you predict their choice?  That's an interesting question, especially since they're playing the same game against you.  Over many rounds, you might be able to.  You could bait them by picking LOVE repeatedly until they started always counter-hashing LOVE, and then after they got in that pattern, you could counter-hash their counter-hash.  Of course, they have 5,000 counter-hashes for LOVE to chose from, each with 5,000 different counter-hashes!  This is like RPS with 10,000 moves for each player and pairwise X BEATS Y relationships for every pair of moves.

Scaling the problem down, what if there was a list of 2 known words to pick from?  At that point, I think you'd start having a good shot at predicting your opponent's behavior and playing accordingly.

But at what point, when you scale it up, does it cross the point where it becomes essentially random?  From a theoretical standpoint, never.  From a legal standpoint, I have no idea.

Richard Garfield's recent book has an example game like this to illustrate a point about chance vs. randomness.  I've loaned the book out, unfortunately.

Actually, support is there, just not documented.  I just added this to the Readme:

If your network requires that you use a proxy server to connect to the web,
edit settings/webProxy.ini and insert your proxy's address and port in the 
address:port format.  Here's an example:

197.211.197.70:3128

You will need to create webProxy.ini yourself in this version.  The next release will ship with a blank file in place for webProxy.ini

Be careful when making the file that the extension is set correctly.  Sometimes Windows will add a hidden .txt to the end of your file name.

Okay, this is in place.  Testing this properly would involve a lot of hassle.  Anyone willing to look at this function and check for mistakes?

ORDER BY RAND() is classic bad practice for large data sets.  This is a small data set, and this function is called once per user created---not very often at all.

function cm_generateRandomName() {
    global $tableNamePrefix;

    $foundUnique = false;
    $tryCount = 0;

    $name = "";

    $numberOfWords = 2;
    
    
    while( ! $foundUnique && $numberOfWords < 5 ) {
        
    
        $query =
            "SELECT GROUP_CONCAT( temp.noun SEPARATOR ' ' ) AS random_name ".
            "FROM ( SELECT noun FROM $tableNamePrefix"."random_nouns ".
            "       ORDER BY RAND() LIMIT $numberOfWords ) AS temp;";

        $result = cm_queryDatabase( $query );

        $name = mysql_result( $result, 0, 0 );

        
        $query = "SELECT COUNT(*) from $tableNamePrefix"."users ".
            "WHERE random_name = '$name';";

        $result = cm_queryDatabase( $query );

        if( 0 == mysql_result( $result, 0, 0 ) ) {
            $foundUnique = true;
            }
        else {
            $tryCount ++;

            if( $tryCount >= 10 ) {
                // can't find unique, try more words
                $numberOfWords ++;
                
                $tryCount = 0;
                }
            }        
        }

    // if we passed the 4-word limit without finding a unique name,
    // give up and use the last 4-word name that we tried.
    
    
    return $name;
    }

No, I meant getting an edge somehow through the chance of two colluding accounts playing each other and thereby giving one account a free win.

One of your suggestions here (amulet players only matched with other amulet players who have the same points so far for that amulet), having two accounts playing through for that same amulet still helps you, because there's still a chance those two accounts, that have both built up points on the amulet, will play each other later.  This is like a normal tournament tree.  If you have two horses in the race, and both are playing well, they are likely to meet each other near the end, where one can throw the game.  Better meet your accomplice near the end then some stranger.

An unskilled player cannot guarantee a win this way, but they would have an edge over someone who wasn't doing this.  That's okay.

Same with earning points toward a final amulet tournament.  If you get two colluding accounts into that tournament, you have an edge there too.

Essentially, in any structure where WINNING counts, having two accounts in the game will give you some edge.

Cobblestone:  they can still create/join normal games without risking the amulet, but the clock is ticking and they're losing amulet points.

HappyWulf:  I've been there before and never want to go back.  Combing through logs looking for patterns, and then finding "enough" evidence through those patterns to accuse someone of cheating.  It's even worse when the person you accuse is NOT actually cheating.  What if they deny it?  Do you call them a liar?  And when you look for patterns long enough, you start finding patterns.  You start seeing "coincidences" that are clearly "not by accident."  But random data sets are full of coincidences.

Gotta build a structure where I don't need to worry about doing that, because it's not possible to win the contest just by cheating.  A small edge, okay.  Just not, "I've never played before, but I used this one easy trick to win!"

To drop the amulet voluntarily:

Join a 1-cent game and then leave immediately.