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But what value is the median? What does it tell you?
That's one of the things I'm trying to figure out. In the analysis I've done so far, no strategy gives either player an advantage over a single player picking randomly. I have found that some boards have a near insignificant bias toward one player (the one I posted gives the player playing rows less than a half a percentage edge). This could be the "variance advantage" alluded to earlier.
So what does it all mean?
Well, if you or your opponent is down to their last chips (say, less than double the ante), and bluffing is no longer an option, if either player picks randomly the game is up to Minosons.
That's a very unusual sample magic square.
I picked a spiked variance one on purpose just to see if anything interesting would come of it.
EDIT:
Whoops, turns out I'm wrong, there are strategies that give about a 5% edge against random picks, but picking for the median isn't one of them. I'm still building the spreadsheet.
Alright, I've been through the forums for a bit and found a few mentions of picking strategy, the common methods I've heard are "Lowest high number for opponent" and "Pick randomly". This game is designed with multiple strategies in mind, but being able to calculate them twice manually (once for your columns, and again for opponent's rows) is time-prohibitive. A topic I've heard mentioned by Jason, but not really expanded upon, is row/column variance, but actually crunching the numbers isn't practical by hand.
I believe it's possible to extract the magic square from the game somehow. I haven't figured it out how to do it automatically, but typing a square out into a prepared spreadsheet can visually display picks for just about every strategy imaginable, and can give some insight into your opponent's picks.

I don't believe this is cheating, but I do believe it gives an advantage to those that do it, since certain strategies become glaringly obvious when displayed this way.
I haven't found it yet, but is there a simple way to extract the 6x6 square from the game? I've included five non random basic strategies, what others have y'all noticed?
Edit:
If anyone would like the spreadsheet, let me know and I'll post it.
Poker fixes this problem by having players ante upon entry. A joining player mid-round in Holdem must pay the big blind, giving every other player a "free" round.
Paying on exit is fine, but currently the penalty for leaving early is not communicated to the leaving player very well, if at all.
I was one of the skilled players to walk off with $20 in winnings against a stranger. I haven't had a chance to register for the game yet, but I will soon. I'd heard of the game before, and was relatively active around Castle Doctrine's launch last year, so seeing your booth on the PAX map was enough to get me to show up.
The booth was very intimidating to my friends, who opted to stay away on the first day. In the hotel room Saturday I explained the premise of the game and was able to bring them in for a dollar game on Sunday. The scary back alley look of the booth was thematically appropriate, but definitely initially off-putting. The SoundSelf booth was also enclosed and seemed to exist in a similar fashion, but they had hour+ lines early on Sunday once word got out. I hope booth attendance improved through the weekend.
Were the losers of individual games given the entry url?