Speaking of Variance

Just saw "Word Wars" - a documentary on Scrabble tournaments.  A lot of bitching about variance, there.  "I'm just not picking."  "He's picking better than me."  "I got double blanked."  Including one scene where two guys played twenty games against each other, and the loser was convinced it was because he just wasn't "picking."

Reminded me of college:  the guys I played bridge and MacRisk with would often call "bad randoms."  Or, we used it as consolation:  "God I suck."  "No, dude, it was just bad randoms."

How variant is Scrabble, I wonder?  How many games of Scrabble do you have to win to know there's a 95% chance, let's say, that you're better than the other guy?

Play chess, guys.

Or, here's an idea:  duplicate Scrabble.  You know, like duplicate bridge, where they play the same hands at every table, and then compare how well you did with everyone else to see how good you actually are?  You'd have to change the rules:  divide the tiles evenly between the players, preorder them, change the end conditions (as soon as one player runs out his queue it's over?), and work out the logistics.  That's the tricky part, probably why they don't do it.  With duplicate bridge you can keep your cards sorted as you play and then hand the unchanged deck to the next table.  With Scrabble you'd have to sort the letters after your game and hand the stacks on.

Great documentary, anyhow.

Comments

[Ian McMeans]

The problem with pre-arranged tiles in duplicate scrabble is that because people will use the tiles differently, the games will quickly diverge based on which tiles are chosen to be put down, and blind choices you make have completely unpredictable effects on the future, which accumulate quickly.

I'm not sure how you could fix that. Maybe have pre-arranged "hands" (groups of 7 tiles) that you're given for each turn? The problem with that is you can no longer use knowledge of the tile-sack's distribution of tiles, and there's still a lot of variance based on what tiles are on the board. So unless you fix the board AND the hands at each turn, people won't be playing similar games, and the divergence between how well people play will still be totally independant. (Because just getting the tiles in a certain order is not good or bad by itself - it's so context dependant on unpredictable game events).

For example in a game of duplicate scrabble, if on table A, player 1 puts down "tan", and A's player 2 fills it out to "expectance" (with all sorts of awesome bonuses), but on table B player 1 puts down "nat", then it was through no flaw of B's player 2 that he couldn't put down "expectance". And now the future of table B's game has diverged completely.

[greggman]

Maybe you could argue that knowing you have the same tiles you should also know, as a good player, that you shouldn't put down "tan" for exactly that reason ?

[Jeffool]

It would seem players using the tiles differently is exactly the point. Given that both players will take turns (game-wise) playing the same 'picks', the ability to spot either 'expectance' or 'cetane' is exactly what decides if a player is good or not. "But it depends on the other player's game!" you say? Well, that's part of the game in Scrabble, like most games. Basketball isn't just scoring points. It's also keeping your opponent from scoring. An example: If there is a triple word score, a space, and the letter 'x', would you put down an 'A' to spell "ax"? This opens it up for 'fax', 'zax', and who knows what else by your opponent. But they may have an 'a' themselves... What do you do?

It's all about your personal strategy, your knowledge and skills as a player. No variance per se, just strategic variables.

[Wyatt]

It reminds me of "Duplicate Tetris" or "Duplicate Bust-A-Move" in which identical pieces are given in a typical head-to-head puzzle game scenario. The fact that you've got duplicate setups and pieces is irrelevant. Early moves which have identical worth based on available information rapidly diverge. It's basicly a Chaotic (with a capital C) situation. It's taking a game that's supposed to be about dealing with and managing Chaos and trying to standardize it to measure "who is the best at dealing with random situations".

The best approach in highly divergent games is to simply play a lot of games. Have a rating system that tracks wins over time if you need to.

Oh, all that said, the fact that people can declare "bad randoms" is, I think, an important property in many games. It's an ego-preserving excuse. The people who don't need ego-preserving excuses are indeed playing Chess. The fact you can blame losses on luck (whether it was the true culprit or not) helps make games more palatable to many people.

[Ian McMeans]

Jeffool and greggman, you're both right that it's part of the game to anticipate unpredictable future plays.

What I was arguing is that the variance in scores is not removable by changing it to "duplicate scrabble". Good players will play a certain way, but the game remains a high-variability statistical one, like poker.

And Wyatt - I totally agree about variability as ego preservation. As game developers, should we intentionally build it into our games to satisfy (placate? coddle?) our sensitive-ego'd players?