Cheap THIS!

Recently I read the suggestion that the US Border Problem is not so much a failure of political will as a determination to reduce the cost of labor. unskilled employees (and employee wannabees) suffer, and ownership reaps the benefits.

My recommendation is that if unskilled immigration is desirable then so is skilled immigration. Want cheap lawn care? Sure, in exchange for cheap health care! Cheap laborers? Cheap Lawyers! Cheap cherry-pickers? Cheap Management! Fair is fair.

Fitzgerald for USSC!

Just an idea. Wouldn't it be a Rovian masterstroke?

Equality, in the year 2005 (continued)

After two screw-ups involving hitting the "b" key, it's dawned on me that I need to compose offline and cut-n-paste. Sad.

Chess ratings -- often referred to as ELO ratings -- are such that a difference of 400 corresponds to a 10 to 1 difference in projected long-run scores, if played head-to-head. more generally, a difference of z points corresponds to a 10^(z/400) to 1 difference in relative scoring. The model is not unreasonable on its face, and I don't know of any significant flaws in the model.

Ratings fluctuate with each tournament played. You might reasonably depict the rating system as players contributing rating points to a common pot as they start a game. The stronger player contributes more than the weaker player, the actual contribution based on the difference in ratings. The game winner takes the ratings pot; if the game is drawn, the points are shared.

Newcomers operate on a different system, in effect new players develop a rating from scratch for about 20 games or so, not significantly affecting the sum of the ratings of their opponents.

One if the issues of this kind of ratings event is that there's no guarantee that ratings as a whole are stable. There's some evidence that ratings are not, that a 1500 rating of today doesn't mean the same thing as a 1500 rating of several years ago. Why would this be?

People don't play in tournaments at a uniform rate. Some play often, some play sporadically, some -- like me -- can take a decade off (or more). The players who play often occasionally get better, even if their opponents don't get worse. When this happens the players who haven't gotten better lose ratings points, so the standard of ratings gets depressed.


The total strength of current USCF players is a variable, but the average rating is more or less a constant. So the rating system must be adjusted.

A couple possibilities come to mind.

1: As players get better, they make fewer mistakes. At the top ranks at match play, the percentage of decisive games goes down. The Karpov-Kasparov series went (and I'll have to check this) about 3/4 draws. The most recent championship, which Topolov won, had 32 draws in 56 games, or 4/7ths with a rating spread of 112 ELO points.

With some statistical analysis, someone could probably figure out the point where evenly matched players tend to draw more often than not in match play, and use that point as some kind of marker for long-term consistency. This is a reasonable approach.

2: Another apporach is to develop a standardized player that can give many of its opponents an interesting game. 1500 is pretty much the average, and so a computer program rated somewhere in that range would be appropriate.

I prefer to define a standard player with three benchmarks. Consider a player with a home-grown openings repertiore that adjusts to results (necessary if it isn't to be beaten with a cheat sheet), which doesn't analyze very very far ahead, perhpas 12 or fewer plies plus forced moves, yet within its range makes no tactical boo-boos. Probably due to this, it may flounder in the endgame.

The player who can beat this standard is one who is developing strategic concepts and is playing with tactical accuracy. It is also likely that such a player knows his way around the endgame. My off-the-cuff assessment is that such a computer opponent would be useful for the 1000 to 1400 group. Which is fine. Call it the definition 1200 player.

The general way this would work is that any applicable tournament would have one or two of these computer players injecting or extracting rating points from the tournament at large. If the tournament is underrated, the tournamenters will beat down the standards (which, due to their nature won't actually lose rating points), and if the tournament players are over-rated, the reverse will happen.

If a player of low strength, makes a breakthrough, he'll beat up on the standards directly, and improve his score directly with small effect on other players. If a player of high strength makes a breakthrough, it may take time for the ratings to re-adjust, but the ratings should always be reverting to the mean.

Or... we could create a different rating system entirely.

(to be continued)

Voting. Beyond automatic runoff and proportional voting.

America's house of representatives has 435 voting members. I'm going to argue that 1: this is far too few, and 2: far too many. (I love having it both ways.)

Why is it far too many? More than three people can hardly agree on what to have for lunch, much less draft intelligent bills.

Why far too few? 640,000 constituents per house member. A house member won't be responsive to the masses -- he can't be.

It might be reasonable to have a house member for every... 5000 people, and have 5,600 house members, and then let them work things out. Don't kid yourself that there wouldn't be work for everyone. Probably these 5,600 would then select an elite few to run the place (as is done now), and the rest could focus on constituent service -- better yet, they could rewrite law towards eliminating the need for constituent service. But that's a topic for another day.

Over the next few weeks, I'll monologue about proportional voting and some adjustments, leading into a new paradigm of electing representatives.

Silly governmental thoughts: The newly proposed dollar coins.

I don't have an issue with dollar coins. but it seems silly from this perspective to have in excess of three dollar coins and a dollar bill. Bipartisan legislation has passed the house with the intent of adding several new dollar coins to the currency.

Fine with me, but let's now fail to print future issues of the dollar bill. And quit minting pennies, too. I've seen suggestions that we quit coining nickels, too, but that's extreme. In the unlikely event you're reading this, call your senator.

Gamesmanship, General

What's the best way to play a game? I see two competing theories. One is "Play as perfectly as possible"; the other is "Play to the opponent's weakness." Both theories have their place, and in a typical fact-free discourse I lay out my views...

The two ideas are: to play as perfectly as possible; or to exploit the opponent's weaknesses even if that means making moves that would lose to a competent opponent. These ideas are unharmonious.

Fortunately so are the circumstances.

(to be continued)

Equality, in the year 2005

Most two-entity games of skill are asymmetric, that is, one player has an inherent advantage over another. In most games, the first player to act has the advantage. In poker, the last has the edge. Contract bridge and team chess are games with no inherent edge to any contestant.

What can be done to make playable games when the players themselves are unequal?

Not a lot in most cases. I'm not an especially good chess player, but if given knight odds, I could probably beat anyone on the planet-- just as most average tournament players could. As a game, Chess is not likely to be interesting if the odds are more than 3:1 in favor of one or he other players. Which translates into about 200 ELO points.

what can be done is to utilize the rating system formulas to come up with a target for match play.

If I played an opponent eleven games and he had a 400 point rating edge on me, then a fair target for me in the match would be 1.0 points (one win or two draws). This is unlikely to be enjoyable for me, and likely not for the opponent unless he really gets off on winning.

Another scheme is to vary the amount of clock time allocated to each player. I haven't any practical experience with this kind of arrangement.

..

GO has a built-in equalization scheme with variations.

When equals play in a tournament, the second player is given additional points for the purpose of determining the winner.

when mismatched players meet, the weaker player goes first, and is given a handicap, normally from 1 to 9 initial stones. In the standard variant, the nine stones are pre-placed, and there's a movement that permits self-selection of the handicap stones.

Normally the appropriate handicap is the maximum that still allows the stronger player to normally win. Success is measured by forcing an adjustment to the appropriate handicap over time.

My limited experience (as the weak player) is that the fact that the odds can be equalized doesn't mean that the stronger player finds the game a challenge. It means that the stronger player must actively seek out the weaker player's weaknesses and encourage miscues.

This doesn't translate well. Imagine a poker game where the weaker players accepted a per-pot transfer. No. It just doesn't work that way. Poker is meaningless when not played for money, and a handicapping mechanism would merely delay exposing the lack of long-run money transfer.

Perhaps in a poker tournament, players could receive varying amounts of initial funds. When added to the natural amount of play variance, this might prove a useful handicap mechanism. but then, why would anyone want to become a good poker player, other than for recognition?

Ko Rules, and inability to move.

In many games, there is the opportunity for duplicating a previous position. Chess and Go, the premiere full information games take remarkably different approaches to the issue.

Chess has many ways to end a game. Checkmate; resignation; runing out of time; insufficient mating material, fifty moves by each player without a capture or pawn move, repetition, and stalemate. there are other ways that a game can be adjudicated for tournament purposes, but those do not concern me now, as I am focusing on repetition and stalemate.

In chess, a player may claim a draw if he can prove that the opponent has created a position for the third time, or if he, himself can do so with his move. This is called 'Draw by repetition."

A chess game also ends in a draw if the player on move is not in check and has no legal move. In chess, at the highest levels, two players of equal strength will draw about three quarters of the time, if they're actually fighting. And even more if at least one player has no intention of winning.

Go (Weiqi, Baduk) takes a very different approach.

As a point of novelty, While most games (Bridge and chess, for example) have one rule set, I know of seven rule sets for GO. They're all quite similar and you might well play several games before even hitting on a single effective difference between any of those rules sets. Depending on the rule set in play (Broadly speaking, the Japanese have one, the Chinese another, and theoreticians a third), draws range from uncommon to rare to never. There's no particular reason for the rarity of draws except as a bow to history. It's not to my taste, but it's the way it is.

Notwithstanding the seven rule sets, a player may never place a stone such that it alone would be captured. (there is disagreement about whether a player may sacrifice a larger group of stones.) Let's call this the Null-Ko rule: A play must change the board.

The normal, single-ko rule is: A player may not recreate the position that existed just after his most recent move. This rule is fundamental to all forms of the game. otherwise, as soon as a ko-situation arose, a game would go on forever, there being no "draw by repetition" in GO.

Some rule sets have a "SuperKo rule", which makes it illegal for a player to repeat any previous position (and a player who may not move loses). The SuperKo rule at least ensures that all games are finite.

Most games have at least a rudimentary version of the ko-rule or a draw-by repetition provision. Resolving issues like this is part of the fun of game design.

C-Diplo (fin)

So, where were we? Oh, yes. As the French, cutting off play at the end of 1907 (must check and see if this was a famous date in French history), as the Americans, playing until the cows come home. Let's see if we can find a happy medium from first principles...

It is a principle of economics that a subsidy creates more of a product or service, and in America the subsidy is that of time, which has become free, and thus suboptimal. In France, the issue is dealt with by strict rationing, again, suboptimal.

The first point to get straight is that a player's tournament score is the sum of his game scores. Each faction of a point is precious, and players with similar records will want to win the tiebreakers.

The concept behind the proposal may be considered simply. As the tournament winds down, there are players who have completed (and who would like closure), and there are players that have not. The longer a player has to wait around, the more irritated he will get. Perhaps this isn't a linear function of time, but certainly the trend is upward.) Tables that are eliminating players are doing their jobs. Tables that have concluded have done their jobs. Tables that indulge in Calhamer's fantasy of a perpetual pendulum of procrastination are not.

It works this way:

Each table starts with X points in a prize pool. Probably about 10, on gut feel. We'll assume a straight division of the prize pool among the active players at the end of play. There is also a survival pool. Points that go into the survival pool are immediately divided among the players then in play. Recap: Big bonus for making it to the end; dribbles along the way.

Let's assume N tables are playing in a tournament round of Diplomacy, and further assume that the tables are full.

Each year (two turns) after a player is eliminated, wins, or participates in a draw, 1/(7(N-1)) points in total are removed from the prize pools of the other tables in still play. Half of the amount extracted from a table's prize pool is placed in the survival pool. The other half is lost.

The consequences? Not much for quite some time. I'll illustrate how it works with a ten-table tournament. The first eliminee gets nothing for the round, which is what he deserves. At this point every other table is in a figurative hourglass with the sands running out. Starting with the next year, the elimination causes 1/63 of a point in total to be deducted from the other nine tables (or 1/567) from each table, of which half (1/1134) is split among each of the players at each other table. Virtually nothing -- except for the purpose of tie breaking. Each further elimination causes the same amount of carnage. Not much at first.

Even as the number of eliminees approaches half of the total players, there still isn't much real issue. 35 players gone of the above 10 tables, and let's assume seven tables are still in play...

35/63 points are removed from the prize pools at the remaining 7 tables, or an average 5/63 of a point per table per year (this will vary. Tables that have not eliminated players will lose points faster than other tables), and 1/126th of a point flows to the survivors to date (again, on average).

With two tables left, an average of just under 1/2 point will be deducted per year per table, and the final table will lose (exactly) a full point from its prize pool every year. If the table runs out of points, there's no point in playing. And there's considerable point in coming to terms before the sand runs out Perhaps the proposed starting value of 10 points is too much, but that's my gut feel for a reasonable amount.

Why this complicated mechanism?

1: It's reasonable not to penalize tables for taking a normal number of turns, and even reasonable not to penalize them much for taking a bit more than average.

2: The point of winning or drawing is a share of the prize pool.

3: The survival pool is designed to encourage losing players to fight to the end. Pride only goes so far in the face of certain doom. While the survival pool is a comparative pittance per year (at least until you're at the final table), it can add up for breaking ties. And you get the added satisfaction of taking your treacherous opponents to Hell with you.

4: The prize pool decrements are designed to be more psychological than actual in the early stages -- and positively nerve-racking at the end.

Why, you ask, are the deductions on a yearly basis, and not per turn? Simple. It's difficult to kill someone in a spring turn. If you understand Diplomacy you'll know why, and if you don't, the explanation is tedious.

.....................................................................................................................................................................

One other possibility occured to me today. Tournaments make a big deal about how to score points for games, and you wouldn't believe how much literature and variation there is on topic. (I think there's an earlier post about nearly optimal ideas get the most intense scrutiny.) C-Diplo is merely one of about 15 ways to score tournaments that I know about.

One idea that seems not to have been considered in the literature is: Let the players decide how to divvy up the points. My guess is that this could give nightmares to games in flux, as the weak sisters in a game bargain for more status than they might deserve, as the sand in the hourglass (and points in play for the game) start(s) running out...