Tag-Team Chess
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i really like that idea
I'm a mathematician too, so this sounds interesting. As for the rating system, assuming it's accurate, etc, etc, it means the following: against a player rated 200 points higher than you, you have about 24% chance of winning; against a player 100 points higher than you, you have about 36% chance of winning; against an equally rated player you have 50% chance of winning (where a draw counts as half a win for each player). Source: http://www.chessbase.com/newsdetail.asp?newsid=4326
Of course, this assumes you're playing the full game - once you start tag-teaming everything goes out the window. If player A is 2000 then he is an expert, whereas player C (at 1000) is a beginner. Player A will make moves based on deep calculations and important positional considerations, player C will drop pieces, miss simple tactics, and ruin the game for his team. Someone who achieves a 2000 rating does so because they can play a strong game, with very few tactical errors, from start to finish - not because they can pull rabbits out of hats. If your 1000 rating teammate blunders away his queen and walks into a forced mate, the 2000 rating points are not a magic bullet that can save you.
My money would be on the 1500 player here. I think a more interesting question would be, what sort of odds does a 2000 player have to give so that a 1500 player has a 50% chance of winning? Knight-odds? Rook-odds?
By odds you mean handicap? I played against Larry Kaufman (I think he's some sort of a master, but I could be wrong about that) and his handicap was no queen. He always beat me this way. Once he gave me a queen and a knight, and I destroyed him. I guess small differences can translate into big differences.
This is very clever, Vance. I often have similar thoughts. My suspicion, though, related to your "small differences translate" comment, is that the C player would make enough blunders as that the B player could capitalize on, despite the A player making the best moves when it was his or her turn. Mistakes in chess are large - oftentimes two players advance towards one another, both with perfect play, each awaiting some kind of mistake that they're capable of capitalizing on.
A good way of asking the question is who would you like to be in the equation - the A player or the B player. My initial instinct is that I'd like to be the B player, unburdened by another player making potentially bad moves during their turn.
But, of course, one might imagine that the A player is so good, that if they got to move first, that they could arrange the game such as that the "best" moves would "suggest" themselves to the C-player... almost like setting another player up for a hat trick or a slam dunk with the right serve.
Intriguing question Vance.
Thank you Rael, coming from you, I am flattered! Anyway, the equally-spaced model was just an example. One could postulate A=1000, B=1800, C=2000. Really the question would be where does B fall to make it a fair game. And I certainly agree that the influence of a bad move is more than that of a good move. At one extreme, if someone as bad a player as I am gets a lead, king plus rook vs. king alone, then I will win no matter how strong the opponent. This is not like soccer -- or American football or basketball -- in which one player (I suppose one move would be the correct analogy) can make that much of a difference. Bounded influence function I suppose it could be called.
My last post had an error. The middle player (B) should have been below 1500, not above it. In fact, the more I think about it, the more it seems like a disadvantage to "be of two minds", even if both minds are brilliant. That is, if A and B and C are all equally rated, then I would pick B to beat the A & C tag team, because when A disguises an attack from B, he might also be disguising it from his partner, C. The lack of coordination might render A & C, say both rated 2000, unable to beat B, rated 1800.
Depends if their chess playing styles are similar or not.
The stronger half would have to improvise a lot. A chain is a strong as its weakest link, is it not?
That is the expression, to be sure, but empirically is this always the case? I am not so certain that a master could not help a weaker player with some well placed moves, but I do agree that it would not be easy.
What if A and C, 2100 and 1900 respectively played against B and D, both rated 2000? Or what if both teams could communicate?
Two good questions. I would speculate that if there were two tag teams, both with the same mean, then the variance would dictate who wins. The larger variance would lose. But communications would render the experiment useless, because then this would degenerate to a de facto game of better player against better player. By the way, we all know that not all players with the same rating are equally good, but this is a separate issue, and I suppose that here we are talking about on average, right?
With communication, it would be as simple as the player with the better idea being able to demonstrate it to the other partner. Teams with communication should be about as good as their strongest player, assuming that the player with the decision power either trusts his judgment or knows chess well enough to understand its reasoning and agree. (This is different but similar to Vote Chess. Similar in that there is more than one mind. Different in that the result is not democratic. Probably a good thing, as people who vote don't necessarily pay attention, while giving one person the power puts a burden on them for the team.)
As to... tag teaming without communication?
I would expect the 2000+2000 to do better than the 1500+2500, e.g. I don't know if the difference of 2000+2000 vs. 2100+1900 would become apparent rapidly; indeed, I suspect that first move advantage might be even stronger than having to cope with a partner 200 points below against two opponents 100 points below. That is, you'd have to do a few dozen games to find out how severe the advantage is for 2000+2000.
It may be fairly easy to set up a game like this in a play-by-email format. Get a referee of sorts, or a tournament director, to find players 1, 2, 3, and 4. Put 1 and 2 on the white pieces and 3 and 4 on the black. Hand the game in the starting position over to 1. Tell player 1 about the black players 3 and 4, that he'll hand off to 3 (and receive from 4). Tell player 3 about the white players 1 and 2, that he'll hand off to 2 (and receive from 1). Tell player 2 about black players 3 and 4, that he'll hand off to 4 (and receive from 3). Tell player 4 about white players 1 and 2, that he'll hand off to 1 (and receive from 2). Although each white player initially knows both black players, and each black player initially knows both white players, one can assume that the players don't talk across the board to reveal who each is playing with (because that would give the opponents communication--and, you'd have to stipulate the same rule against, just in case).
A similar setup could be used for 2 players in a tag-team versus 1, or for a predesignated string of 2 or 3 moves from a pair of the players at a time.
With a little less work and a little more trust, you could have all four (or three) players know each other. Just create two games and, after each pair of moves by people on the one board, have that pair of moves copied (by the respective partners) before playing another pair of moves on the other board. Deviation from your partner's play could be considered forfeit for the tag-team match.
Great idea!
For a fun idea: Take two equally strong players (or roughly equal) and have them play a game against each other (say, 1800 vs. 1800). Give each player a junior partner (rated 1400-1500, say). Let the junior partner suggest each move first. Let the stronger player override at will but count the number of times he does. At the end of the game, there are three outcomes of the game variable (white wins, draw, black wins) and two outcomes of the "who overrode their partner more" variable (white used less overrides, black used less overrides). Score the game as follows.
White wins - white used less overrides - 1.0 / 0.0
Draw - white used less overrides - 0.5 / 0.5
Black wins - white used less overrides - 0.5 / 0.5
White wins - black used less overrides - 0.5 / 0.5
Draw - black used less overrides - 0.5 / 0.5
Black wins - black used less overrides - 0.0 / 1.0
In effect, using less overrides is an off-the-board winning condition. You can't lose if the opponent ignores their junior partner more, and you can win only if you ignore yours less.
I like it!
Being mathematically inclined, I often wonder which is the larger of two effects. For example, could my soccer team beat a professional team if we had all 11 and they had to play with only seven? Maybe six? What if they play with all 11 but only after they have played two other games against comparable professional teams, so that they are already exhausted? And on and on my mind spins.
Now my mind turns to chess. This rating system we have appears not to be interval scaled, so if A is rated 2100, B 2000, and C 1900, then P{A beats B} need not equal P{B beats C}. What would happen if A and C were to play against B, as a tag-team event, alternating moves, but with no communication between A and C? Better yet, suppose now that A is 2000, B 1500, and C 1000. Now how does the game turn out? What happens if A and C alternate moves but not one at a time? Suppose that A makes the first two or three moves for this team, then C makes the next two or three, and so on? Clearly, it would not be hard to introduce variations on this theme. Would this be as much fun as, or even more fun than, vote chess? Would it be theoretically interesting?