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Topic: Correlation of winning to first capture (Read 3221 times) |
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Fritzlein
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Re: Correlation of winning to first capture
« Reply #15 on: Apr 26th, 2006, 2:31pm » |
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on Apr 26th, 2006, 2:19am, Janzert wrote:| FAME favored the wrong side in 1486 games (21.67%) |
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Wow, this really shows what a mediocre indicator material advantage is. I wonder what percentage of chess games are won by a player that never leads in material at any point in the game. I'll bet it is way less than 20%.
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chessandgo
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Re: Correlation of winning to first capture
« Reply #16 on: Apr 26th, 2006, 3:01pm » |
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on Apr 26th, 2006, 2:31pm, Fritzlein wrote:
Wow, this really shows what a mediocre indicator material advantage is. I wonder what percentage of chess games are won by a player that never leads in material at any point in the game. I'll bet it is way less than 20%.
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Quite sure. But I don't understand, does the 20 % figure given by Clauchau correspond to that ??
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Fritzlein
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Re: Correlation of winning to first capture
« Reply #17 on: Apr 26th, 2006, 8:08pm » |
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on Apr 26th, 2006, 3:01pm, chessandgo wrote:| Quite sure. But I don't understand, does the 20 % figure given by Clauchau correspond to that ?? |
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Hmm... I should be more precise. Janzert seems to be saying that in about 60% of Arimaa games, one side is materially ahead at some point while the other side is never materially ahead. It would be interesting to know how often this occurs in chess, as opposed to games in which material is even the whole way, or the material lead switches at some point.
However many such games there are in chess, it would be interesting to know further: Of those games, how often did the player that led but never trailed materially end up losing the game? For example, in the Muzio Gambit, Black my lead materially the whole way and yet be checkmated in short order.
I guess that in chess, if one side leads in material at some point and also never trails, they are more than 80% likely to have won the game, Muzio notwithstanding.
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mouse
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Re: Correlation of winning to first capture
« Reply #18 on: Apr 27th, 2006, 5:25am » |
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on Apr 26th, 2006, 8:08pm, Fritzlein wrote:
However many such games there are in chess, it would be interesting to know further: Of those games, how often did the player that led but never trailed materially end up losing the game? For example, in the Muzio Gambit, Black my lead materially the whole way and yet be checkmated in short order.
I guess that in chess, if one side leads in material at some point and also never trails, they are more than 80% likely to have won the game, Muzio notwithstanding. |
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I think you are thinking about top level chess between GM's. In that case you are probably correct in assuming very few winners never being ahead materially.
But I think in lower level of chess (which is probably more comparable to the level in arimaa) it is much more common to have winners never being ahead on material. As a result of blunders leading to a quick mate by the opponent. And because different types of gambits are a lot more common at lower levels of chess.
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mouse
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Re: Correlation of winning to first capture
« Reply #19 on: Apr 27th, 2006, 5:56am » |
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on Apr 26th, 2006, 2:08pm, Fritzlein wrote:
Actually, I thought of a query I could do, namely correlating the first capture with the second capture. In 17398 rated games in which there were at least two piece deaths (and the first wasn't apparent suicide on move 2), I found that 58% of the time both of the first two piece deaths were from the same army. Breaking this down by the type of the first piece captured gives:
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I wonder if there is a difference between h vs h games and h vs b games. I tend to believe there would be.
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Janzert
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Re: Correlation of winning to first capture
« Reply #20 on: Apr 27th, 2006, 12:26pm » |
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Still not really answering Fritzlein's question, but something I wanted to look at for a while and I think it will answer the spirit of his question.  If not let me know Fritzlein and I can take a look at your actual question as well.
Here is a graph showing the percentage of times a side wins after getting that FAME score in a game.
Once again games with captures in move 2 are excluded. "All" includes all other games. HvH are human vs. human and BvB are bot vs. bot respectively. The "200" lines are limited to players within 200 rating points of each other. Each set is stopped when the number of samples falls below 100.
and one showing fame scores up to 15.
There are several things that surprised me here. But possibly the most striking was that a large material advantage is much more important in HvH games than it is in BvB. Also related, note that a very small material advantage (1 rabbit or less) is most important in overall BvB but least important in closely rated BvB.
Janzert
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Fritzlein
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Re: Correlation of winning to first capture
« Reply #21 on: Apr 27th, 2006, 1:28pm » |
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Janzert, that is a totally awesome graph. Thanks. I'm not sure what my question was, but I love your answer.
Would you mind spelling out the methodology in a little more detail? In particular, did you take all positions in your database, and for each positoin put it in a bin corresponding to its FAME score, and then calculate a win percentage for each bin? In hindsight, I wish I had thought to ask for that graph, because it is exactly what I want to know, and a much more interesting indicator than the crude notion of "first capture". You rock.
One thing that jumps out at me from the graph is that if FAME is computing any advantage whatsoever, even 0.1 rabbits, the side with the material lead has almost a 2/3 chance of winning.
Another interesting feature is the little jumps that occur at values of 1, 1.5, 2, 2.5, 3.1, and 5.6. These correspond to an initial capture of a rabbit, cat, dog, (something), horse, and camel. I can't figure out what the common material difference would be that results in an advantage of 2.5. Maybe a cat and a rabbit for nothing is a common advantage to have?
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| « Last Edit: Apr 27th, 2006, 1:43pm by Fritzlein » |
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Fritzlein
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Re: Correlation of winning to first capture
« Reply #22 on: Apr 27th, 2006, 3:31pm » |
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on Apr 27th, 2006, 5:56am, mouse wrote:| I wonder if there is a difference between h vs h games and h vs b games. I tend to believe there would be. |
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Wow, you are totally right. I should have checked for this myself, but thanks for reminding me since I didn't.
Across all games there is a 58% percent chance that the first two captures will be of the same type, but in human games there is only a 48% chance the first two captures will be of the same type. If you restrict it to humans within 200 points of each other, it drops further to 45%.
However, that is still quite a high probability of consecutive captures rather than exchange. This is another number I'd like to compare to chess. My subjective guess is that only 20% of the time in chess the first two captures come from the same army rather than being an exchange.
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Janzert
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Re: Correlation of winning to first capture
« Reply #23 on: Apr 27th, 2006, 9:45pm » |
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on Apr 27th, 2006, 1:28pm, Fritzlein wrote:| Would you mind spelling out the methodology in a little more detail? In particular, did you take all positions in your database, and for each positoin put it in a bin corresponding to its FAME score, and then calculate a win percentage for each bin? |
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Sure, in trying to fit the description into one sentence I think I lost some important details.
I did recently refactor my database to seperate positions from moves, but I didn't use that for this graph at all.
The method you describe above would be a similiar idea but not quite the same as what I actually did here. In particular your method would show the percentage of wins after a game had been exactly at a FAME score. What I looked at was percentage of wins after achieving at least a certain FAME score. Unfortunately my rather bad description above does imply what you describe instead of what I actually did.
The actual steps were to examine each game and find the largest FAME score in favor of the winner and of the loser (or opposing the winner, same thing just different ways to look at it).
That's the easy part to describe. With the concept and the implementation of it matching. For the second part the abstract idea I'm trying to accomplish is not very straight forward in the implementation. So let me first describe the concept, then I'll give the actual implementation steps so someone can double check that I got it right.
Secondly, for any FAME score the percentage of sides (players) that made it at least to that score are noted.
Which of course is only conceptually what I'm doing. Here's the details of what I'm actually doing.
Take both lists of scores reached by the winning and losing sides in a game. While both lists have values, pop the value off the list with the smallest value. If both lists are the same pop it off both. If this score is different (larger) than the last iteration, note the score and percentage of winning sides remaining (number of winning scores divided by number of the total (winning and losing) scores remaining).
Janzert
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