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Topic: More Material Analysis (Read 5309 times) |
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IdahoEv
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Re: More Material Analysis
« Reply #15 on: Apr 28th, 2006, 4:18pm » |
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Perhaps another, simpler explanation for the rabbit upset: good players have focussed on pulling rabbits the last couple of years. Therefore rabbit captures indicate likely wins because the players are good, end of story.
I can re-run the analysis with different game selection criteria if anyone is interested. Only humans, only bots, both players > 1750, whatever.
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Fritzlein
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Re: More Material Analysis
« Reply #16 on: Apr 28th, 2006, 5:58pm » |
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on Apr 28th, 2006, 3:51pm, jdb wrote:| Fritzlein, this may seem like a silly question, but why does it matter if "causality is reversed"? |
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It isn't a silly question at all; it's the very center of my argument about correlation not being the same as causality.
I'm not disputing IdahoEv's numbers at all. I accept that there is a greater correlation between winning and capturing an initial rabbit than between winning and capturing an initial cat. I am disputing his conclusion that therefore an inital rabbit capture is worth more. I assume he means that if one player starts a game without a rabbit, that incurs a greater chance of losing than starting without a cat. This conclusion may be true, but I think it is false, and it certainly doesn't follow from the correlation.
Suppose for a moment that cats really are more valuable than rabbits in the opening, and suppose that everyone correctly makes this evaluation. This precise fact could cause (at least in part) the higher correlation between winning and an initial rabbit capture.
Example 1: Consider any game where I get a camel hostage. That means I'm winning. The causal chain is now that I will try to capture something in my other home trap while my opponent is trying to free up his defending elephant. Naturally while he tries to engineer a defense, he will want to lose as little material as possible in the mean time. So he may (correctly!) use a rabbit to unfreeze and retreat any threatened piece, including a cat, so that I only win a rabbit in the mean time.
Note that my advantage caused me to win an initial rabbit, not an initial cat, in part because cats are more valuable than rabbits. Note also that after capturing an initial rabbit, I still have the camel hostage as well, so I have a greater chance of winning from that point than if I had been given a cat capture but nothing else.
Example 2: Suppose that I frame a rabbit in one of my home traps, for no compensation. This means I am winning. Next I try to create a second threat to force material gain. Suppose my second threat is to take a cat hostage, and threaten it with capture. My opponent (correctly!) realizing that a cat is worth more than a rabbit, abandons his framed rabbit to prevent the cat capture. If he waited too long to give up the rabbit, though, I can often frame the cat as well, or keep it as a hostage in a very favorable way.
Note that again my winning caused a rabbit capture (not a cat capture). Note further that, because I have a rabbit capture plus a cat hostage, I have a greater chance of winning than I would have had I captured a cat for nothing.
Example 3: Suppose I somehow manage to get a cat frame right off the bat. Having tied down the opposing elephant, I go hunting for a second threat. My opponent (correctly!) protects his pieces at the expense of letting a rabbit be pulled. When I'm about to take the rabbit, he considers abandoning his cat to save the rabbit, but correctly lets the rabbit go and maneuvers to break the frame of his cat instead. Therefore I win a rabbit.
For the third time, my winning has caused me to capture a rabbit, not a cat. For the third time the position I end up with may be worth more than it would be worth had I started the game with a free cat.
In summary, the higher correlation between winning and initial rabbit captures than between winning an initial cat captures may be due to the fact that cats really are worth more than rabbits, which in turn means that winning positionally causes more initial rabbit captures than it causes initial cat captures.
For the sake of fairness, I must also speculate about what causes a cat capture. It may well be that I can capture a cat because I have a second, bigger threat that must be defended. When this happens winning can also cause cat captures just like it causes rabbit captures. I contend, however, that these cases are less likely than the cases of winning causing a rabbit capture.
Perhaps it is much more common that an initial cat capture is totally isolated from advantage of any other kind. For example it may be that 50% of initial cat captures happen when the capturing player has no other advantage in addition to the cat, whereas only 30% of initial rabbit captures happen when the player has no other advantage in addition to the rabbit.
I'm hope I'm not being too pedantic in my efforts to be clear. The distinction between correlation and causality bedevils all applied statistics. For example, there's a known correlation between abstinence from alcohol and death. People who drink moderately are less like to die at any given time than people who don't drink at all. However, you can't necessarily draw the conclusion that, if you currently abstain from alcohol, taking up moderate drinking will lower your chance of death. The medical studies must first eliminate the possibility of reverse causality. In particular, some people who are near death are absolutely forbidden to drink by their doctors. Even after they stop drinking, they're still likely to die. In this fashion, being likely to die can cause a higher rate of abstinence rather than abstinence causing a higher likelihood of dying. We have to be careful what the correlation means.
Check out http://www.eurekalert.org/pub_releases/2006-03/uoc--isq032706.php
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| « Last Edit: Apr 28th, 2006, 6:01pm by Fritzlein » |
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Swynndla
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Re: More Material Analysis
« Reply #17 on: Apr 28th, 2006, 6:06pm » |
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on Apr 28th, 2006, 3:51pm, jdb wrote:
Fritzlein, this may seem like a silly question, but why does it matter if "causality is reversed"?
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In my opinion, there are two different things going on here. 1) Knowing who is winning and 2) Knowing why they are winning.
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Hmmm I'm not sure if I'm interpreting what you are saying correctly, but I though I'd throw my 2c in anyways ...
An extreme, made up example:
Lets say it is shown, that in rated games of players rated 1700 and above, where gold got a rabbit on the 7th rank, that 90% of those games were won by gold.
If cause and effect were not taken into account, then it would be easy to fall into the trap of programming a bot to try really hard to get a rabbit on the 7th, or at least put its rabbit on the 7th given an opportunity. It may do this even at the expense of giving up its horse, at that has a lower % win according to the database.
This would be a serious weakness for the bot, and further more, the evaluation (as a result of the 7th rank analysis) would fail in 1) Knowing who is winning and 2) Knowing why they are winning.
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IdahoEv
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Re: More Material Analysis
« Reply #18 on: Apr 28th, 2006, 6:43pm » |
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Fritz's logic is sound, and those effects could account for the difference seen, if they occur with sufficient frequency to mask the underlying, hypothetically larger value of a cat. For Fritz's reasoning to be the only reason that cats are undervalued relative to rats in the DB (assuming their natural 'worth' is greater than the 1st rabbit), a very large fraction of initial rabbit captures would have to be as a result of sacrificing a rabbit to save a cat in one of Fritz' scenarios ... without any large fraction of rabbits being sacrificed to save dogs or horses.
(And no, you're not being pedantic in the slightest. 
However, parallel scenarios would exist for sacrificing rabbits in the rescue of dogs and horses. While they might not be sufficient to pull the piece's value (in the P(win|capture) sense) down below that of the rabbit, it should reduce it somewhat. Yet while P(win|captureC) is 55%, P(win|captureD) is 66%, above rabbits and actually very close to horses.
So there's an 11% gap in eventual win probability between the initial capture of cats and dogs, and that implies me that something is going on beyond the analysis done so far.
I'll try to compile some other examples that will possibly help; RR vs CR and so forth.
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99of9
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Re: More Material Analysis
« Reply #19 on: Apr 28th, 2006, 7:09pm » |
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on Apr 28th, 2006, 1:01pm, IdahoEv wrote:| * An initial cat capture by silver is *more* common (739 instances) ( (112218-112218 ) but leads to a silver win only 51% of the time! |
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This could be due to people baiting bomb.
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IdahoEv
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Re: More Material Analysis
« Reply #20 on: Apr 28th, 2006, 7:13pm » |
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on Apr 28th, 2006, 2:20pm, chessandgo wrote:| How do you intent to interpolate a fonction from your data Idaho ? |
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I'm not sure yet, it's a lot of degrees of freedom.
A simple neural net/perceptron would have no trouble mapping the 12 variables to a %age, but because the data are sparse it would overfit badly.
I'd like to come up with a simple function in Tn, Gn for each row, using a single constant An, then sum them over all levels. It might include one or more of:
T(n+1 .. 6) (total pieces below this level)
G(n+1 .. 6) (gold advantage at below this level)
T(all) total pieces alive
G(all) gold advantage in total pieces
But in any case, I'd like it to be the same for all non-rabbit rows, differing only by a constant An for each row. Then I only need to fit six total parameters, making it of similar complexity to FAME.
Trouble is, I can't think of an obvious form for the function that will be easy to fit and fast to compute. But I haven't spent much time on it yet, either.
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chessandgo
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Re: More Material Analysis
« Reply #21 on: Apr 28th, 2006, 8:50pm » |
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on Apr 28th, 2006, 5:58pm, Fritzlein wrote:
abstinence causing a higher likelihood of dying. We have to be careful what the correlation means.
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Another conlusion that might be drawn is : hey buddies, abstinence is bad your health as well as your arimaa strength ! Don't forget your sexual life !
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IdahoEv
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Re: More Material Analysis
« Reply #22 on: Apr 28th, 2006, 9:12pm » |
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on Apr 28th, 2006, 8:50pm, chessandgo wrote:| Don't forget your sexual life ! |
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This is something one is capable of "forgetting"?
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clauchau
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Re: More Material Analysis
« Reply #23 on: May 1st, 2006, 9:29am » |
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Since some unwanted aspects are biasing statistics on materials in recorded games, how about sampling random board positions among all possible positions having given material states?
At first, positions would get a score like say +1000, -1000 or 0, according to whether they definitely are won, lost, or neither. The material states would average over them.
Then, positions would get the previous scores after having completed a 2-ply minmaxing search. The material states would get updated averages score.
And we repeat that step somehow.
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