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Topic: Gold advantage impossible to measure? (Read 4561 times) |
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Fritzlein
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Arimaa player #706
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Re: Gold advantage impossible to measure?
« Reply #15 on: Mar 3rd, 2007, 9:25pm » |
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Nice idea, 99of9. I don't think I can do it with an Access query, but it would be interesting to segregate the data into games where Silver sets up similarly to Gold (which could hardly be a setup advantage), and games where Silver sets up differently (which could be a setup advantage).
I waver between thinking we are using the Gold advantage sub-optimally, and thinking that it is a statistical fluke. The notion that Silver actually has an inherent advantage from moving second is a distant third on my list of hypotheses.
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aaaa
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Arimaa player #958
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Re: Gold advantage impossible to measure?
« Reply #16 on: Apr 17th, 2007, 12:10pm » |
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I have a hypothesis that the reason for the apparent slight advantage for Silver may be psychological in nature. Namely, that by having the first move a player may subconsciously assume a too high of an advantage (perhaps by analogy with chess) and consequently feel the need to capitalize on it and play more brazenly than the nature of the game would justify, resulting in a shift of advantage to the defensive side. One possible way of testing this theory could be to classify the games based on the first move of Gold, with more elephant moves indicating a more aggressive opening.
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seanick
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SeaNICK
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Re: Gold advantage impossible to measure?
« Reply #17 on: Apr 18th, 2007, 11:17am » |
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I think the symmetry angle might be the reason that silvers advantage is not greater between HvH, and also the reason that the bots are the opposite.
of course, the numbers are still too small to make any real conclusions. but Karl's choice of games seems appropriate and likely to be optimal for the given amount of data.
<ripped off from karls post>
Game Type Pairs Gold Wins Mismatch Gold Adv. # Std. Dev.
--------- ----- --------- -------- --------- -----------
ALL . 4692 4725 . 189 . 3.23 . 0.79
H v B . 3839 3851 . 192 . 1.45 . 0.32
B v B . 608 630 . 152 . 15.1 . 1.38
H V H . 245 244 . 237 . -2.19 . 0.12
</jack move>
to attempt to explain my thoughts I'll separate them into some questions and my thoughts about their cause:
Q1. Why do bots (vs bots) have a large advantage as gold?
A1. The majority of bots don't respond with a silver position that neutralizes gold's advantage of going first
Q2. Why do humans have less of an advantage vs. bots (than bots vs bots) when playing as gold, and why do bots have less of an advantage over humans (than vs bots)? (these two are not separable by the above numbers, so I'll consider them both here as inseparable. mainly because I'm too lazy to mine that data myself.)
A2. lower level players on the bot ladder are less knowledgable on how to best respond with a good silver setup. But this skill is developing, hence there being less of an advantage to be gold in h vs bot than in bot vs. bot. Note that the knowledge of preparing an appropriate setup response is orthogonal to the ability to actually beat the opponent so the gold advantage is not entirely regained when gold is played by the human.
Q3. why do hvh games appear to show an advantage to being silver? Even more than golds advantage in hvb?
A3. because silver can respond appropriately to golds setup and it is more likely that gold be psychologically affected by silvers response than vs. a bot (which, in some ways, couldn't care less about the opening position.)
this is all very shaky in terms of a root cause analysis but as mentioned many times already, more understanding will come with time (provided games continue to be played).
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