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Topic: How great an advantage is the first move? (Read 3816 times) |
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Fritzlein
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How great an advantage is the first move?
« on: Sep 16th, 2004, 11:42am » |
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I've done a quick analysis of the game database which Omar has made available (Thanks, Omar!), to see how much of an advantage it is to play first. Gold has indeed won more often (across all 5047 rated games) than one would expect from the ratings alone. So I calculated the expected winnings by adding N points to the rating of Gold for various values of N, until the expected number of wins balances the actual number of wins. As it turns out, the value of N which compensates exactly is 3.
What? Is it possible that the first move is worth only 3 rating points? That isn't my experience at all. In fact, when I do the calculation over only the 59 rated games I have played, the value of N jumps to 113. Apparently for me, at least, going first is worth 113 rating points.
If I remember correctly, studies have shown that in chess the first move is worth about 40 rating points. I expected it would be approximately the same for Arimaa, but the data doesn't bear me out.
What do other people think? Is moving first a significant advantage in your experience? Maybe there is some anomaly created by people being allowed to choose their own color? Or maybe I am the anomaly and for everyone else moving first is irrelevant?
Just curious,
-Karl
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| « Last Edit: Sep 16th, 2004, 4:18pm by Fritzlein » |
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99of9
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Re: How great an advantage is the first move?
« Reply #1 on: Sep 16th, 2004, 3:19pm » |
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Wow, this game database could allow some really interesting studies. Where is it? I haven't stumbled upon it yet. [EDIT: Ah, I found it in the download section... duh!]
I think the first move is pretty important. I'd say worth about 50 ratings points.
The ratings difference of 3 that you calculate is so small because many of the games were played dumbbot vs dumbbot ... and for weaker players, the colour matters much less.
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| « Last Edit: Sep 16th, 2004, 3:23pm by 99of9 » |
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omar
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Re: How great an advantage is the first move?
« Reply #2 on: Sep 21st, 2004, 4:07pm » |
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Would be interesting so see what the numbers are if you limit this to games where both players had a rating above some value like 1700.
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #3 on: Sep 24th, 2004, 6:37pm » |
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Limiting to the 958 rated games with both players over 1650, the advantage of moving first turns out to be 4 points. I still don't believe it, but that's what the data says.
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #4 on: Sep 24th, 2004, 8:25pm » |
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More data:
Over his last 86 rated games, 99of9's advantage from going first was 56 points.
Over his last 76 rated games, omar's advantage from going first was -58 points.
Over his last 200 rated games, Belbo's advantage from going first was 10 points.
No, that's not a typo: Omar has actually done worse with gold than silver. No wonder (when I asked by e-mail) he didn't think going first was a significant advantage! Meanwhile 99of9's subjective estimate of the value of the first move was extremely accurate, at least for his games.
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maker
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Re: How great an advantage is the first move?
« Reply #5 on: Sep 25th, 2004, 10:48pm » |
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hehe, I'd bet that for me, I actually get a negative chance of winning, every time I play. Ah, being a newbie...
happy with his station,
maker
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omar
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Re: How great an advantage is the first move?
« Reply #6 on: Sep 26th, 2004, 3:30pm » |
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So Im the one who is bring down the advantage stats for going first. 
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99of9
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Re: How great an advantage is the first move?
« Reply #7 on: Nov 3rd, 2004, 11:14am » |
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on Sep 26th, 2004, 3:30pm, omar wrote:| So Im the one who is bring down the advantage stats for going first. |
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on 09/16/04 at 9:19pm, 99of9 wrote:| ... and for weaker players, the colour matters much less. |
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 QED
(just kidding of course)
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| « Last Edit: Nov 3rd, 2004, 11:15am by 99of9 » |
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #8 on: Apr 11th, 2005, 6:27pm » |
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Recently I was thinking again about the advantage of moving first. It occurred to me that my previous statistics might have been skewed by a couple of factors: (1) Maybe humans start to play bots primarily with Silver once they start to master the bot and (2) Maybe in human vs. human matches, the stronger player offers to play Silver.
I therefore decided to generate a new statistic, in which I would not count multiple games between a pair of opponents unless they alternated colors. That is to say, if Naveed plays Fritzlein with Gold, then subsequent games between Naveed and Fritzlein don't count until Fritzlein plays Gold, and then their games don't count until Naveed plays Gold, etc. And of course I counted only rated games.
Under these rules, there were 6286 games I could count. Alas, Gold won only 3160 a.k.a. 50.27% a.k.a. an advantage of 2 ratings points. Sigh.
My intuition that Gold has a significant advantage is strong, but the data simply refuse to support my conviction.
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #9 on: Apr 12th, 2005, 9:22am » |
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on Apr 12th, 2005, 1:10am, Arimanator wrote:Fourth, what ?!  . You've only played 59 rated games ! That's incredible!
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5th, I believe that you should limit your studies to human vs human players, that how it's done in chess and I am persuaded that the bot factor completely crooks the deal
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I'm curious where you find that I've only played 59 rated games. When I click on my profile it shows me that I have played 371 games, but it doesn't show me how many were rated. The only way I can think of to check is to download the entire game database (which is updated weekly) and run a query. That method tells me I have played 330 rated games.
(Incidentally, you have already played 281 rated games, 7th most among humans over the life of the server. You have played 6917 moves in rated games which ranks 10th among humans over the life of the server, and gives you an average of 24.6 moves per rated game. Aren't databases fun?)
As to eliminating the bot factor, I re-ran my query for human vs. human games only, and this time Gold won only 177 of 398, i.e. 44.5%, which is a rating advantage of 39 points to Silver! I disbelieve this implication even more than the previous one. If Silver truly has an edge it must be due to psychology, or time zones, or numerology, or perturbations in the ether, or something other than the actual game mechanics, which slightly favor Gold. That's my story and I'm sticking to it. 
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jdb
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Re: How great an advantage is the first move?
« Reply #10 on: Apr 12th, 2005, 9:50am » |
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I believe Silver has (at least) two helping factors.
First, the games are long. It is not unusual to see the momentum shift back and forth several times in a game. I haven't seen an opening system were Gold gets the advantage from the outset and directly converts the win. The Elephant/Horse attack has promise, but time will tell.
Second, Silver gets to place his pieces after he has seen Gold's placement. This can only help Silver.
My current opinion is that the advantage of the first move is negligible at best.
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #11 on: Apr 12th, 2005, 11:51am » |
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Ah, now I see. On September 16th, 2004, I did indeed write that I had played 59 rated games. Mystery solved.
At that time I also wrote that the first move was an advantage of 113 rating points for me. Out of curiosity I ran the same query over the 330 rated games I played up until April 9, 2005, and over that dataset the first move is an advantage of 55 rating points to me.
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #12 on: Apr 12th, 2005, 1:59pm » |
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Good thought. When I run the stats over the last 100 rated games I have played, it appears to be a rating advantage of 8 points to Silver! Just as you predicted.
In fact it was so stunning I rechecked my original query over all 330 rated games for me, and the advantage to Gold over the whole set was only 21 points, not 55 points.
I guess I must admit that the early data on myself was heavily skewed by one fact: I initially had trouble beating bot_Arimaanator with Silver but much less difficulty with Gold. Apart from that fluke, the color seems not to have made much difference to my winning percentages. It's amazing what a deep psychological impression an experience like that can leave behind, even when there is nothing afterwards to reinforce it.
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| « Last Edit: Apr 12th, 2005, 2:00pm by Fritzlein » |
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omar
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Re: How great an advantage is the first move?
« Reply #13 on: Apr 13th, 2005, 7:44pm » |
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I guess what we want to know is if there is inherently an advantage for the first player and try to eliminate other factors such as psychology, speed of the game, readiness of the player, difference between the players abilities, etc.
I guess the best way to determine this would be to have the same program play many many games against itself and look the number of times it wins as gold vs silver. It should be done with a random bot at first to eliminate any skew due to the evaluation function.
Maybe Toby or Jeff could make a copy of their bot that plays randomly and run it locally to collect the results.
It would be interesting to see if they both independently come up with similar numbers.
We could then repeat the experiment with a bot that looks 1 ply deep and then one that looks 2 plys deep. Although we probably will not be able to collect as many games since they will run slower and slower with increasing depth.
We may also want to try it with two versions of the random bot. One that does the setup completely randomly and another that does the setup by randomly selecting a setup from a list of commonly used setups.
These results would not apply to human games or games between much stronger bots, but still it will give us some insight into some simple cases and maybe we can extrapolate at bit from it. It would be very interesting to see what the numbers are in these simple cases.
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Fritzlein
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Re: How great an advantage is the first move?
« Reply #14 on: Apr 13th, 2005, 9:48pm » |
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on Apr 13th, 2005, 7:44pm, omar wrote:Maybe Toby or Jeff could make a copy of their bot that plays randomly and run it locally to collect the results.
It would be interesting to see if they both independently come up with similar numbers.
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Clauchau already posted in the deflation thread that he ran random stepper against random stepper a million times and the results were
Gold won 50.3%, Silver won 49.7%
Interestingly that's almost exactly the percentage I got from the database with my alternating game methodology
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