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Topic: First Move Advantage vs. Second Setup Advantage (Read 16574 times) |
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chessandgo
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #30 on: Apr 13th, 2008, 5:27pm » |
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on Apr 13th, 2008, 3:01pm, aaaa wrote:| Based on my calculations, Gold's winning percentage varies wildly depending on how the games are weighted by rating. In order for me to come to a more reliable number, Fritzlein and chessandgo would need to play a bunch of games against each other with alternating colors (cf. Karpov vs. Kasparov). |
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I fear it would be more like John Doe vs Jean Dupont, but I have nothing against playing a lot of games with Karl 
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Fritzlein
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #31 on: Jun 10th, 2011, 11:15pm » |
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Nowadays there is a persistent rumor that Silver has an advantage in Arimaa due to the second setup. I suddenly realized that it had been over three years since my last statistical investigation of the subject. What if modern playing styles have changed so much that the results have started to change as well? So I have repeated my former experiment over the most recent three years of data using the same methodology described earlier in this thread.
Rated Pairs from 3/24/2008 to 5/31/2011
Game Type Pairs Gold Wins Mismatch Gold Adv. # Std. Dev.
--------- ----- --------- -------- --------- -----------
ALL . 35329 35451.5 . 231 . 1.8 . 1.13
B v B . 1615 1672 . 203 . 16.9 . 1.94
H v B . 32966 33019.5 . 233 . 0.9 . 0.51
H v H . 748 760 . 216 . 8.0 . 0.74
The draw that appears is this game from a time when elimination wasn't always a victory. None of the results are statistically significant, not even the BvB games where we are pretty sure Gold has an advantage because bots don't use the second setup to react.
To capture the largest dataset possible, I queried for all color-reversed pairs of games since the beginning of time. Note that this includes 69% of all rated games ever played, which reflects a natural tendency of all participants to swap colors between rematches. If color assignment were completely random, I would only be picking up 2/3 of the games.
Rated Pairs from 11/22/2002 to 5/31/2011
Game Type Pairs Gold Wins Mismatch Gold Adv. # Std. Dev.
--------- ----- --------- -------- --------- -----------
ALL . 57725 57914.5 . 231 . 1.7 . 1.37
B v B . 3491 3571 . 193 . 10.7 . 2.22
H v B . 52494 52602 . 233 . 1.1 . 0.82
H v H . 1740 1741.5 . 251 . 0.5 . 0.06
At last, a statistically significant result! In BvB games, Gold has a measurable advantage. My best guess at the size of the advantage is about 11 Elo points. But of course that is attributable to bots failing to use the second setup to gain tempi in any way. Bot developers take note of the points you are giving away.
One objection to my methodology might be that I haven't looked at the best dataset, namely games between strong human players. I doubt that it is the best dataset, because it is smaller and thus less likely to give a significant result. Nevertheless, leaving no stone unturned, I looked. I limited the games to both players being human and rated over 1900. This might have a weird edge effect in that one game will count but the rematch won't count because one of the players fell below 1900 rating in the mean time. That's the way my code works, so hopefully the effect is small.
Rated Good Game Pairs from 11/22/2002 to 5/31/2011
Game Type Pairs Gold Wins Mismatch Gold Adv. # Std. Dev.
--------- ----- --------- -------- --------- -----------
good . 524 529 . 181 . 4.3 . 0.35
We can't reject the null hypothesis, and not just because the data set is small. Even in relative terms the colors are coming out even.
As I reread what I wrote in years past, I was quite persistent in my belief that Gold had an inherent advantage. Now I am less sure. The BvB data can be neglected, because bots are dumb. Otherwise the data are totally inconclusive. The only thing I feel confident in saying at the moment is that the statistics give us no reason whatsoever to prefer one color over the other.
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| « Last Edit: Jun 10th, 2011, 11:26pm by Fritzlein » |
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Saposhiente
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Arimaa player #5970
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #32 on: Apr 3rd, 2013, 6:41pm » |
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Included in your data is probably a lot of symmetric 99of9 vs 99of9 setups, where Silver does nothing to use his second setup advantage. Would it be possible to filter to only include games where one player uses a different setup than the other, varied by more than just swapping cats and dogs?
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Boo
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #33 on: Apr 4th, 2013, 1:48am » |
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High rated postal games have the less blunders, so long-term tendencies should be best visible there.
E.g. I took 15 best players acording to current postal ratings:
Player Gold% Silver% difference
Fritzlein (2823) 92 - 90 +2
Alfons (2527) 76 - 96 -20
chessandgo (2493) 88 - 83 +5
Adanac (2420) 73 - 62 +11
99of9 (2377) 80 - 66 +14
Boo (2331) 70 - 89 -19
bot_briareus (2314) 80 - 63 +17
Hippo (2281) 84 - 70 +14
jdb (2280) 67 - 83 -16
RonWeasley (2225) 67 - 73 -6
browni3141 (2215) 52 - 91 -39
rabbits (2211) too little games(4) 0
ChrisB (2209) 62 - 75 -13
robinson (2208 ) 50 - 54 -4
Asger (2200) 100 - 100 0
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Total difference -56
Of course it would be better to calculate by the number of games... Before doing this table my guess was that silver has a slight advantage (because I do better with silver  ). But most probably I am wrong, because the players preferring silver have played less games (I think).
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| « Last Edit: Apr 4th, 2013, 1:49am by Boo » |
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browni3141
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #34 on: Apr 4th, 2013, 12:57pm » |
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on Apr 4th, 2013, 1:48am, Boo wrote:| (because I do better with silver ) |
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Well just look at that horrible gold setup  . Yeah, yeah, I know I lost to it.
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Ail
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #35 on: Feb 20th, 2014, 7:11pm » |
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Is the statement that Bots would not make use of the second-setup-advantage still thought to be true?
I'm pretty sure that at least Sharp does it all the time since I even immitated his way of doing it, which kinda boils down to:
Put elephant on the line of opponents camel and place own camel as far away as possible from the opponents elephant.
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johncf1018
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #36 on: Jan 21st, 2015, 3:58pm » |
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A bit of thread necro but there is any easy theoretical solution to player advantage in arimaa, consisting of slight modifications to the rules. My idea (I'm sure others have had it before) is simply to start with an empty board. Gold places any 2 gold pieces, then silver places any 4 silver pieces. Players alternate placing pieces 4 at a time. When a player has no more pieces to place s/he may start moving his pieces. Play progresses as normal. When I've suggested this in the past I've always met with the response that this modification isn't needed as there is no significant advantage for either player. However, it seems like now the data suggests there could be an advantage. Even if there isn't, the overhead of these rules changes are so minor that I can't see any reason NOT to adopt them aside from tradition - which is a bit of a moot point in a game this young. In any case, this is how I play with my friends and we like it so I thought I'd perform a bit of thread necro and toss this idea out there again.
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aaaa
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #37 on: Jan 21st, 2015, 4:23pm » |
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on Jan 21st, 2015, 3:58pm, johncf1018 wrote:| A bit of thread necro but there is any easy theoretical solution to player advantage in arimaa, consisting of slight modifications to the rules. My idea (I'm sure others have had it before) is simply to start with an empty board. Gold places any 2 gold pieces, then silver places any 4 silver pieces. Players alternate placing pieces 4 at a time. When a player has no more pieces to place s/he may start moving his pieces. Play progresses as normal. When I've suggested this in the past I've always met with the response that this modification isn't needed as there is no significant advantage for either player. However, it seems like now the data suggests there could be an advantage. Even if there isn't, the overhead of these rules changes are so minor that I can't see any reason NOT to adopt them aside from tradition - which is a bit of a moot point in a game this young. In any case, this is how I play with my friends and we like it so I thought I'd perform a bit of thread necro and toss this idea out there again. |
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This is actually pretty close to something Omar himself already proposed as a possible future rule change.
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browni3141
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Arimaa player #7014
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #38 on: Jan 21st, 2015, 4:52pm » |
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on Jan 21st, 2015, 3:58pm, johncf1018 wrote:| A bit of thread necro but there is any easy theoretical solution to player advantage in arimaa, consisting of slight modifications to the rules. My idea (I'm sure others have had it before) is simply to start with an empty board. Gold places any 2 gold pieces, then silver places any 4 silver pieces. Players alternate placing pieces 4 at a time. When a player has no more pieces to place s/he may start moving his pieces. Play progresses as normal. When I've suggested this in the past I've always met with the response that this modification isn't needed as there is no significant advantage for either player. However, it seems like now the data suggests there could be an advantage. Even if there isn't, the overhead of these rules changes are so minor that I can't see any reason NOT to adopt them aside from tradition - which is a bit of a moot point in a game this young. In any case, this is how I play with my friends and we like it so I thought I'd perform a bit of thread necro and toss this idea out there again. |
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I thought the data indicated no advantage whatsoever with any amount of reliability. There is also no good logical argument favoring one side or another. I personally prefer silver. Which side are you implying has the advantage? For me there is more than just tradition as a reason not to adopt a rule change. I don't see any advantage to your rule set over the current one. For all we know your change could increase advantage for one side
I don't think your idea would necessarily make Arimaa worse, but I can't see how it would make Arimaa better.
Finally, this rule and rules like the pie rule I don't personally very much like. I think achieving equality through imbalance (like setup response advantage vs. first move advantage) is much more interesting than equality through clear balance, although the former is much harder to achieve.
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| « Last Edit: Jan 21st, 2015, 8:55pm by browni3141 » |
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Ail
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #39 on: Jan 22nd, 2015, 3:52am » |
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I indeed see a disadvantage in that rule-change.
It would take more time to set the board up.
I'd rather just start quickly into the game with a standard-setup as gold and a slightly adapted setup as silver instead of spending several turns of setting up the board first.
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Fritzlein
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Re: First Move Advantage vs. Second Setup Advantag
« Reply #40 on: Jan 22nd, 2015, 9:22am » |
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Taking longer to start the game is a small nuisance, a small price to pay to fix a problem. The problem itself, however, is absolutely minuscule, to the point that we don't even know which side has the advantage. Thus the vanishingly small size of the problem makes the price of the solution way too high to be worth paying.
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