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Topic: Statistic wanted: Average pieces remaining (Read 3888 times) |
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PMertens
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Arimaa player #692
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Re: Statistic wanted: Average pieces remaining
« Reply #15 on: Dec 9th, 2004, 11:49am » |
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well - after a second look I find you 
I somehow used only 2000 sets for my statistics 
let me see if something changed during 2004 - mea culpa
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PMertens
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Arimaa player #692
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Re: Statistic wanted: Average pieces remaining
« Reply #16 on: Dec 9th, 2004, 12:06pm » |
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ok not much changed - just 0.1-0.3 less pieces (checked 1700+)
now some player specific data:
for Fritzlein-Games its:
Gold Silver G-rabbits S-rabbits count
10.70 10.84 5.56 5.63 82
13.15 8.73 6.88 4.55 40 (gold)
8.36 12.86 4.31 6.67 42 (silver)
for Belbo its:
11.23 11.22 5.77 5.77 111
12.61 9.88 6.51 4.98 57
9.76 12.63 5.00 6.61 54
for 99of9 its:
10.21 9.87 5.38 5.24 63
11.72 7.69 6.09 3.94 32
8.65 12.13 4.65 6.58 31
for Omar its:
11.06 11.68 5.97 6.23 71
13.38 9.59 7.14 5.14 29
9.45 13.12 5.17 6.98 42
for me its:
11.33 10.75 6.00 5.65 55
12.08 9.00 6.23 4.81 26
10.66 12.31 5.79 6.41 29
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Fritzlein
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Arimaa player #706
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Re: Statistic wanted: Average pieces remaining
« Reply #17 on: Dec 10th, 2004, 11:38am » |
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I'm not sure if the differences between us are statistically significant, but if they are, then 99of9 has more captures per game than the rest of us. I will go out on a limb to suggest that this isn't correlated to game length, i.e. it doesn't happen because his games are longer than ours, but rather results from a greater density of captures.
I guess that would be another statistic of potential interest: the number of captures per 100 moves. I'll bet you are higher in that category than any of us, Paul.
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| « Last Edit: Dec 10th, 2004, 11:38am by Fritzlein » |
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PMertens
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Arimaa player #692
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Re: Statistic wanted: Average pieces remaining
« Reply #18 on: Dec 10th, 2004, 6:00pm » |
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average moves and captures per move (gold/silver)
total
45.0436 0.1149 0.1139 436
45.7626 0.1492 0.0772 219
44.3180 0.0802 0.1509 217
Fritzlein
47.2561 0.1125 0.1182 82
48.2000 0.1573 0.0596 40
46.3571 0.0699 0.1740 42
99of9
49.0952 0.1274 0.1354 63
53.9375 0.1515 0.0988 32
44.0968 0.1026 0.1732 31
PMertens
43.4727 0.1312 0.1128 55
48.1538 0.1564 0.0870 26
39.2759 0.1086 0.1359 29
no guarantees
thats like before games with person involved ...
if persons plays gold and wins its:
99of9: 56.9583 0.1598
Fritzlein: 48.4444 0.1823
PMertens: 52.0000 0.1117
I got only 8 games where I won against 1700+
2 "no kill"-game against 'nator - without the its more like 0.1611
anyway your prediction seems wrong and you go out on a limb ?
(I hope its not my mistake)
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Fritzlein
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Re: Statistic wanted: Average pieces remaining
« Reply #19 on: Dec 10th, 2004, 8:42pm » |
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On the contrary, my prediction was at least partially right. 99of9 has a higher density of captures in his games than I do in mine, and you have the highest capture density of all.
When you cut it down to a specific person playing gold and winning, the numbers may be getting so small as to be not very significant statistically, as you point out with your two captureless wins against Arimaanator throwing off your statistics.
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mouse
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Re: Statistic wanted: Average pieces remaining
« Reply #20 on: Jan 17th, 2005, 11:19am » |
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The reason why the number of pieces remaining is interesting is a high number of remaining pieces makes it difficult to produce a endgame database. But in principle there can be a high number of remaining pieces on average but still be a significant number of games with only a few pieces remaining. If this is the cases there could still be some advantages of producing a endgame database.
So I wonder how big a percentage of the games has ended with 10 or less pieces remaining? This seems to me to be the relevant number of pieces it would be possible to make a endgame database for at this time. Of course this number will increase over time.
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MrBrain
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Re: Statistic wanted: Average pieces remaining
« Reply #21 on: Jan 17th, 2005, 2:40pm » |
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I don't think there's any way you could make anywhere close to a 10-piece database. Chess has similar pieces to arimaa, but they can only do something like 6-piece databases. Checkers (American version) just recently completed a 10-piece database, but there's only two kinds of pieces.
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Fritzlein
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Re: Statistic wanted: Average pieces remaining
« Reply #22 on: Jan 18th, 2005, 2:42am » |
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I agree that anything larger than 6-piece endgame tablebases will be tough, and 6-piece endgames almost never come up. I suspect there have been about 2 in 11000 games so far, apart from losers Arimaa. Something drastic would have to change about how Arimaa games are played before chess-like endgames come into play.
Even so, I would be curious what the tablebases say about several endgames, including the simplest one: ER vs. E. This could be a good little warmup project that is actually small enough to assign in a computer science course.
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mouse
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Re: Statistic wanted: Average pieces remaining
« Reply #23 on: Jan 18th, 2005, 4:07am » |
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I agree that it will probably not be possible to make a complete database of all endgames with 10 pieces remaining for the moment but it should be in the duration of the Arimaa challenge. Hence I think it is a relevant question.
on Jan 18th, 2005, 2:42am, Fritzlein wrote:I agree that anything larger than 6-piece endgame tablebases will be tough, and 6-piece endgames almost never come up. I suspect there have been about 2 in 11000 games so far, apart from losers Arimaa.
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I think that a endgame with less than 6 pieces on the board is more common than that. At least I can remember 3 recent games. GnoBot against Arimaanator, Naveed against Speedy and bleitner against Arimaanator + Belbo against Bomb2004CC with 7 pieces.
on Jan 18th, 2005, 2:42am, Fritzlein wrote:Even so, I would be curious what the tablebases say about several endgames, including the simplest one: ER vs. E. This could be a good little warmup project that is actually small enough to assign in a computer science course.
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Another interesting project could be to test whether or not bleitners game against Arimaanator was a draw. So to make a endgame database for E+R against E+R+C(or another pieces).
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| « Last Edit: Jan 18th, 2005, 4:08am by mouse » |
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MrBrain
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Re: Statistic wanted: Average pieces remaining
« Reply #24 on: Jan 18th, 2005, 3:09pm » |
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on Jan 18th, 2005, 4:07am, mouse wrote:So to make a endgame database for E+R against E+R+C(or another pieces).
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This does bring up an interesting point about Arimaa, which is the effective equivalence of intermediate pieces. For example, a position with E+M+R against E+R is equivalent to say E+H+R against E+R. This could lead to a reduction in the number of positions that must be computed compared with chess.
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mouse
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Re: Statistic wanted: Average pieces remaining
« Reply #25 on: Jan 18th, 2005, 3:19pm » |
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I think it will mainly simplify the task in the case with very few pieces. In the cases with 5 pieces on both sides, there will likely by something like E+R+R and 2 different other pieces against E+R+R+R+another piece or E+R + 3 other (different) pieces.
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Fritzlein
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Re: Statistic wanted: Average pieces remaining
« Reply #26 on: Sep 2nd, 2005, 6:44pm » |
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As JDB was educating me about how searching works, it occurred to me that the statistic of captures per game (as I originally asked for) is not as relevant as the number of captures per ply. That is to say, the moves which really help the alpha-beta pruning are the ones which are obviously better or obviously worse than others (i.e. captures, most often), so it is important to know how often a ply will contain a capture move.
I don't know how to calculate how much alpha-beta pruning helps out in Arimaa, but I wrote a little program to calculate how often a step actually results in a capture. Among rated games in 2004 and 2005, only 3% of steps resulted in captures. That is staggeringly low compared to chess.
Do other folks think this stat is relevant? I think I'm going to update the Wikipedia article to include it.
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