Perft(13) betting pool

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Sven
Posts: 3578
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Location: Berlin, Germany

Re: Perft(13) betting pool

Post by Sven » Mon Jul 11, 2011 7:02 pm

JuLieN wrote:
Daniel Shawul wrote:Yes so far Uri or HG are looking good. Me and Julien (if I may) are fillers :)
By the way you and also Juline seem to take into consideration the odd-even effect. Isn't that for alpha-beta only ? perft is min-max
If you look at the graph, you'll see that there is an odd-even effect. Now where does it come from? From the fact that black is a ply late compared with white? Is this another evidence that white has an advantage by starting the game? Will this effect eventually disappear after a while?

And by the way, would the interpolation curve allow us to determine the medium duration of a game, or would it change its general shape with time instead of being symetrical?
One possible explanation for the odd-even effect might be that there are many move sequences from the starting position that keep white and black pieces totally decoupled from each other so that black frequently has about the same number of move choices as white in the previous ply. But then, for the next ply, white will now have increased its choices, presumably after having "developed" one more piece. At some point this effect will smoothly disappear (this might be the real border to "middlegame" :-) ), when the increase of average piece mobility has becomes less likely than the interference between white and black moves. Based on my interpolation I would currently expect this at ply 22/23 where the BF would settle at about 33. But I know this is "Hocus Pocus", so in fact I won't bet on it, nor on any attempt to predict an "average game duration".

Sven

Sven
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Re: Perft(13) betting pool

Post by Sven » Mon Jul 11, 2011 7:04 pm

Daniel Shawul wrote:Btw your plot is for an even ply (12), may be it will be different for ply(11)
Julien's plot is for all plies from 1 up to 12, based on the known perft(1) .. perft(12) values.

Sven

Daniel Shawul
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Re: Perft(13) betting pool

Post by Daniel Shawul » Mon Jul 11, 2011 7:09 pm

Hmm..I am too confused today :(

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hgm
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Re: Perft(13) betting pool

Post by hgm » Mon Jul 11, 2011 7:54 pm

From the opening position, your own moves on the average develop pieces, giving them more moves. Pawn moves unblock them, moving from behind the Pawn wall opens other directions to them, etc. Opponent moves have no such effects on your moility. His Pawns nd pieces are normally not blocking your pieces, and they are in fact more likely to block them after they move. And worse of all, they might capture your developed pieces, so your mobility takes another hit.

So your mobility increases a lot when you move, and decreases a little bit when the opponent moves. That means the number of moves you have depends on the number of moves you did so far. Which is the same for the white and black move with the same move number. But the black move suffers a little bit from the fact that white has already done one move more by the time it is his turn.

Uri Blass
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Re: Perft(13) betting pool

Post by Uri Blass » Mon Jul 11, 2011 8:01 pm

Daniel Shawul wrote:Hopefull again after seeing Uri's result 1.997*10^18 is more closer to my value 2*10^18 than to yours. Sven's estimate however is close to yours.
All that I have to do now is bet smart with the standard deviation. Are you sure you like your sd ? :)
I think the following:

1)H.G.Muller's method is probably better than my method
2)More games with my method are needed for a better estimate
to get a smaller error and the program that Sven used to generate the estimate use full makemove and is clearly not optimized for generating estimates.

Daniel Shawul
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Re: Perft(13) betting pool

Post by Daniel Shawul » Mon Jul 11, 2011 9:09 pm

My "improved" estimate is now 2.04*10^18 from calculating each move's BF. Doing that for the total nodes searched gave a much lower 1.94*10^14 so I prefer the new estimate. Additional credit for calculating each move's nodes ?:)

Code: Select all

			perft(11)		perft(12)				
	m1	m2	count						
	a2a3	a7a5	2490170591441	a7a5	72665331130084	13.39460522	14.29257911	15.190553	2293277425253770
	a2a3	a7a6	1860954056181	a7a6	52240581495625	13.04459241	13.90488283	14.76517325	1585262227934740
	a2a3	b7b5	2441922142492	b7b5	70832193411277	13.37080138	14.26217926	15.15355715	2221721843568800
	a2a3	b7b6	2402995112291	b7b6	68828719890548	13.35128264	14.22811853	15.10495441	2130847871799050
	a2a3	b8a6	2132744059006	b8a6	61140891499069	13.20725651	14.08837752	14.96949852	1895371177652800
	a2a3	b8c6	2697902252015	b8c6	79580647397864	13.49252688	14.40126435	15.31000182	2539090314080590
	a2a3	c7c5	2958457569388	c7c5	88953429066195	13.60608605	14.53550834	15.46493062	2894167674976420
	a2a3	c7c6	2648687762208	c7c6	79328915867793	13.46996394	14.39746263	15.32496132	2571532579782220
	a2a3	d7d5	5577971560157	d7d5	182556087468747	14.41353717	15.43297644	16.45241572	6471214125234350
	a2a3	d7d6	4363682786084	d7d6	130494144657416	14.09540507	15.00718555	15.91896602	4215927410168320
	a2a3	e7e5	6582848832572	e7e5	218781166802947	14.6322244	15.66754057	16.70285673	7875530687676390
	a2a3	e7e6	6513293932180	e7e6	214642037503057	14.61810142	15.64262252	16.66714362	7659409849825030
	a2a3	f7f5	2091957988668	f7f5	59111707329682	13.18409334	14.0488074	14.91352146	1805271992077450
	a2a3	f7f6	1681297435361	f7f6	44562128777067	12.92475239	13.72188665	14.51902091	1274046554651800
	a2a3	g7g5	2267166109628	g7g5	63838870856898	13.28084653	14.13916512	14.99748372	1941955118342300
	a2a3	g7g6	2468961409498	g7g6	71531672456757	13.38419358	14.27386325	15.16353291	2240810740333470
	a2a3	g8f6	2673865279427	g8f6	77737501513793	13.48155403	14.37316953	15.26478504	2443312445347090
	a2a3	g8h6	2138996265326	g8h6	61472317703694	13.2107716	14.09472583	14.97868005	1910539740419350
	a2a3	h7h5	2552311861490	h7h5	75046500179133	13.42465295	14.33103435	15.23741575	2386970906245610
	a2a3	h7h6	1857105882411	h7h6	52051331873986	13.0421379	13.90067813	14.75921835	1576970798971880
									
	a2a4	a7a5	2704594653270	a7a5	77778262385061	13.49556613	14.37379742	15.25202871	2416901673647010
	a2a4	a7a6	2594760709819	a7a6	72765171767241	13.44479861	14.29421456	15.1436305	2202876035691940
	a2a4	b7b5	4274118995132	b7b5	124685845205799	14.06885594	14.95035239	15.83184884	3925647066636260
	a2a4	b7b6	3460506418911	b7b6	99506957116457	13.80135691	14.67194827	15.54253963	3088771528766790
	a2a4	b8a6	3035472405970	b8a6	87518398685605	13.63791077	14.51582132	15.39373186	2725655269534350
	a2a4	b8c6	3753020724759	b8c6	110935308713286	13.90354485	14.8054797	15.70741454	3542918578329300
	a2a4	c7c5	4154387427658	c7c5	124923810649497	14.03256296	14.95272807	15.87289318	4060029749485700
	a2a4	c7c6	3695958968906	c7c6	110486927467621	13.88419323	14.80048367	15.71677411	3570461428126670
	a2a4	d7d5	7987342923715	d7d5	261933284151767	14.89174759	15.90434876	16.91694993	9293661113906230
	a2a4	d7d6	6267885152140	d7d6	187847228615832	14.56715157	15.46976558	16.37237959	6073701804812430
	a2a4	e7e5	9091003079745	e7e5	303014980335516	15.06800025	16.09862096	17.12924166	10929386237254000
	a2a4	e7e6	8985044803750	e7e6	296778862396787	15.0519494	16.07074761	17.08954581	10604660480562400
	a2a4	f7f5	2954358030495	f7f5	83496412660445	13.60437097	14.4590242	15.31367744	2547026337242240
	a2a4	f7f6	2380569002864	f7f6	63150846993516	13.33990687	14.12640322	14.91289956	1804293593293180
	a2a4	g7g5	3210254021991	g7g5	90450613726530	13.70749598	14.55574012	15.40398427	2749348944662230
	a2a4	g7g6	3486398694765	g7g6	101120597009803	13.81071285	14.69162954	15.57254623	3167197708051820
	a2a4	g8f6	3779345461854	g8f6	109964266892237	13.91238246	14.79463648	15.6768905	3454450905452000
	a2a4	g8h6	3021336717900	g8h6	86899022556653	13.63212492	14.5072326	15.38234028	2699550064829590
	a2a4	h7h5	3600488537669	h7h5	105917371652320	13.85120009	14.74848009	15.64576009	3366329830931980
	a2a4	h7h6	2617494395751	h7h6	73390162544065	13.45546483	14.30440576	15.15334669	2221320740158570
									
	b1a3	a7a5	2998408533739	a7a5	87112726457222	13.6226877	14.51020229	15.39771689	2734842324067190
	b1a3	a7a6	2191612559252	a7a6	61211806080331	13.23998876	14.0897385	14.93948824	1846564018478420
	b1a3	b7b5	2789256409584	b7b5	80265837110112	13.53343496	14.41155671	15.28967845	2495620694455790
	b1a3	b7b6	2799165628378	b7b6	79486175018475	13.53779877	14.39983889	15.26187902	2437272482560900
	b1a3	b8a6	2464959342683	b8a6	70164254747876	13.38221984	14.25092298	15.11962613	2157911749106020
	b1a3	b8c6	3132579337260	b8c6	91710661510033	13.67700791	14.57253092	15.46805393	2901775497659080
	b1a3	c7c5	3426179031597	c7c5	101956640896317	13.78885443	14.70171366	15.61457289	3280132755548850
	b1a3	c7c6	3095764582250	c7c6	92057453487994	13.66231697	14.57711499	15.49191302	2960503970227140
	b1a3	d7d5	6579029121397	d7d5	213782760833766	14.63145235	15.63739441	16.64333647	7518394495716620
	b1a3	d7d6	5141418848126	d7d6	152569571614918	14.30714566	15.20392297	16.10070028	4886320519194050
	b1a3	e7e5	7420367747309	e7e5	245413911922747	14.79240114	15.8182438	16.84408646	8786522094364010
	b1a3	e7e6	7329868644724	e7e6	240156512798893	14.77590871	15.78972371	16.80353871	8515492285480570
	b1a3	f7f5	2440597347251	f7f5	68386284663519	13.37014177	14.22047438	15.07080698	2069067221266150
	b1a3	f7f6	1965798356509	f7f6	51715576377483	13.10975126	13.89318378	14.67661631	1466010997159380
	b1a3	g7g5	2652993780206	g7g5	74156576416427	13.47195323	14.31679499	15.16163674	2237170750206180
	b1a3	g7g6	2885619153844	g7g6	82992220161143	13.57528641	14.4517281	15.32816978	2578540333968630
	b1a3	g8f6	3127063653396	g8f6	90221933390595	13.6748169	14.55266987	15.43052284	2811566393974650
	b1a3	g8h6	2496011135572	g8h6	71156085799766	13.3974582	14.2676026	15.13774699	2191775912854710
	b1a3	h7h5	2979246425479	h7h5	86892547773711	13.61475013	14.50714252	15.39953491	2739043062004750
	b1a3	h7h6	2164860429612	h7h6	60202664686828	13.22521431	14.07023365	14.915253	1807998718212130
									
	b1c3	a7a5	3780055952064	a7a5	108906368196855	13.91262021	14.78272302	15.65282582	3386146819116070
	b1c3	a7a6	2833513005135	a7a6	78676358383620	13.5528167	14.38755579	15.22229489	2356360326926130
	b1c3	b7b5	3579740360135	b7b5	102185619671872	13.84392475	14.70446231	15.56499987	3147303171154960
	b1c3	b7b6	3627872380722	b7b6	102560000180389	13.8607441	14.70894422	15.55714434	3126716146223180
	b1c3	b8a6	3202933435947	b8a6	90758239085058	13.70465137	14.55985908	15.4150668	2775174801602590
	b1c3	b8c6	4038709426025	b8c6	117590239133269	13.99658401	14.87753359	15.75848317	3695620424858880
	b1c3	c7c5	4673523038061	c7c5	139185758453322	14.1835797	15.08804255	15.99250539	4476252487267630
	b1c3	c7c6	4132170654683	c7c6	122505336153024	14.02572422	14.9283881	15.83105199	3923079198746100
	b1c3	d7d5	8609528039799	d7d5	280324148882774	14.99364463	15.99453834	16.99543205	9870035727681740
	b1c3	d7d6	6721024593427	d7d6	198772677238487	14.65988281	15.54281665	16.42575049	6336185460912810
	b1c3	e7e5	9734312019845	e7e5	319396782574956	15.16194874	16.16941142	17.17687409	11331142974101500
	b1c3	e7e6	9673949983287	e7e6	315156256587375	15.15337741	16.15141196	17.14944651	11098170777801100
	b1c3	f7f5	3194995401764	f7f5	89324486777629	13.70156015	14.54055145	15.37954275	2693174586844690
	b1c3	f7f6	2562043660418	f7f6	67204161826865	13.42929829	14.19982572	14.97035315	1896778372513340
	b1c3	g7g5	3426367497609	g7g5	95191429602316	13.78892338	14.61783832	15.44675326	2850255039540170
	b1c3	g7g6	3726438023071	g7g6	106545180770398	13.89456325	14.75574532	15.61692739	3286568477725550
	b1c3	g8f6	4024438317949	g8f6	115505065598737	13.99208059	14.85536816	15.71865572	3576022353368990
	b1c3	g8h6	3240273318363	g8h6	91933283370793	13.71909944	14.57547547	15.4318515	2814715223194400
	b1c3	h7h5	3863264762126	h7h5	112124844055370	13.94018664	14.81864478	15.69710292	3512801232503040
	b1c3	h7h6	2806400656142	h7h6	77655399822670	13.54097606	14.37190391	15.20283177	2317492656146290
									
	b2b3	a7a5	3392746291242	a7a5	99703595086608	13.77656783	14.67436222	15.5721566	3166167701351230
	b2b3	a7a6	2469931985467	a7a6	69488231228498	13.38467181	14.23942999	15.09418818	2111187857524490
	b2b3	b7b5	3151467717621	b7b5	91223879261746	13.6844845	14.56606951	15.44765452	2852417706050720
	b2b3	b7b6	3193820815740	b7b6	91681330906227	13.70110215	14.57214249	15.44318282	2841702218002610
	b2b3	b8a6	2797897757258	b8a6	80458176033797	13.53724121	14.41443139	15.29162156	2499746914217850
	b2b3	b8c6	3545526713842	b8c6	104829482106135	13.83184359	14.73579666	15.63974973	3349557118677950
	b2b3	c7c5	3931512931660	c7c5	118726060034807	13.96239672	14.88945625	15.81651578	3876507661846320
	b2b3	c7c6	3506861529421	c7c6	104999996358379	13.81806232	14.73779259	15.65752287	3399379959031820
	b2b3	d7d5	7500785612313	d7d5	246268851935772	14.80690364	15.82282861	16.83875357	8750426815262220
	b2b3	d7d6	5841814524668	d7d6	175576169231529	14.47422273	15.38292057	16.2916184	5695540935742860
	b2b3	e7e5	8260975132155	e7e5	275532636219159	14.93741937	15.97157532	17.00573127	9948075129143260
	b2b3	e7e6	8330314205186	e7e6	275160001120401	14.94877414	15.96977419	16.99077423	9834928317246880
	b2b3	f7f5	2784806563374	f7f5	78819639073981	13.53147075	14.38973745	15.24800416	2408624072614480
	b2b3	f7f6	2223872954788	f7f6	59187737478412	13.25758875	14.05031232	14.8430359	1697444528247390
	b2b3	g7g5	3053406633605	g7g5	86226025100059	13.64521623	14.49783648	15.35045674	2627706927887970
	b2b3	g7g6	3304237301841	g7g6	96027558980297	13.74350119	14.62849533	15.51348947	3014556577126850
	b2b3	g8f6	3532224248451	g8f6	102925470984976	13.82711773	14.71330503	15.59949232	3239187154463750
	b2b3	g8h6	2843083658936	g8h6	81899397746760	13.55697186	14.43577349	15.31457512	2548967996997960
	b2b3	h7h5	3386854648570	h7h5	99790318581093	13.77439124	14.67542546	15.57645967	3177560407150650
	b2b3	h7h6	2458184799219	h7h6	68990292060239	13.37887212	14.23089886	15.08292559	2090800767083130
									
	b2b4	a7a5	4214199334835	a7a5	124714790868246	14.0508103	14.95064159	15.85047287	3986106538695820
	b2b4	a7a6	2534135536803	a7a6	70967692472406	13.41593343	14.26445085	15.11296828	2145591397572970
	b2b4	b7b5	2510632775992	b7b5	71432265477277	13.40457403	14.27220917	15.13984431	2195726882340970
	b2b4	b7b6	3168206992805	b7b6	89981827453815	13.69107644	14.54943853	15.40780063	2758217130904410
	b2b4	b8a6	2823139118362	b8a6	80317944517769	13.54829838	14.41233612	15.27637387	2467536699549540
	b2b4	b8c6	3543231212640	b8c6	103534931545894	13.83102924	14.72054565	15.61006206	3267835493045620
	b2b4	c7c5	5005816841824	c7c5	151800319146164	14.27242348	15.19752	16.12261653	4973496529954990
	b2b4	c7c6	3689572411914	c7c6	109547072782694	13.88201045	14.78995087	15.6978913	3515095479473580
	b2b4	d7d5	7480064221874	d7d5	243244158746903	14.80318033	15.80654195	16.80990357	8557519333207300
	b2b4	d7d6	5971634511894	d7d6	179009748816733	14.50317275	15.40776775	16.31236276	5790543401920480
	b2b4	e7e5	7826183695293	e7e5	257520753105329	14.86417852	15.88184742	16.89951633	9169920625838060
	b2b4	e7e6	7877602808973	e7e6	256671145158687	14.87303027	15.87747438	16.88191849	9046558358892250
	b2b4	f7f5	2802100009348	f7f5	78511529598780	13.53908831	14.38504152	15.23099474	2373927685987780
	b2b4	f7f6	2244501309336	f7f6	59260582516917	13.26872149	14.05175254	14.83478359	1685216870582410
	b2b4	g7g5	3085721951365	g7g5	86633872498825	13.65828189	14.50353867	15.34879546	2624012387079760
	b2b4	g7g6	3333196448322	g7g6	96218859571020	13.75440794	14.63092162	15.5074353	2999298656913400
	b2b4	g8f6	3565234358363	g8f6	103101015466315	13.83881541	14.71539458	15.59197376	3218950042824040
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	h2h4	g7g5	4140088084305	g7g5	117634502885289	14.02816518	14.8780002	15.72783521	3603266246413620
	h2h4	g7g6	3606352273893	g7g6	104715522171468	13.8532493	14.73446106	15.61567281	3283137794832080
	h2h4	g8f6	3811697656815	g8f6	110823970590036	13.92316726	14.80424086	15.68531445	3478660012403890
	h2h4	g8h6	3122711452039	g8h6	90052762990721	13.67308559	14.550394	15.42770242	2804892954315660
	h2h4	h7h5	2810849732357	h7h5	81300261025135	13.5429262	14.42694341	15.31096062	2541158269423590
	h2h4	h7h6	2630485414415	h7h6	73538385526439	13.46152222	14.30681103	15.15209984	2218945853053790
									
			2.09765E+15		6.2855E+16				2039797540246810000
									25.61119095
			24.71068812		25.11086278			25.51103744	
			24.617706		25.025674			25.433642	
									
			2.09765E+15		6.2855E+16			1.9385E+18	
			2.09765E+15		6.2855E+16			1.93969E+18	
Last edited by Daniel Shawul on Mon Jul 11, 2011 9:21 pm, edited 1 time in total.

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Re: Perft(13) betting pool

Post by Daniel Shawul » Mon Jul 11, 2011 9:12 pm

Here is the same observation from by francois with the same zig-zag plot
http://wismuth.com/chess/statistics-games.html

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Re: Perft(13) betting pool

Post by Daniel Shawul » Mon Jul 11, 2011 9:20 pm

I am afraid so. Another guy also estimated using what he called "random pruning" a value of 1.981 & 10^18, but who knows these methods may have blind spots which can only be revealed when the number is revealed.
2)More games with my method are needed for a better estimate
to get a smaller error and the program that Sven used to generate the estimate use full makemove and is clearly not optimized for generating estimates.
Yes you need a legal-move generator for bulk counting, may be iperft can help there. There is still time to do more games anyway.

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Re: Perft(13) betting pool

Post by hgm » Mon Jul 11, 2011 9:27 pm

It sounds like this guy is using exactly the same method as I do.

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Re: Perft(13) betting pool

Post by Daniel Shawul » Mon Jul 11, 2011 9:33 pm

Sounds like it. He is a researcher in mathematics http://wismuth.com/ so you guys think alike I guess. But he only said "random pruning" so we can't know where he starts pruning, by how much he prunes (N = 16) and other details..

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