Perft(13) betting pool

[Sven]

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]

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]

Hmm..I am too confused today

[hgm]

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]

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]

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
	b2b4	g8h6	2860973277032	g8h6	81591532694267	13.56470476	14.4312436	15.29778244	2512871276103570
	b2b4	h7h5	3409031058957	h7h5	99539774200319	13.7825662	14.67235144	15.56213668	3139785143961700
	b2b4	h7h6	2474130685279	h7h6	68758101660174	13.38673866	14.22690145	15.06706424	2062397240548530
									
	c2c3	a7a5	3805833679230	a7a5	109707505907822	13.92121866	14.79175467	15.66229068	3412861293224750
	c2c3	a7a6	2855601945870	a7a6	79064925249030	13.56238759	14.39346387	15.22454015	2360882602033830
	c2c3	b7b5	3803985735864	b7b5	109643897255738	13.92060402	14.79103979	15.66147556	3410552985595320
	c2c3	b7b6	3675184413522	b7b6	103955280568953	13.87708036	14.72551682	15.57395329	3170919968634970
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	f2f4	b8c6	3080116882427	b8c6	90452720906517	13.65602461	14.55576838	15.45551215	2871337301757620
	f2f4	c7c5	3360073894844	c7c5	100426318478322	13.76445386	14.6831971	15.60194034	3245801568248480
	f2f4	c7c6	2988091870384	c7c6	89073781956231	13.61841995	14.53714618	15.45587242	2872207516129460
	f2f4	d7d5	6251457198685	d7d5	203227089554421	14.56367651	15.57154839	16.57942028	7151570588830580
	f2f4	d7d6	4929661802059	d7d6	146946105539601	14.25254648	15.15641564	16.06028481	4729248719381120
	f2f4	e7e5	8012065908836	e7e5	263580357905865	14.89593207	15.91265891	16.92938574	9382868043649840
	f2f4	e7e6	6555007293484	e7e6	210673252801486	14.62658759	15.61831281	16.61003802	7325177397314280
	f2f4	f7f5	1852887585712	f7f5	51451345032010	13.03944199	13.8872545	14.735067	1543751860811640
	f2f4	f7f6	1927567505546	f7f6	50932537770092	13.08636575	13.87553092	14.6646961	1450607356505840
	f2f4	g7g5	3284766701770	g7g5	93418107742001	13.73611911	14.59494924	15.45377937	2867155173236820
	f2f4	g7g6	2846766260326	g7g6	82059877870086	13.55856729	14.43812859	15.3176899	2555715750878240
	f2f4	g8f6	3025285961546	g8f6	88094345261522	13.63374385	14.52375796	15.41377207	2772146146313430
	f2f4	g8h6	2368172336968	g8h6	67831080969382	13.33357671	14.21081748	15.08805825	2100069060094480
	f2f4	h7h5	2907712025120	h7h5	85205287829675	13.58470233	14.48345627	15.3822102	2699253321340430
	f2f4	h7h6	2107802937505	h7h6	58618161993812	13.19314034	14.0389949	14.88484947	1760669375526070
									
	g1f3	a7a5	3753409830676	a7a5	109162481044862	13.90367589	14.78561692	15.66755794	3427812233604920
	g1f3	a7a6	2770139087782	a7a6	77292941915066	13.52497612	14.36630183	15.20762754	2327014420090400
	g1f3	b7b5	3586015209700	b7b5	103253053151632	13.84612906	14.7172017	15.58827433	3209035512524560
	g1f3	b7b6	3571832395015	b7b6	101614863990448	13.84114173	14.69760044	15.55405915	3118664804108540
	g1f3	b8a6	3155894118512	b8a6	90078169579744	13.68623071	14.55073605	15.41524139	2775583442231890
	g1f3	b8c6	3971526687066	b8c6	116418827037198	13.97525598	14.86512624	15.75499649	3685004649130250
	g1f3	c7c5	4480294436827	c7c5	134405219773799	14.12923921	15.04416234	15.95908548	4356161877846340
	g1f3	c7c6	3983485524791	c7c6	118824827992751	13.97907634	14.89048807	15.80189979	3830195517710220
	g1f3	d7d5	8271240847062	d7d5	268329275238247	14.93910591	15.93635534	16.93360477	9413311874280170
	g1f3	d7d6	6591769371530	d7d6	196479858403060	14.63402587	15.5277967	16.42156753	6315241138891050
	g1f3	e7e5	9753646891597	e7e5	324620019503379	15.16468405	16.19128342	17.21788279	11687906046763500
	g1f3	e7e6	9536400329338	e7e6	312971265310368	15.13366245	16.14205064	17.15043883	11106521980856400
	g1f3	f7f5	3135512850898	f7f5	87848163003436	13.67817177	14.52037136	15.36257095	2654793360427460
	g1f3	f7f6	2514485879664	f7f6	66268672145028	13.40644293	14.18324775	14.96005256	1879881843957310
	g1f3	g7g5	3393349225371	g7g5	95124165550470	13.77679039	14.61697727	15.45716415	2875329688366220
	g1f3	g7g6	3665542792013	g7g6	105517492965827	13.8737668	14.74383194	15.61389709	3278287699612200
	g1f3	g8f6	4027549726209	g8f6	116613625465479	13.99306367	14.86719741	15.74133115	3643669006537920
	g1f3	g8h6	3212552957717	g8h6	91840225266988	13.70838807	14.57424542	15.44010276	2834343123316120
	g1f3	h7h5	3773866880671	h7h5	109982481273195	13.91054784	14.79484068	15.67913352	3460881749056910
	g1f3	h7h6	2784531346525	h7h6	77702412690627	13.53134917	14.37262878	15.21390839	2339539377429620
									
	g1h3	a7a5	2983959169540	a7a5	86751124601788	13.6167066	14.50517344	15.39364028	2725444479413930
	g1h3	a7a6	2205526414009	a7a6	61551859184193	13.2476083	14.09624474	14.94488117	1855248384714770
	g1h3	b7b5	2846198115239	b7b5	82004404737202	13.55832127	14.43731498	15.3163087	2552721528702640
	g1h3	b7b6	2851307360414	b7b6	81161727207899	13.56053208	14.42489321	15.28925434	2494720926021030
	g1h3	b8a6	2505051591829	b8a6	71429018900998	13.40186233	14.27215511	15.1424479	2200640715711240
	g1h3	b8c6	3182196254756	b8c6	93380276202472	13.69656118	14.5944566	15.49235203	2961594792705570
	g1h3	c7c5	3527392570078	c7c5	105530929921313	13.82539722	14.7439884	15.66257957	3413679746931940
	g1h3	c7c6	3158751563223	c7c6	94174814456752	13.68735679	14.6047647	15.52217261	3036565217997450
	g1h3	d7d5	6598437035501	d7d5	214946643861536	14.63537094	15.64447123	16.65357153	7578722876145020
	g1h3	d7d6	5172596013514	d7d6	153997481564535	14.31501104	15.21573029	16.11644955	4948822164476250
	g1h3	e7e5	7550082279630	e7e5	249284938805459	14.81572405	15.83888735	16.86205065	8909125233072360
	g1h3	e7e6	7420897316330	e7e6	242489703908586	14.7924971	15.80245062	16.81240414	8574082841557240
	g1h3	f7f5	2415371417328	f7f5	67415968718962	13.35751932	14.2035498	15.04958028	2031501012261380
	g1h3	f7f6	1977820118684	f7f6	52073117173671	13.11701946	13.90116286	14.68530626	1477335399131700
	g1h3	g7g5	2692355192719	g7g5	75638824672128	13.49000256	14.34042638	15.1908502	2293860775657570
	g1h3	g7g6	2925820472523	g7g6	84238167879211	13.59237172	14.46968498	15.34699823	2620020925769580
	g1h3	g8f6	3189961862519	g8f6	92332416842324	13.69959637	14.58073836	15.46188035	2886755533146970
	g1h3	g8h6	2535337090711	g8h6	72410877360410	13.41651159	14.28840168	15.16029177	2234592193250720
	g1h3	h7h5	3088421638153	h7h5	90315875696709	13.65936779	14.553932	15.44849621	2854438813847590
	g1h3	h7h6	2218784201934	h7h6	61931135196799	13.25482801	14.10346267	14.95209733	1866927707066660
									
	g2g3	a7a5	3462042063272	a7a5	101143479417071	13.80191358	14.69190656	15.58189953	3192017013929730
	g2g3	a7a6	2558093963139	a7a6	71687959685730	13.4274149	14.27645952	15.12550415	2168843256847630
	g2g3	b7b5	3347159357670	b7b5	96937643533392	13.75963598	14.6399987	15.52036142	3031962290935270
	g2g3	b7b6	3332271634289	b7b6	95410047910027	13.75406097	14.62063301	15.48720505	2948829286963060
	g2g3	b8a6	2913902489708	b8a6	83531892698009	13.58732903	14.45953611	15.33174319	2586365921340770
	g2g3	b8c6	3669701347445	b8c6	108188016556602	13.87519695	14.77457272	15.67394849	3446032715109900
	g2g3	c7c5	4080540803847	c7c5	122476858285782	14.00970157	14.92809888	15.84649619	3973125273169150
	g2g3	c7c6	3613100109803	c7c6	108065973644676	13.85560373	14.77318311	15.69076249	3494400129381530
	g2g3	d7d5	7492061645416	d7d5	244765168230904	14.80533722	15.81475499	16.82417275	8652435054715990
	g2g3	d7d6	5978930494904	d7d6	178550417555891	14.50478273	15.40446923	16.30415574	5752784382520040
	g2g3	e7e5	9034320840980	e7e5	300345292387514	15.05943515	16.08675333	17.1140715	10804220732991200
	g2g3	e7e6	8863546280836	e7e6	292317793673444	15.03333131	16.05047678	17.06762225	10429159019634800
	g2g3	f7f5	2887504270582	f7f5	81719890071911	13.5760924	14.43313414	15.29017587	2496676369734430
	g2g3	f7f6	2309333928674	f7f6	61073379996908	13.30311482	14.0870805	14.87104618	1739561504924750
	g2g3	g7g5	3104044182919	g7g5	87113692726148	13.66563474	14.51021571	15.35479667	2637381219206540
	g2g3	g7g6	3401127309207	g7g6	98450494010483	13.77965818	14.65890369	15.53814921	3077448105775630
	g2g3	g8f6	3663605248960	g8f6	106314238303473	13.87309997	14.75307735	15.63305472	3330964668305960
	g2g3	g8h6	2939400277587	g8h6	84396415977443	13.59809486	14.47194823	15.3458016	2617366440460700
	g2g3	h7h5	3558153588215	h7h5	104638412988316	13.83631455	14.73355658	15.63079862	3324720811716910
	g2g3	h7h6	2553986732598	h7h6	71472940687713	13.42545357	14.27288624	15.12031891	2159197475223770
									
	g2g4	a7a5	3101123892672	a7a5	90104255390618	13.66446545	14.55108715	15.43770885	2828635573389210
	g2g4	a7a6	2288083822645	a7a6	63697273450084	13.29193954	14.13654902	14.98115851	1914653487853300
	g2g4	b7b5	3014401317587	b7b5	86962955421099	13.6292772	14.50812173	15.38696626	2710123113527220
	g2g4	b7b6	2992396204874	b7b6	85308570329092	13.62020217	14.48491848	15.34963479	2625878383064710
	g2g4	b8a6	2609168662709	b8a6	74346372601899	13.45156836	14.31984494	15.18812152	2288510043815020
	g2g4	b8c6	3286537014348	b8c6	96254120986842	13.73679195	14.63136836	15.52594478	3046172424032350
	g2g4	c7c5	3694058778117	c7c5	110810246314544	13.88354415	14.80408807	15.72463199	3593737673543760
	g2g4	c7c6	3251953081105	c7c6	97084855329079	13.72358767	14.64185013	15.5601126	3134480404288070
	g2g4	d7d5	6388692190366	d7d5	207321791906722	14.59245492	15.59745517	16.60245543	7281824340928030
	g2g4	d7d6	5071957660106	d7d6	149951425522576	14.28946488	15.18200802	16.07455116	4784153650430360
	g2g4	e7e5	7722441535346	e7e5	253853503244365	14.84615728	15.86287603	16.87959477	9030383881003300
	g2g4	e7e6	7627152700907	e7e6	249211708642782	14.82940951	15.83849956	16.84758961	8810307686927500
	g2g4	f7f5	3275766238746	f7f5	93412836657688	13.73269322	14.59488061	15.457068	2875097174970050
	g2g4	f7f6	2176294463955	f7f6	57917277183035	13.2315492	14.02492922	14.81830923	1661049196865370
	g2g4	g7g5	2198378721317	g7g5	60888120438021	13.24369954	14.08351457	14.92332959	1820767535473100
	g2g4	g7g6	3007731961919	g7g6	86449817897748	13.6265331	14.50096843	15.37540375	2683767419419230
	g2g4	g8f6	3300672664999	g8f6	95315387917771	13.74215266	14.61942365	15.49669465	2972405002297890
	g2g4	g8h6	2652952491488	g8h6	75580283395814	13.47193417	14.33950115	15.20706812	2325901872173340
	g2g4	h7h5	3970520772231	h7h5	117982667976545	13.97493415	14.88166479	15.78839542	3787860125032720
	g2g4	h7h6	2335902148587	h7h6	65309272482273	13.31695609	14.16602174	15.01508738	1971797135818950
									
	h2h3	a7a5	2505982957208	a7a5	73260246530057	13.40231523	14.30229389	15.20227256	2316384711346130
	h2h3	a7a6	1855923393159	a7a6	52087178055127	13.04138273	13.90147562	14.76156851	1580238306329920
	h2h3	b7b5	2388419449919	b7b5	69179094948589	13.34390009	14.23414022	15.12438035	2166749351055500
	h2h3	b7b6	2391628234190	b7b6	68415649134749	13.34552885	14.22098312	15.09643739	2115281222093500
	h2h3	b8a6	2106198196442	b8a6	60389141405493	13.1922269	14.07386037	14.95549384	1872448390256350
	h2h3	b8c6	2672313740065	b8c6	78822140279150	13.48084268	14.38977551	15.29870833	2514849178478310
	h2h3	c7c5	2963507688158	c7c5	89188732306415	13.60819584	14.53870862	15.4692214	2904623968684320
	h2h3	c7c6	2646757661990	c7c6	79320966034808	13.46907132	14.39734239	15.32561346	2572955520871410
	h2h3	d7d5	5744657915164	d7d5	187657849896090	14.4521715	15.46846532	16.48475914	6638559909590620
	h2h3	d7d6	4525656326258	d7d6	135235518693219	14.14218475	15.05188521	15.96158567	4365042047881750
	h2h3	e7e5	6328330508011	e7e5	210306401043510	14.5798669	15.61604461	16.65222232	7570744768552460
	h2h3	e7e6	6246206986214	e7e6	205704463106172	14.56256417	15.58727902	16.61199387	7336398407912360
	h2h3	f7f5	2081383218980	f7f5	58792545262990	13.17802073	14.04247055	14.90692038	1794911800371760
	h2h3	f7f6	1679359742495	f7f6	44542035614681	12.92339752	13.72137094	14.51934436	1274415582547160
	h2h3	g7g5	2303801720326	g7g5	64950608413048	13.3002145	14.15952231	15.01883011	1978196189514460
	h2h3	g7g6	2461604613575	g7g6	71309420808506	13.38056311	14.27016219	15.15976126	2233575857076670
	h2h3	g8f6	2681701113477	g8f6	77905651056649	13.48514089	14.37575778	15.26637468	2446622246314600
	h2h3	g8h6	2149244850751	g8h6	61683534767995	13.21651337	14.09875524	14.98099711	1914385354426360
	h2h3	h7h5	2517045793000	h7h5	73770742953023	13.40768314	14.31057266	15.21346218	2338647520533300
	h2h3	h7h6	1848155315337	h7h6	51746258222500	13.03641095	13.89387048	14.75133001	1566048920954530
									
	h2h4	a7a5	3608846445097	a7a5	105500114211367	13.85412002	14.74362957	15.63313912	3331198447380730
	h2h4	a7a6	2669482509213	a7a6	74891547461938	13.47954364	14.32856617	15.17758871	2267963898234740
	h2h4	b7b5	3447759267200	b7b5	99848751664463	13.79672745	14.67614137	15.5555553	3122566871314270
	h2h4	b7b6	3448651915597	b7b6	98709976255557	13.79705214	14.66211947	15.5271868	3049341840475640
	h2h4	b8a6	3034131522782	b8a6	87021512667642	13.63736298	14.50893558	15.38050817	2695373183943490
	h2h4	b8c6	3847826735803	b8c6	113526623843569	13.93511319	14.83399552	15.73287785	3618313740995350
	h2h4	c7c5	4262845668242	c7c5	128256515413957	14.06547846	14.98557068	15.9056629	4170355333085870
	h2h4	c7c6	3818245147954	c7c6	114451887528427	13.92533978	14.84403307	15.76272636	3708577623512350
	h2h4	d7d5	8078915869521	d7d5	264231322510205	14.90718822	15.91593016	16.92467211	9348962687198460
	h2h4	d7d6	6351381210950	d7d6	189935366110401	14.5846868	15.48402343	16.38336006	6126870317863310
	h2h4	e7e5	9362283648945	e7e5	311596726321626	15.10833225	16.13613086	17.16392947	11220633447220500
	h2h4	e7e6	9252486968888	e7e6	305348735315816	15.09213812	16.108917	17.12569588	10900011504522700
	h2h4	f7f5	3010450407618	f7f5	85002875391032	13.62765227	14.48058592	15.33351956	2590264247264360
	h2h4	f7f6	2424429686586	f7f6	64232914757489	13.36206559	14.14641743	14.93076928	1832603021124870
	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	

[Daniel Shawul]

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

[Daniel Shawul]

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.

[hgm]

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

[Daniel Shawul]

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..