The number of possible positions in international draughts. This includes positions
that can not be reached by normal gameplay. The given numbers are only
approximations, but are accurate within a few percent.
white:1 black 1 n=8.840
2 pieces: n=8840
white:2 black 1 n=402.690
white:1 black 2 n=402.690
3 pieces: n=805.380
white:3 black 1 n=11.968.100
white:2 black 2 n=17.952.150
white:1 black 3 n=11.968.100
4 pieces: n=41.888.350
white:4 black 1 n=260.955.695
white:3 black 2 n=521.911.390
white:2 black 3 n=521.911.390
white:1 black 4 n=260.955.695
5 pieces: n=1.565.734.170
white:5 black 1 n=4.450.557.420
white:4 black 2 n=11.126.393.550
white:3 black 3 n=14.835.191.400
white:2 black 4 n=11.126.393.550
white:1 black 5 n=4.450.557.420
6 pieces: n=45.989.093.340
white:6 black 1 n=61.812.689.400
white:5 black 2 n=185.438.068.200
white:4 black 3 n=309.063.447.000
white:3 black 4 n=309.063.447.000
white:2 black 5 n=185.438.068.200
white:1 black 6 n=61.812.689.400
7 pieces: n=1.112.628.409.200
white:7 black 1 n=718.723.272.960
white:6 black 2 n=2.515.531.455.360
white:5 black 3 n=5.031.062.910.720
white:4 black 4 n=6.288.828.638.400
white:3 black 5 n=5.031.062.910.720
white:2 black 6 n=2.515.531.455.360
white:1 black 7 n=718.723.272.960
8 pieces: n=22.819.463.916.480
white:8 black 1 n=7.138.082.088.720
white:7 black 2 n=28.552.328.354.880
white:6 black 3 n=66.622.099.494.720
white:5 black 4 n=99.933.149.242.080
white:4 black 5 n=99.933.149.242.080
white:3 black 6 n=66.622.099.494.720
white:2 black 7 n=28.552.328.354.880
white:1 black 8 n=7.138.082.088.720
9 pieces: n=404.491.318.360.800
white:9 black 1 n=61.478.770.147.520
white:8 black 2 n=276.654.465.663.840
white:7 black 3 n=737.745.241.770.240
white:6 black 4 n=1.291.054.173.097.920
white:5 black 5 n=1.549.265.007.717.504
white:4 black 6 n=1.291.054.173.097.920
white:3 black 7 n=737.745.241.770.240
white:2 black 8 n=276.654.465.663.840
white:1 black 9 n=61.478.770.147.520
10 pieces: n=6.283.130.309.076.544
white:10 black 1 n=464647864989440
white:9 black 2 n=2323239324947200
white:8 black 3 n=6969717974841600
white:7 black 4 n=13939435949683200
white:6 black 5 n=19515210329556480
white:5 black 6 n=19515210329556480
white:4 black 7 n=13939435949683200
white:3 black 8 n=6969717974841600
white:2 black 9 n=2323239324947200
white:1 black 10 n=464647864989440
11 pieces: n=86424502888035840
white:11 black 1 n=3110754491120640
white:10 black 2 n=17109149701163520
white:9 black 3 n=57030499003878400
white:8 black 4 n=128318622758726416
white:7 black 5 n=205309796413962240
white:6 black 6 n=239528095816289248
white:5 black 7 n=205309796413962240
white:4 black 8 n=128318622758726416
white:3 black 9 n=57030499003878400
white:2 black 10 n=17109149701163520
white:1 black 11 n=3110754491120640
12 pieces: n=1061285740553991680
white:12 black 1 n=18589318684601596
white:11 black 2 n=111535912107609600
white:10 black 3 n=408965011061235200
white:9 black 4 n=1022412527653087872
white:8 black 5 n=1840342549775558912
white:7 black 6 n=2453790066367412224
white:6 black 7 n=2453790066367410688
white:5 black 8 n=1840342549775558400
white:4 black 9 n=1022412527653087616
white:3 black 10 n=408965011061235264
white:2 black 11 n=111535912107609584
white:1 black 12 n=18589318684601600
13 pieces: n=11711270771299010560
white:13 black 1 n=99778510213329904
white:12 black 2 n=648560316386644480
white:11 black 3 n=2594241265546577920
white:10 black 4 n=7134163480253087744
white:9 black 5 n=14268326960506177536
white:8 black 6 n=21402490440759263232
white:7 black 7 n=24459989075153477632
white:6 black 8 n=21402490440759263232
white:5 black 9 n=14268326960506179584
white:4 black 10 n=7134163480253089792
white:3 black 11 n=2594241265546578432
white:2 black 12 n=648560316386644608
white:1 black 13 n=99778510213329920
14 pieces: n=116755111022483636224
white:14 black 1 n=483549053265008576
white:13 black 2 n=3384843372855059968
white:12 black 3 n=14667654615705260032
white:11 black 4 n=44002963847115800576
white:10 black 5 n=96806520463654764544
white:9 black 6 n=161344200772757848064
white:8 black 7 n=207442543850688675840
white:7 black 8 n=207442543850688675840
white:6 black 9 n=161344200772757880832
white:5 black 10 n=96806520463654748160
white:4 black 11 n=44002963847115800576
white:3 black 12 n=14667654615705260032
white:2 black 13 n=3384843372855058944
white:1 black 14 n=483549053265008512
15 pieces: n=1056264551952084893696
white:15 black 1 n=2124976801504297216
white:14 black 2 n=15937326011282225152
white:13 black 3 n=74374188052650377216
white:12 black 4 n=241716111171113779200
white:11 black 5 n=580118666810672939008
white:10 black 6 n=1063550889152900759552
white:9 black 7 n=1519358413075572326400
white:8 black 8 n=1709278214710018965504
white:7 black 9 n=1519358413075572588544
white:6 black 10 n=1063550889152900366336
white:5 black 11 n=580118666810673004544
white:4 black 12 n=241716111171113713664
white:3 black 13 n=74374188052650393600
white:2 black 14 n=15937326011282225152
white:1 black 15 n=2124976801504296960
16 pieces: n=8703639356861412540416
white:16 black 1 n=8498681602988913664
white:15 black 2 n=67989452823911309312
white:14 black 3 n=339947264119556669440
white:13 black 4 n=1189815424418447884288
white:12 black 5 n=3093520103487963136000
white:11 black 6 n=6187040206975930466304
white:10 black 7 n=9722491753819313012736
white:9 black 8 n=12153114692274144411648
white:8 black 9 n=12153114692274146508800
white:7 black 10 n=9722491753819313012736
white:6 black 11 n=6187040206975929417728
white:5 black 12 n=3093520103487964184576
white:4 black 13 n=1189815424418447622144
white:3 black 14 n=339947264119556538368
white:2 black 15 n=67989452823911309312
white:1 black 16 n=8498681602988913664
17 pieces: n=65524835159044505206784
white:17 black 1 n=31027739084717502464
white:16 black 2 n=263735782220098797568
white:15 black 3 n=1406590838507194810368
white:14 black 4 n=5274715644401978179584
white:13 black 5 n=14769203804325527158784
white:12 black 6 n=31999941576038660702208
white:11 black 7 n=54857042701780550418432
white:10 black 8 n=75428433714948262068224
white:9 black 9 n=83809370794387021234176
white:8 black 10 n=75428433714948262068224
white:7 black 11 n=54857042701780550418432
white:6 black 12 n=31999941576038664896512
white:5 black 13 n=14769203804325533450240
white:4 black 14 n=5274715644401976082432
white:3 black 15 n=1406590838507193761792
white:2 black 16 n=263735782220098797568
white:1 black 17 n=31027739084717506560
18 pieces: n=451870754397001034498048
white:18 black 1 n=103669176099342909440
white:17 black 2 n=933022584894085922816
white:16 black 3 n=5287127981066487332864
white:15 black 4 n=21148511924265949331456
white:14 black 5 n=63445535772797877354496
white:13 black 6 n=148039583469861674680320
white:12 black 7 n=274930655015457345503232
white:11 black 8 n=412395982523185900814336
white:10 black 9 n=504039534195004982427648
white:9 black 10 n=504039534195005183754240
white:8 black 11 n=412395982523185967923200
white:7 black 12 n=274930655015457311948800
white:6 black 13 n=148039583469861741789184
white:5 black 14 n=63445535772797852188672
white:4 black 15 n=21148511924265961914368
white:3 black 16 n=5287127981066486284288
white:2 black 17 n=933022584894086053888
white:1 black 18 n=103669176099342909440
19 pieces: n=2860647245285267379060736
white:19 black 1 n=317659202277681397760
white:18 black 2 n=3017762421637973540864
white:17 black 3 n=18106574529827837050880
white:16 black 4 n=76952941751768291737600
white:15 black 5 n=246249413605658567114752
white:14 black 6 n=615623534014146602336256
white:13 black 7 n=1231247068028292399366144
white:12 black 8 n=2000776485545976424038400
white:11 black 9 n=2667701980727966596857856
white:10 black 10 n=2934472178800764169224192
white:9 black 11 n=2667701980727967670599680
white:8 black 12 n=2000776485545976692473856
white:7 black 13 n=1231247068028293473107968
white:6 black 14 n=615623534014146065465344
white:5 black 15 n=246249413605658533560320
white:4 black 16 n=76952941751768291737600
white:3 black 17 n=18106574529827837050880
white:2 black 18 n=3017762421637973016576
white:1 black 19 n=317659202277681397760
20 pieces: n=16654459018455872073367552
white:20 black 1 n=894192494415377072128
white:19 black 2 n=8941924944153772294144
white:18 black 3 n=56632191312973898186752
white:17 black 4 n=254844860908382575394816
white:16 black 5 n=866472527088500514750464
white:15 black 6 n=2310593405569334348087296
white:14 black 7 n=4951271583362858243588096
white:13 black 8 n=8664725270885007831859200
white:12 black 9 n=12515714280167231029510144
white:11 black 10 n=15018857136200667356987392
white:10 black 11 n=15018857136200678094405632
white:9 black 12 n=12515714280167246061895680
white:8 black 13 n=8664725270885006758117376
white:7 black 14 n=4951271583362861464813568
white:6 black 15 n=2310593405569334348087296
white:5 black 16 n=866472527088500514750464
white:4 black 17 n=254844860908382407622656
white:3 black 18 n=56632191312973898186752
white:2 black 19 n=8941924944153772294144
white:1 black 20 n=894192494415377203200
21 pieces: n=89297894745867066563100672
white:20 black 2 n=24313344782393002688512
white:19 black 3 n=162088965215953340071936
white:18 black 4 n=769922584775778038185984
white:17 black 5 n=2771721305192801098530816
white:16 black 6 n=7853210364712940740804608
white:15 black 7 n=17950195119343861789360128
white:14 black 8 n=33656615848769756155871232
white:13 black 9 n=52354735764752882437455872
white:12 black 10 n=68061156494178813311188992
white:11 black 11 n=74248534357285945359728640
white:10 black 12 n=68061156494178821901123584
white:9 black 13 n=52354735764752916797194240
white:8 black 14 n=33656615848769751860903936
white:7 black 15 n=17950195119343859641876480
white:6 black 16 n=7853210364712940740804608
white:5 black 17 n=2771721305192801098530816
white:4 black 18 n=769922584775778306621440
white:3 black 19 n=162088965215953407180800
white:2 black 20 n=24313344782392998494208
22 pieces: n=441456453940736281364398080
white:20 black 3 n=425193936708802415951872
white:19 black 4 n=2125969683544012952174592
white:18 black 5 n=8078684797467247983460352
white:17 black 6 n=24236054392401747171606528
white:16 black 7 n=58858989238689980118728704
white:15 black 8 n=117717978477379857158242304
white:14 black 9 n=196196630795632986457899008
white:13 black 10 n=274675283113886270376378368
white:12 black 11 n=324616243680047429186486272
white:11 black 12 n=324616243680047497905963008
white:10 black 13 n=274675283113886442175070208
white:9 black 14 n=196196630795633089537114112
white:8 black 15 n=117717978477379908697849856
white:7 black 16 n=58858989238689988708663296
white:6 black 17 n=24236054392401734286704640
white:5 black 18 n=8078684797467246909718528
white:4 black 19 n=2125969683544012683739136
white:3 black 20 n=425193936708802550169600
23 pieces: n=2013862056231517174582214656
white:20 black 4 n=5373392928584068763746304
white:19 black 5 n=21493571714336249285181440
white:18 black 6 n=68062977095398170696876032
white:17 black 7 n=175019083959595406519697408
white:16 black 8 n=371915553414140333343637504
white:15 black 9 n=661183206069582509413236736
white:14 black 10 n=991774809104373626680901632
white:13 black 11 n=1262258847951020104800534528
white:12 black 12 n=1367447085280271230444765184
white:11 black 13 n=1262258847951020929434255360
white:10 black 14 n=991774809104373214364041216
white:9 black 15 n=661183206069582371974283264
white:8 black 16 n=371915553414139921026777088
white:7 black 17 n=175019083959595200361267200
white:6 black 18 n=68062977095398179286810624
white:5 black 19 n=21493571714336257875116032
white:4 black 20 n=5373392928584065542520832
24 pieces: n=8481609969754331918196801536
white:20 black 5 n=52270174570217109914124288
white:19 black 6 n=174233915234056981507473408
white:18 black 7 n=472920627063869273769246720
white:17 black 8 n=1064071410893704766469177344
white:16 black 9 n=2009912665021444413519298560
white:15 black 10 n=3215860264034308862607622144
white:14 black 11 n=4385263996410420676505108480
white:13 black 12 n=5116141329145490972507897856
white:12 black 13 n=5116141329145492072019525632
white:11 black 14 n=4385263996410423425284177920
white:10 black 15 n=3215860264034311611386691584
white:9 black 16 n=2009912665021443314007670784
white:8 black 17 n=1064071410893705178786037760
white:7 black 18 n=472920627063868998891339776
white:6 black 19 n=174233915234056878428258304
white:5 black 20 n=52270174570217101324189696
25 pieces: n=32981348764747030906783399936
white:20 black 6 n=407080942139366592860913664
white:19 black 7 n=1163088406112475802895384576
white:18 black 8 n=2762334964517129499300593664
white:17 black 9 n=5524669929034262297136070656
white:16 black 10 n=9391938879358241836938297344
white:15 black 11 n=13661002006339262652929277952
white:14 black 12 n=17076252507924067870801133568
white:13 black 13 n=18389810393149004457181184000
white:12 black 14 n=17076252507924067870801133568
white:11 black 15 n=13661002006339269249999044608
white:10 black 16 n=9391938879358239637915041792
white:9 black 17 n=5524669929034257899089559552
white:8 black 18 n=2762334964517132248079663104
white:7 black 19 n=1163088406112476352651198464
white:6 black 20 n=407080942139366524141436928
26 pieces: n=118362545663998618662416154624
white:20 black 7 n=2606511500940419617104330752
white:19 black 8 n=6516278752351046568859664384
white:18 black 9 n=13756588477185529318006063104
white:17 black 10 n=24761859258933995433462071296
white:16 black 11 n=38268327945625267269185568768
white:15 black 12 n=51024437260833663303968358400
white:14 black 13 n=58874350685577300429158481920
white:13 black 14 n=58874350685577247652600348672
white:12 black 15 n=51024437260833619323503247360
white:11 black 16 n=38268327945625245278953013248
white:10 black 17 n=24761859258933991035415560192
white:9 black 18 n=13756588477185535915075829760
white:8 black 19 n=6516278752351048767882919936
white:7 black 20 n=2606511500940418517592702976
27 pieces: n=391616707762894328430768160768
white:20 black 8 n=13982411216156789391665135616
white:19 black 9 n=31072024924792878508950945792
white:18 black 10 n=59036847357106483680560283648
white:17 black 11 n=96605750220719695770320633856
white:16 black 12 n=136858146146019542619675164672
white:15 black 13 n=168440795256639271974469632000
white:14 black 14 n=180472280632113508200101183488
white:13 black 15 n=168440795256639307158841720832
white:12 black 16 n=136858146146019472250930987008
white:11 black 17 n=96605750220719590217204367360
white:10 black 18 n=59036847357106439700095172608
white:9 black 19 n=31072024924792882906997456896
white:8 black 20 n=13982411216156798187758157824
28 pieces: n=1192464230874982792508966174720
white:20 black 9 n=63717208336570275889435115520
white:19 black 10 n=127434416673140586963242319872
white:18 black 11 n=220113992435424434305135280128
white:17 black 12 n=330170988653136493128028520448
white:16 black 13 n=431762062084871047702978232320
white:15 black 14 n=493442356668424064570367148032
white:14 black 15 n=493442356668423994201622970368
white:13 black 16 n=431762062084870695859257344000
white:12 black 17 n=330170988653136704234261053440
white:11 black 18 n=220113992435424399120763191296
white:10 black 19 n=127434416673140463817940008960
white:9 black 20 n=63717208336570249501156048896
29 pieces: n=3333282049703133048654373322752
white:20 black 10 n=249213285689434549247635619840
white:19 black 11 n=453115064889881190546821611520
white:18 black 12 n=717432186075645347375165210624
white:17 black 13 n=993367642258585854770421956608
white:16 black 14 n=1206232137028283074966741581824
white:15 black 15 n=1286647612830169195012809555968
white:14 black 16 n=1206232137028283074966741581824
white:13 black 17 n=993367642258585854770421956608
white:12 black 18 n=717432186075645769587630276608
white:11 black 19 n=453115064889881260915565789184
white:10 black 20 n=249213285689434654800751886336
30 pieces: n=8525368244713828806613916450816
white:20 black 11 n=843130425350456235369879830528
white:19 black 12 n=1405217375584095461378822766592
white:18 black 13 n=2053779241238291764388411998208
white:17 black 14 n=2640573310163521883224064131072
white:16 black 15 n=2992649751518652242111093538816
white:15 black 16 n=2992649751518655056860860645376
white:14 black 17 n=2640573310163518505524343603200
white:13 black 18 n=2053779241238291482913435287552
white:12 black 19 n=1405217375584095461378822766592
white:11 black 20 n=843130425350456516844856541184
31 pieces: n=19870700207710033765569660977152
white:20 black 12 n=2481616239489463269374302355456
white:19 black 13 n=3817871137676095778560594149376
white:18 black 14 n=5181396543988987128046520631296
white:17 black 15 n=6217675852786787030635619811328
white:16 black 16 n=6606280593585956364606997790720
white:15 black 17 n=6217675852786784778835806126080
white:14 black 18 n=5181396543988986002146613788672
white:13 black 19 n=3817871137676094652660687306752
white:12 black 20 n=2481616239489462706424348934144
32 pieces: n=42003400141468620526041258000384
white:20 black 13 n=6381200015078724691285233369088
white:19 black 14 n=9116000021541042832878279327744
white:18 black 15 n=11546933360618658083038837080064
white:17 black 16 n=12990300030695977958519716446208
white:16 black 17 n=12990300030695975706719902760960
white:15 black 18 n=11546933360618662586638464450560
white:14 black 19 n=9116000021541042832878279327744
white:13 black 20 n=6381200015078725817185140211712
33 pieces: n=80068866855868820642243014557696
white:20 black 14 n=14375481822688943817836889899008
white:19 black 15 n=19167309096918585752316350038016
white:18 black 16 n=22761179552590799751727389081600
white:17 black 17 n=24100072467449132159495445676032
white:16 black 18 n=22761179552590817766125898563584
white:15 black 19 n=19167309096918583500516536352768
white:14 black 20 n=14375481822688934810637635158016
34 pieces: n=136708013411845790803256703713280
white:20 black 15 n=28418428565749987106698328801280
white:19 black 16 n=35523035707187452358175519408128
white:18 black 17 n=39702216378621296509511645790208
white:17 black 18 n=39702216378621287502312391049216
white:16 black 19 n=35523035707187474876173656260608
white:15 black 20 n=28418428565749955581500937207808
35 pieces: n=207287361303117480955970242740224
white:20 black 16 n=49324063985621278918023191724032
white:19 black 17 n=58028310571319174981013590769664
white:18 black 18 n=61252105603059152165023552372736
white:17 black 19 n=58028310571319202002611354992640
white:16 black 20 n=49324063985621296932421701206016
36 pieces: n=275956854716940123013491900547072
white:20 black 17 n=75119476257355682532230013386752
white:19 black 18 n=83466084730395170787991553572864
white:18 black 19 n=83466084730395224831187082018816
white:17 black 20 n=75119476257355637496233739681792
37 pieces: n=317171121975501706640443133919232
white:20 black 18 n=100219714859813508763979800903680
white:19 black 19 n=105494436694540504252865537114112
white:18 black 20 n=100219714859813508763979800903680
38 pieces: n=305933866414167539795223648403456
white:20 black 19 n=116792105439213924476159132696576
white:19 black 20 n=116792105439213942490557642178560
39 pieces: n=233584210878427848952318265393152
white:20 black 20 n=118385665882089783323935809470464
40 pieces: n=118385665882089783323935809470464
total: n=1750575183183387335993140331937792
Nb. Allis estimates the total number of legal positions to
be 10^30.