크랩스 연속 롤 확률 통계는 크랩스에서 슈터가 7을 굴리지 않고 연속으로 주사위를 굴릴(Roll) 확률을 말합니다. 크랩스에서 주사위를 던지는 플레이어를 슈터(Shooter)라 부릅니다.
다른 카지노 게임과 달리, 크랩스는 슈터가 7을 굴리지 않으면 계속 주사위를 던질 수 있습니다. 7이 나오면 세븐 아웃(Seven Out)이 되어 패배하고 다음 슈터의 차례로 넘어갑니다. 크랩스는 7의 출현 확률이 가장 높기 때문에, 7이 나오지 않은 채 연속으로 주사위를 굴릴 수 있다는 것은 곧 슈터에게 큰 행운이 따라준다는 것을 의미합니다.
그래서 세계 카지노는 1시간 이상 연속으로 주사위를 굴리는 사람들을 모아 골든 암 클럽(Golden Arm Club)에 등록합니다. 크랩스 게임의 명예의 전당(Hall of Fame)과 같은 것입니다.
크랩스 연속 롤 확률
주사위를 n회 굴렸을 때 7이 나올 확률과 때까지 7이 나오지 않을 확률입니다. 모든 확률은 이전의 횟수가 다음 횟수에 영향을 미치는 종속 시행(Dependant Trial)입니다.
n회 주사위를 던져 7이 나오지 않을 확률 = ( 5 ÷ 6 )n
n회 주사위를 던지고 n+1 차례에 7이 나올 확률 = ( 5 ÷ 6 )n × ( 1 ÷ 6 )
예를 들어 주사위를 4번 굴렸을 때까지 7이 나오지 않을 확률은 66.7352%입니다. 4번째 굴렸을 때 66.7352% 확률로 5번째 굴릴 기회가 주어진다는 의미입니다. 그리고 5번째 주사위를 굴릴 때 7이 출현할 확률은 9.1223%입니다.
1~50회 연속 롤 확률
| 횟수 | 7 출현 확률 | 7 이외 확률 |
|---|---|---|
| 1 | 0% | 100% |
| 2 | 11.11111% | 88.88889% |
| 3 | 11.67695% | 77.21193% |
| 4 | 10.47668% | 66.73525% |
| 5 | 9.122363% | 57.61289% |
| 6 | 7.891804% | 49.72109% |
| 7 | 6.816676% | 42.90441% |
| 8 | 5.885276% | 37.01913% |
| 9 | 5.080065% | 31.93907% |
| 10 | 4.384414% | 27.55466% |
| 11 | 3.783614% | 23.77104% |
| 12 | 3.264850% | 20.50619% |
| 13 | 2.817002% | 17.68919% |
| 14 | 2.430433% | 15.25876% |
| 15 | 2.096801% | 13.16196% |
| 16 | 1.808886% | 11.35307% |
| 17 | 1.560445% | 9.792625% |
| 18 | 1.346084% | 8.446541% |
| 19 | 1.161138% | 7.285403% |
| 20 | 1.001580% | 6.283823% |
| 21 | 0.8639309% | 5.419892% |
| 22 | 0.7451869% | 4.674705% |
| 23 | 0.6427548% | 4.031950% |
| 24 | 0.5543963% | 3.477554% |
| 25 | 0.4781795% | 2.999374% |
| 26 | 0.4124373% | 2.586937% |
| 27 | 0.3557310% | 2.231206% |
| 28 | 0.3068195% | 1.924387% |
| 29 | 0.2646317% | 1.659755% |
| 30 | 0.2282437% | 1.431511% |
| 31 | 0.1968585% | 1.234653% |
| 32 | 0.1697884% | 1.064864% |
| 33 | 0.1464404% | 0.9184241% |
| 34 | 0.1263027% | 0.7921214% |
| 35 | 0.1089340% | 0.6831874% |
| 36 | 0.09395362% | 0.5892338% |
| 37 | 0.08103321% | 0.5082006% |
| 38 | 0.06988952% | 0.4383111% |
| 39 | 0.06027824% | 0.3780328% |
| 40 | 0.05198867% | 0.3260442% |
| 41 | 0.04483907% | 0.2812051% |
| 42 | 0.03867267% | 0.2425324% |
| 43 | 0.03335427% | 0.2091782% |
| 44 | 0.02876726% | 0.1804109% |
| 45 | 0.02481107% | 0.1555998% |
| 46 | 0.02139894% | 0.1342009% |
| 47 | 0.01845605% | 0.1157448% |
| 48 | 0.01591789% | 0.09982695% |
| 49 | 0.01372878% | 0.08609818% |
| 50 | 0.01184072% | 0.07425745% |
51~100회 연속 롤 확률
| 횟수 | 7 출현 확률 | 7 이외 확률 |
|---|---|---|
| 51 | 0.010212320% | 0.06404513% |
| 52 | 0.008807867% | 0.05523726% |
| 53 | 0.007596559% | 0.04764071% |
| 54 | 0.006551837% | 0.04108887% |
| 55 | 0.005650790% | 0.03543808% |
| 56 | 0.004873660% | 0.03056442% |
| 57 | 0.004203405% | 0.02636101% |
| 58 | 0.003625328% | 0.02273569% |
| 59 | 0.003126751% | 0.01960893% |
| 60 | 0.002696741% | 0.01691219% |
| 61 | 0.002325869% | 0.01458632% |
| 62 | 0.002006001% | 0.01258032% |
| 63 | 0.001730124% | 0.01085020% |
| 64 | 0.001492187% | 0.009358012% |
| 65 | 0.001286972% | 0.008071040% |
| 66 | 0.001109980% | 0.006961061% |
| 67 | 0.0009573283% | 0.006003732% |
| 68 | 0.0008256706% | 0.005178062% |
| 69 | 0.0007121193% | 0.004465942% |
| 70 | 0.0006141842% | 0.003851758% |
| 71 | 0.0005297178% | 0.003322040% |
| 72 | 0.0004568677% | 0.002865173% |
| 73 | 0.0003940364% | 0.002471136% |
| 74 | 0.0003398461% | 0.002131290% |
| 75 | 0.0002931083% | 0.001838182% |
| 76 | 0.0002527982% | 0.001585384% |
| 77 | 0.0002180319% | 0.001367352% |
| 78 | 0.0001880468% | 0.001179305% |
| 79 | 0.0001621854% | 0.001017120% |
| 80 | 0.0001398806% | 0.0008772390% |
| 81 | 0.0001206434% | 0.0007565956% |
| 82 | 0.0001040518% | 0.0006525439% |
| 83 | 0.00008974191% | 0.0005628020% |
| 84 | 0.00007740004% | 0.0004854019% |
| 85 | 0.00006675550% | 0.0004186464% |
| 86 | 0.00005757487% | 0.0003610715% |
| 87 | 0.00004965681% | 0.0003114147% |
| 88 | 0.00004282770% | 0.0002685870% |
| 89 | 0.00003693777% | 0.0002316493% |
| 90 | 0.00003185785% | 0.0001997914% |
| 91 | 0.00002747656% | 0.0001723148% |
| 92 | 0.00002369781% | 0.0001486170% |
| 93 | 0.00002043874% | 0.0001281783% |
| 94 | 0.00001762788% | 0.0001105504% |
| 95 | 0.00001520358% | 0.00009534683% |
| 96 | 0.00001311269% | 0.00008223414% |
| 97 | 0.00001130935% | 0.00007092478% |
| 98 | 0.000009754019% | 0.00006117076% |
| 99 | 0.000008412586% | 0.00005275818% |
| 100 | 0.000007255634% | 0.00004550254% |
101~150회 연속 롤 확률
| 횟수 | 7 출현 확률 | 7 이외 확률 |
|---|---|---|
| 101 | 0.000006257794% | 0.00003924475% |
| 102 | 0.000005397183% | 0.00003384757% |
| 103 | 0.000004654929% | 0.00002919264% |
| 104 | 0.000004014754% | 0.00002517788% |
| 105 | 0.000003462620% | 0.00002171526% |
| 106 | 0.000002986419% | 0.00001872885% |
| 107 | 0.000002575708% | 0.00001615314% |
| 108 | 0.000002221480% | 0.00001393166% |
| 109 | 0.000001915969% | 0.00001201569% |
| 110 | 0.000001652473% | 0.00001036322% |
| 111 | 0.000001425214% | 0.000008938002% |
| 112 | 0.000001229210% | 0.000007708792% |
| 113 | 0.000001060161% | 0.000006648631% |
| 114 | 0.0000009143612% | 0.000005734269% |
| 115 | 0.0000007886126% | 0.000004945657% |
| 116 | 0.0000006801576% | 0.000004265499% |
| 117 | 0.0000005866181% | 0.000003678881% |
| 118 | 0.0000005059427% | 0.000003172938% |
| 119 | 0.0000004363623% | 0.000002736576% |
| 120 | 0.0000003763510% | 0.000002360225% |
| 121 | 0.0000003245929% | 0.000002035632% |
| 122 | 0.0000002799529% | 0.000001755679% |
| 123 | 0.0000002414520% | 0.000001514227% |
| 124 | 0.0000002082460% | 0.000001305981% |
| 125 | 0.0000001796067% | 0.000001126375% |
| 126 | 0.0000001549061% | 0.0000009714685% |
| 127 | 0.0000001336024% | 0.0000008378661% |
| 128 | 0.0000001152286% | 0.0000007226375% |
| 129 | 0.00000009938163% | 0.0000006232559% |
| 130 | 0.00000008571405% | 0.0000005375419% |
| 131 | 0.00000007392611% | 0.0000004636157% |
| 132 | 0.00000006375933% | 0.0000003998564% |
| 133 | 0.00000005499075% | 0.0000003448657% |
| 134 | 0.00000004742808% | 0.0000002974376% |
| 135 | 0.00000004090547% | 0.0000002565321% |
| 136 | 0.00000003527990% | 0.0000002212522% |
| 137 | 0.00000003042799% | 0.0000001908242% |
| 138 | 0.00000002624334% | 0.0000001645809% |
| 139 | 0.00000002263419% | 0.0000001419467% |
| 140 | 0.00000001952140% | 0.0000001224253% |
| 141 | 0.00000001683669% | 0.0000001055886% |
| 142 | 0.00000001452120% | 0.0000000910674% |
| 143 | 0.00000001252416% | 0.00000007854324% |
| 144 | 0.00000001080176% | 0.00000006774148% |
| 145 | 0.000000009316232% | 0.00000005842525% |
| 146 | 0.000000008035006% | 0.00000005039024% |
| 147 | 0.000000006929981% | 0.00000004346026% |
| 148 | 0.000000005976927% | 0.00000003748334% |
| 149 | 0.000000005154943% | 0.00000003232839% |
| 150 | 0.000000004446003% | 0.00000002788239% |
151~200회 연속 롤 확률
| 횟수 | 7 출현 확률 | 7 이외 확률 |
|---|---|---|
| 151 | 0.000000003834561% | 0.00000002404783% |
| 152 | 0.000000003307208% | 0.00000002074062% |
| 153 | 0.000000002852380% | 0.00000001788824% |
| 154 | 0.000000002460103% | 0.00000001542814% |
| 155 | 0.000000002121774% | 0.00000001330637% |
| 156 | 0.000000001829975% | 0.00000001147639% |
| 157 | 0.000000001578305% | 0.000000009898086% |
| 158 | 0.000000001361247% | 0.000000008536839% |
| 159 | 0.000000001174039% | 0.000000007362800% |
| 160 | 0.000000001012578% | 0.000000006350222% |
| 161 | 0.0000000008733222% | 0.000000005476899% |
| 162 | 0.0000000007532174% | 0.000000004723682% |
| 163 | 0.0000000006496303% | 0.000000004074052% |
| 164 | 0.0000000005602891% | 0.000000003513763% |
| 165 | 0.0000000004832346% | 0.000000003030528% |
| 166 | 0.0000000004167772% | 0.000000002613751% |
| 167 | 0.0000000003594594% | 0.000000002254292% |
| 168 | 0.0000000003100243% | 0.000000001944267% |
| 169 | 0.0000000002673878% | 0.000000001676880% |
| 170 | 0.0000000002306150% | 0.000000001446265% |
| 171 | 0.0000000001988993% | 0.000000001247365% |
| 172 | 0.0000000001715455% | 0.000000001075820% |
| 173 | 0.0000000001479535% | 0.0000000009278663% |
| 174 | 0.0000000001276060% | 0.0000000008002603% |
| 175 | 0.0000000001100568% | 0.0000000006902035% |
| 176 | 0.0000000000949211% | 0.0000000005952824% |
| 177 | 0.00000000008186696% | 0.0000000005134155% |
| 178 | 0.00000000007060810% | 0.0000000004428074% |
| 179 | 0.00000000006089764% | 0.0000000003819097% |
| 180 | 0.00000000005252261% | 0.0000000003293871% |
| 181 | 0.00000000004529938% | 0.0000000002840877% |
| 182 | 0.00000000003906952% | 0.0000000002450182% |
| 183 | 0.00000000003369644% | 0.0000000002113218% |
| 184 | 0.00000000002906229% | 0.0000000001822595% |
| 185 | 0.00000000002506546% | 0.0000000001571940% |
| 186 | 0.00000000002161831% | 0.0000000001355757% |
| 187 | 0.00000000001864522% | 0.0000000001169305% |
| 188 | 0.00000000001608101% | 0.00000000010084950% |
| 189 | 0.00000000001386945% | 0.00000000008698004% |
| 190 | 0.00000000001196204% | 0.00000000007501800% |
| 191 | 0.00000000001031694% | 0.00000000006470106% |
| 192 | 0.000000000008898094% | 0.00000000005580296% |
| 193 | 0.000000000007674372% | 0.00000000004812859% |
| 194 | 0.000000000006618945% | 0.00000000004150965% |
| 195 | 0.000000000005708666% | 0.00000000003580098% |
| 196 | 0.000000000004923575% | 0.00000000003087741% |
| 197 | 0.000000000004246454% | 0.00000000002663095% |
| 198 | 0.000000000003662455% | 0.00000000002296850% |
| 199 | 0.000000000003158771% | 0.00000000001980973% |
| 200 | 0.000000000002724357% | 0.00000000001708537% |
크랩스 연속 롤 확률 예시
1989년 5월 28일 라스베이거스의 한 카지노에서 스탠리 후지타케(Stanley Fujitake)는 약 3시간 6분 동안 단 한 번도 7이 나오지 않았습니다. 이 시간 동안 그가 주사위를 연속으로 굴린 횟수는 118회입니다. 그리고 119번째에 드디어 7이 나오고 차례를 넘겼습니다. 이는 크랩스 게임의 전설로 남아, 골든 암 클럽의 개설을 촉발한 계기가 되었습니다.
118회 동안 한 번도 7이 나오지 않을 확률은 0.000003172938%입니다. 한국의 로또 당첨률이 0.0000122773804%이니, 로또에 386번 당첨될 확률입니다.
현재 세계 기록은 2009년 5월 23일 패트리샤 드마우로(Patricia Demauro)가 4시간 18분 동안 기록한 154회입니다. 154회 연속 7이 나오지 않을 확률은 0.00000001542814%로, 로또에 8만 번 당첨될 확률입니다. 실로 어마어마한 확률이기 때문에, 황금 팔(Golden Arm)이라는 칭호를 받기에 부족함이 없습니다.
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