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Last Updated: August 26, 2016

# Number of rolls table in craps

## Introduction

One question I get asked a lot is "what is the probability of a shooter lasting x rolls in craps?" The following table answers that question for up to 50 rolls. The first column is the roll number. The second column is the probability of a seven-out on exactly that roll. The third column is the probability of surviving PAST that roll.

### Craps Survival Table for 1 to 50 Rolls

Roll
Number
Probability
Seven-Out
Probability
Survival
1 0.00000000 1.00000000
2 0.11111111 0.88888889
3 0.11676955 0.77211934
4 0.10476680 0.66735254
5 0.09122363 0.57612891
6 0.07891804 0.49721087
7 0.06816676 0.42904411
8 0.05885276 0.37019135
9 0.05080065 0.31939070
10 0.04384414 0.27554656
11 0.03783614 0.23771043
12 0.03264850 0.20506193
13 0.02817002 0.17689190
14 0.02430433 0.15258757
15 0.02096801 0.13161956
16 0.01808886 0.11353070
17 0.01560445 0.09792625
18 0.01346084 0.08446541
19 0.01161138 0.07285403
20 0.01001580 0.06283823
21 0.00863931 0.05419892
22 0.00745187 0.04674705
23 0.00642755 0.04031950
24 0.00554396 0.03477554
25 0.00478180 0.02999374
26 0.00412437 0.02586937
27 0.00355731 0.02231206
28 0.00306819 0.01924387
29 0.00264632 0.01659755
30 0.00228244 0.01431511
31 0.00196858 0.01234653
32 0.00169788 0.01064864
33 0.00146440 0.00918424
34 0.00126303 0.00792121
35 0.00108934 0.00683187
36 0.00093954 0.00589234
37 0.00081033 0.00508201
38 0.00069890 0.00438311
39 0.00060278 0.00378033
40 0.00051989 0.00326044
41 0.00044839 0.00281205
42 0.00038673 0.00242532
43 0.00033354 0.00209178
44 0.00028767 0.00180411
45 0.00024811 0.00155600
46 0.00021399 0.00134201
47 0.00018456 0.00115745
48 0.00015918 0.00099827
49 0.00013729 0.00086098
50 0.00011841 0.00074257

The next table shows the same information, but for up to 200 rolls. The probabilities get very small, so this table is in scientific notation.

### Craps Survival Table for 1 to 200 Rolls

Roll
Number
Probability
Seven-Out
Probability
Survival
1 0.000000E+00 1.000000E+00
2 1.111111E-01 8.888889E-01
3 1.167695E-01 7.721193E-01
4 1.047668E-01 6.673525E-01
5 9.122363E-02 5.761289E-01
6 7.891804E-02 4.972109E-01
7 6.816676E-02 4.290441E-01
8 5.885276E-02 3.701913E-01
9 5.080065E-02 3.193907E-01
10 4.384414E-02 2.755466E-01
11 3.783614E-02 2.377104E-01
12 3.264850E-02 2.050619E-01
13 2.817002E-02 1.768919E-01
14 2.430433E-02 1.525876E-01
15 2.096801E-02 1.316196E-01
16 1.808886E-02 1.135307E-01
17 1.560445E-02 9.792625E-02
18 1.346084E-02 8.446541E-02
19 1.161138E-02 7.285403E-02
20 1.001580E-02 6.283823E-02
21 8.639309E-03 5.419892E-02
22 7.451869E-03 4.674705E-02
23 6.427548E-03 4.031950E-02
24 5.543963E-03 3.477554E-02
25 4.781795E-03 2.999374E-02
26 4.124373E-03 2.586937E-02
27 3.557310E-03 2.231206E-02
28 3.068195E-03 1.924387E-02
29 2.646317E-03 1.659755E-02
30 2.282437E-03 1.431511E-02
31 1.968585E-03 1.234653E-02
32 1.697884E-03 1.064864E-02
33 1.464404E-03 9.184241E-03
34 1.263027E-03 7.921214E-03
35 1.089340E-03 6.831874E-03
36 9.395362E-04 5.892338E-03
37 8.103321E-04 5.082006E-03
38 6.988952E-04 4.383111E-03
39 6.027824E-04 3.780328E-03
40 5.198867E-04 3.260442E-03
41 4.483907E-04 2.812051E-03
42 3.867267E-04 2.425324E-03
43 3.335427E-04 2.091782E-03
44 2.876726E-04 1.804109E-03
45 2.481107E-04 1.555998E-03
46 2.139894E-04 1.342009E-03
47 1.845605E-04 1.157448E-03
48 1.591789E-04 9.982695E-04
49 1.372878E-04 8.609818E-04
50 1.184072E-04 7.425745E-04
51 1.021232E-04 6.404513E-04
52 8.807867E-05 5.523726E-04
53 7.596559E-05 4.764071E-04
54 6.551837E-05 4.108887E-04
55 5.650790E-05 3.543808E-04
56 4.873660E-05 3.056442E-04
57 4.203405E-05 2.636101E-04
58 3.625328E-05 2.273569E-04
59 3.126751E-05 1.960893E-04
60 2.696741E-05 1.691219E-04
61 2.325869E-05 1.458632E-04
62 2.006001E-05 1.258032E-04
63 1.730124E-05 1.085020E-04
64 1.492187E-05 9.358012E-05
65 1.286972E-05 8.071040E-05
66 1.109980E-05 6.961061E-05
67 9.573283E-06 6.003732E-05
68 8.256706E-06 5.178062E-05
69 7.121193E-06 4.465942E-05
70 6.141842E-06 3.851758E-05
71 5.297178E-06 3.322040E-05
72 4.568677E-06 2.865173E-05
73 3.940364E-06 2.471136E-05
74 3.398461E-06 2.131290E-05
75 2.931083E-06 1.838182E-05
76 2.527982E-06 1.585384E-05
77 2.180319E-06 1.367352E-05
78 1.880468E-06 1.179305E-05
79 1.621854E-06 1.017120E-05
80 1.398806E-06 8.772390E-06
81 1.206434E-06 7.565956E-06
82 1.040518E-06 6.525439E-06
83 8.974191E-07 5.628020E-06
84 7.740004E-07 4.854019E-06
85 6.675550E-07 4.186464E-06
86 5.757487E-07 3.610715E-06
87 4.965681E-07 3.114147E-06
88 4.282770E-07 2.685870E-06
89 3.693777E-07 2.316493E-06
90 3.185785E-07 1.997914E-06
91 2.747656E-07 1.723148E-06
92 2.369781E-07 1.486170E-06
93 2.043874E-07 1.281783E-06
94 1.762788E-07 1.105504E-06
95 1.520358E-07 9.534683E-07
96 1.311269E-07 8.223414E-07
97 1.130935E-07 7.092478E-07
98 9.754019E-08 6.117076E-07
99 8.412586E-08 5.275818E-07
100 7.255634E-08 4.550254E-07
101 6.257794E-08 3.924475E-07
102 5.397183E-08 3.384757E-07
103 4.654929E-08 2.919264E-07
104 4.014754E-08 2.517788E-07
105 3.462620E-08 2.171526E-07
106 2.986419E-08 1.872885E-07
107 2.575708E-08 1.615314E-07
108 2.221480E-08 1.393166E-07
109 1.915969E-08 1.201569E-07
110 1.652473E-08 1.036322E-07
111 1.425214E-08 8.938002E-08
112 1.229210E-08 7.708792E-08
113 1.060161E-08 6.648631E-08
114 9.143612E-09 5.734269E-08
115 7.886126E-09 4.945657E-08
116 6.801576E-09 4.265499E-08
117 5.866181E-09 3.678881E-08
118 5.059427E-09 3.172938E-08
119 4.363623E-09 2.736576E-08
120 3.763510E-09 2.360225E-08
121 3.245929E-09 2.035632E-08
122 2.799529E-09 1.755679E-08
123 2.414520E-09 1.514227E-08
124 2.082460E-09 1.305981E-08
125 1.796067E-09 1.126375E-08
126 1.549061E-09 9.714685E-09
127 1.336024E-09 8.378661E-09
128 1.152286E-09 7.226375E-09
129 9.938163E-10 6.232559E-09
130 8.571405E-10 5.375419E-09
131 7.392611E-10 4.636157E-09
132 6.375933E-10 3.998564E-09
133 5.499075E-10 3.448657E-09
134 4.742808E-10 2.974376E-09
135 4.090547E-10 2.565321E-09
136 3.527990E-10 2.212522E-09
137 3.042799E-10 1.908242E-09
138 2.624334E-10 1.645809E-09
139 2.263419E-10 1.419467E-09
140 1.952140E-10 1.224253E-09
141 1.683669E-10 1.055886E-09
142 1.452120E-10 9.106740E-10
143 1.252416E-10 7.854324E-10
144 1.080176E-10 6.774148E-10
145 9.316232E-11 5.842525E-10
146 8.035006E-11 5.039024E-10
147 6.929981E-11 4.346026E-10
148 5.976927E-11 3.748334E-10
149 5.154943E-11 3.232839E-10
150 4.446003E-11 2.788239E-10
151 3.834561E-11 2.404783E-10
152 3.307208E-11 2.074062E-10
153 2.852380E-11 1.788824E-10
154 2.460103E-11 1.542814E-10
155 2.121774E-11 1.330637E-10
156 1.829975E-11 1.147639E-10
157 1.578305E-11 9.898086E-11
158 1.361247E-11 8.536839E-11
159 1.174039E-11 7.362800E-11
160 1.012578E-11 6.350222E-11
161 8.733222E-12 5.476899E-11
162 7.532174E-12 4.723682E-11
163 6.496303E-12 4.074052E-11
164 5.602891E-12 3.513763E-11
165 4.832346E-12 3.030528E-11
166 4.167772E-12 2.613751E-11
167 3.594594E-12 2.254292E-11
168 3.100243E-12 1.944267E-11
169 2.673878E-12 1.676880E-11
170 2.306150E-12 1.446265E-11
171 1.988993E-12 1.247365E-11
172 1.715455E-12 1.075820E-11
173 1.479535E-12 9.278663E-12
174 1.276060E-12 8.002603E-12
175 1.100568E-12 6.902035E-12
176 9.492110E-13 5.952824E-12
177 8.186696E-13 5.134155E-12
178 7.060810E-13 4.428074E-12
179 6.089764E-13 3.819097E-12
180 5.252261E-13 3.293871E-12
181 4.529938E-13 2.840877E-12
182 3.906952E-13 2.450182E-12
183 3.369644E-13 2.113218E-12
184 2.906229E-13 1.822595E-12
185 2.506546E-13 1.571940E-12
186 2.161831E-13 1.355757E-12
187 1.864522E-13 1.169305E-12
188 1.608101E-13 1.008495E-12
189 1.386945E-13 8.698004E-13
190 1.196204E-13 7.501800E-13
191 1.031694E-13 6.470106E-13
192 8.898094E-14 5.580296E-13
193 7.674372E-14 4.812859E-13
194 6.618945E-14 4.150965E-13
195 5.708666E-14 3.580098E-13
196 4.923575E-14 3.087741E-13
197 4.246454E-14 2.663095E-13
198 3.662455E-14 2.296850E-13
199 3.158771E-14 1.980973E-13
200 2.724357E-14 1.708537E-13

The mean number of rolls per shooter is 8.525510.

For how I solved this problem, please see my MathProblems.info site, problem 204.

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