Craps Rolls
If you consider yourself to be a serious craps player, you probably know the details on your personal record for longest consecutive roll.
In a highly volatile game of chance like craps – which affords the average shooter just 8.5 rolls before they “seven out” to end the table’s fun – going on an extended streak of success as the shooter can be an unforgettable experience.
There you are playing baccarat, taking center stage while an entire looks on with bated breath as you prepare to roll. You’ve already hit a few point numbers to cash in Pass Line bets for your fellow players, so excitement is in the air. The dice keep tumbling and dodging the dreaded 7 with a point number set, landing on every alternative number a time or two to produce winners for the exotic bettors.
The clock keeps ticking and you keep rolling winners, and before you know it, you’ve just set a new highwater mark for your longest stretch as a shooter without sevening out. Eventually, the party ends when the dice show 4-3 on a 9 point, but no bother – you nearly managed to eclipse the one-hour plateau with a 53-minute roll.
Basic craps Statistics. 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. There are five bets with a shallow house edge in craps. These are: Pass and Don’t Pass. Pass and Don’t Pass are the most straightforward bets in craps. You make this bet before the shooter rolls the dice. Both of these bets pay 1:1. A Pass Line bet wins if the come out roll is 7 or 11. However, you lose the bet if the come out roll is 2, 3, or 12. A pass line bet requires you to place chips on the “Pass Line” section of the table. If the shooter’s come out roll is a 7 or 11, you win even money (1:1). However, if the come out roll is 2,3 or 12 (craps) you lose. If any other number is rolled (4,5,6,8,9 or 10) it’s called the point.
In most Las Vegas casinos, a roll like that would cause an immediate buzz across the gaming floor, both among players and dealers alike. And for good reason, as the average craps roll tends to last for just about 20 minutes.
So what if I told you a tourist from Honolulu, Hawaii once held the dice in hand for three hours and six minutes without ever sevening out?
That incredible craps session lasting 118 straight seven-less rolls might sound like one of Sin City’s infamous myths, like pure oxygen pumped into the air supply to keep losing gamblers blissfully unaware. But if you pay a visit to the classic California casino in Downtown Las Vegas, you can still find a full-fledged shrine to the original “Golden Arm” himself – the late Stanley Fujitake.
Fujitake Sets a World Record for Longest Consecutive Craps Roll
Back on May 28, 1989, Fujitake and his wife Satsuko took advantage of a Hawaii-focused travel promotion offered by the California Hotel & Casino to make one of their regular visits to Las Vegas.
An avid craps enthusiast herself, Satsuko Fujitake taught her husband the game during their courtship. As she told Hawaii News Now in 2009, shortly after Fujitake’s record finally fell (more on this to come), Satsuko soon suspected her husband had been bitten hard by the craps bug:
“Mom, where is Dad going out all the time? I said, ‘Well, he must have trouble with his stomach, he’s going to the bathroom.’
I didn’t believe that, I knew what he was doing – he was on the table every time he went out.”
So it was that Satsuko woke up one morning to find her husband’s side of the bed hadn’t even been slept in. That’s because Fujitake has spent the night putting on one of the greatest gambling shows Las Vegas has ever witnessed.
The action started around midnight when Fujitake – a mild-mannered man of diminutive stature who looked every part the average Las Vegas tourist – placed a simple $5 bet on the Pass Line.
Over the next 3+ hours, Fujitake could do no wrong with the dice, rolling over and over again without sevening out. As the epic rolling session progressed, onlookers crowded the table and wagered everything they had to get in on Fujitake’s good fortune.
Guido Metzger – who worked as a dealer at the California back then before rising to become director of casino operations for parent company Boyd Gaming – recalled the frantic crush of bettors surrounding Fujitake in an interview with Boyd’s Buzz:
“They had trouble keeping up with the chip payouts that night.
My table was empty. But there were at least 30 to 40 people trying to place bets at his table.
They couldn’t get fills to the table fast enough and had to start issuing scrip [casino credit] because not enough people were going to the cage and cashing in their chips.”
With winners coming on every roll, the California’s coffers were soon being drained for six-figure sums. The outlays became so onerous that John Repetti, casino manager for the California at the time, was called in from home to supervise the situation.
As he told the Los Angeles Times in a 2017 retrospective on Fujitake’s record-setting roll. Repetti was literally roused from his slumber in order to personally monitor the increasingly expensive craps game:
“The first call came and he’d been shooting for an hour, and we were losing a couple hundred thousand dollars at the time. I said if he continued, to call me at every $100,000 loss interval.
Well, the calls kept coming every 15 minutes. Another $100,000. And another $100,000.
After the fourth call and fifth call, I decided I’d better get some clothes on and get downtown.”
A seasoned veteran of the casino gambling industry, Repetti knew instantly that he was witnessing a historic run of good luck, as he told News at the Cal a few months afterward:
“Half an hour is average, over an hour is amazing, but more than three hours is totally astounding.”
In the end, Fujitake held the dice for 118 consecutive rolls without sevening out, a feat which earned him $30,000 in winnings.
But according to David Strow, who serves as vice president of corporate communications for Boyd Gaming, Fujitake was hardly the biggest winner to benefit from the legendary roll. As Strow remembered it in a 2017 interview with PokerNews, Fujitake’s fellow players placed larger bets along the way and wound up winning upwards of $1 million:
“That was one of the ironic things about his roll – the other players at the table ended up winning a lot more money than Stanley did!”
Wife Remembers the Late Legend and Love of Her Life
Stanley Fujitake passed away in 2000 at the age of 77, but he was survived by his wife Satsuko and their sons Dennis, Lester, and Kevin.
And while the children may have wondered where Dad was during those late nights at the California’s craps tables, Satsusko told Hawaii News Now that she is glad Stanley was able to enjoy the game he loved so dearly:
“It was a miracle, because it’s impossible to hold the dice.
It doesn’t happen all the time, maybe it’s only once in a lifetime deal.”
Satsuko was there that night, but after wandering the casino floor for a while, she couldn’t find the small of stature Stanley amidst the crowd. Later on, as she played video poker in another area of the casino, Satsuko found herself surrounded by well-wishers celebrating her husband’s new crown as the King of Craps:
“People came up to congratulate me and I thought, geez, I didn’t do anything, I didn’t even hit a royal, why are they congratulating me?
Then I realized, he was the one with the dice.”
Fujitake’s Record Gets Smashed in the Garden State
For 20 years following his world record roll, nobody could top Fujitake’s mark of three hours and six minutes without turning over the dice.
The record stood until 2009, when a craps rookie named Patricia Demauro visited the Borgata casino in Atlantic City, New Jersey on a whim. Bored with the penny slots, her pal invited her to take a crack at craps, leading to one of the more improbable feats in gambling history.
DeMauro rolled 154 times consecutively without sevening out, a session which lasted four hours and 18 minutes altogether – or a full hour longer than Fujitake’s previous record.
When asked about her late husband’s historic feat falling into second place, Satsuko Fujitake told Hawaii News Now that Stanley’s record run will always be number one in her heart:
“As my husband of 54 years, in my heart, he is still the champ to me and will be forever.”
The “Golden Arm” Club Carries on Fujitake’s Legacy in Fine Fashion
In 1992, the California Hotel & Casino commemorated Fujitake’s record roll by creating the “Golden Arm” award.
Ever since then, any craps player at the California who can roll for one hour or more without sevening out earns entrance to the Golden Arm club. Admission comes with a plaque memorializing the date and length of session, while members are given a snazzy blue shirt proclaiming them to be Golden Arms.
The name comes straight from Fujitake himself, after the proud craps player told Repetti that “this arm is golden” upon receiving a check for $30,000. Fujitake went on to top the 60-minute mark without sevening out on three other occasions, proving that his proficiency with the dice was no fluke.
You can learn more about the Golden Arm club – and the California’s annual craps tournament held in Fujitake’s honor – in this profile by the L.A. Times.
Conclusion
Managing to beat the average of 8.5 rolls without sevening out is enough to get most craps players’ heart’s pumping, so just imagine what Fujitake was feeling as the hours passed by. Runs like that are the stuff of gambling lore, but for one unforgettable night back in 1989, a tourist in Sin City simply refused to lose. The next time you’re in Downtown Las Vegas, make sure to pay homage to Fujitake and his record-setting roll by visiting the California and its Golden Arm “wall of fame.”
Please enable JavaScript to view the comments powered by Disqus.- Appendices
- Craps Analysis
- Miscellaneous
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 |
Craps Dice Rolls
The mean number of rolls per shooter is 8.525510.
Greatest Craps Rolls
For how I solved this problem, please see my MathProblems.info site, problem 204.