7craps
Posted by 7craps
Oct 23, 2013

RIP Alan Krigman

Remember the immortal words of Sumner A Ingmark,
the poet laureate of the casino scene:

Those great and gaudy gambling halls
Will treat you like you're rich and famous.
Enjoy that million dollar feel,
Or miss it. Be an ignoramus!

from Alan K
Casinos generate their earnings by nibbling off small percentages of the money players wager. Say, for instance, you're a roulette buff and always bet $5 on each of three rows $15 total per spin. Edge, assuming a double-zero game, is 5.26 percent; the bosses therefore figure your action per spin is worth 5.26 percent of $15 just under $0.79. During a three-hour session on a certain visit, you'd get about 120 spins, making you a $0.79 x 120 or $95 customer.

The $0.79 and $95 are "theoretical" averages over large numbers of bets made by hosts of players, each of whom wins or loses some amount.
Individuals really only care about the results of their rounds and sessions.
You don't notice the $0.79 and wouldn't gamble if you always lost $95 in three hours.
In practice, after this much time, your chances are 50 percent of losing more than $95 and 50 percent of losing less, including 37 percent of winning.
This, because edge isn't the only factor affecting particular players' outcomes. Volatility is the other major determinant.

Edge goes one-way.
From bettors to bosses.
On the average, for every spin with $15 at risk on double-zero roulette, players pay the house $0.79.
And those $0.79 increments mount linearly.
After 25 spins, the expected total is 25 x $0.79 or $19.75; after 100 spins, the casino figures 100 x $0.79 or $79; and after 1,000,000 spins, the joint estimates 1,000,000 x $0.79 or $790,000.

Volatility is bidirectional.
When nothing hits in any of the three $5 rows, your bankroll shrinks by $15.
On a hit, you're paid $55 for the row in question minus $10 for the two misses, raising your fortune by $45. For one spin, the characteristic bankroll jump under these conditions (math wonks call it "standard deviation") is $25.50 up or down. For multiple spins, one standard deviation defines the upper and lower ends of a range covering 68 percent of all net bankroll changes.
And it's balanced so half the remaining 32 percent is below and half above this range.

As with edge, the amount represented by volatility gets bigger as you make more bets.
But because bankroll jumps may be up or down, there's some cancellation and the cumulative value is less than simply the number of spins times $25.50.
Standard deviation accordingly grows more slowly than does edge.
After 25 spins, it doesn't reach 25 x $25.50 or $637, but 5 x $25.50 or $128; after 100 spins, it's not up 100-fold to $2,550 but to 10-fold to $255; and after 1,000,000 spins, the value isn't 1,000,000 x $25.50 or $25,500,000 but 1,000 x $25.50 or $25,500.

The higher rate at which edge increases relative to volatility explains why casinos depend on long-term averages while solid citizens pin their hopes on the short run.
For one spin, the effect of volatility is much greater than that of edge.
Minus $15 or plus $45 swamp the $0.79 penalty.
After 1,000,000 spins, edge dominates $790,000 down as opposed to a standard deviation of $25,500 up or down.
At some number of spins, the two are equal.
For the $15 per spin double-zero roulette example, the crossover is 1,044 spins 26 hours assuming 40 spins per hour.
At this point, edge represents an average loss of $824.21, and one standard deviation a swing of $824.21 above or below this average.
This means players would have 16 percent chance of being more than twice $824.21 in the hole and an equal 16 percent chance of having risen more than $824.21 above the average to find themselves with a profit.

In case you're wondering,
you needn't play 1044 spins for edge to gain enough on volatility to negatively influence your chances of earning a profit.
It's a matter of degree.
The accompanying table shows the effect for sessions of 40, 80, and 120 spins betting as in the example.

Edge rises faster than volatility with extended play
spins, loss due to edge, standard deviation, probability of being even or ahead
40, -$32, $161 , 42%
80 , -$63, $228, 39%
120 , $95, $279 , 37%

The casino views all of this oppositely.
The bosses want the most action possible, over lots of patrons and long periods, so the effect of volatility will be insignificant compared to that of edge.
After 5,622 spins, the chance of players as a group being ahead is only 1 percent.
After 9,950 spins, it's a mere 0.1 percent. After a million spins, the casino has statistically expected earnings due to edge of $790,000 with 99 percent probability of being between $715,000 and $865,000, and virtually no chance of having lost to the hoi polloi..

If you get behind in a game, you may chase your losses and keep playing.
Or, if you get ahead, you may think you can go on forever.
It may work.
You may get lucky, hit a hot streak, and strike it rich.
But the laws of the universe, as applied to edge and volatility, say that the longer you play, the less your chances of success.

The punter's poet, Sumner A Ingmark, put it like this:

Thank You again Alan

Comments

1BB
1BB Oct 23, 2013

I didn't know Al died. That's too bad.

FrankScoblete
FrankScoblete Oct 27, 2013

I always enjoyed his columns. He will be missed.

tournamentking
tournamentking Dec 01, 2013

This man always made sense. Too bad he isn't required reading for every gambler. His line about "the more you play, the more you will lose" always struck me, and he's a good reason why I limit my play. Edge or not, his words are so true. People should keep that in mind before they choose to count cards or go after the +ev poker machines for a boatload of hours.

7craps
Posted by 7craps
Sep 10, 2010

some Craps tables

edit begins (not completed)
10/25/2013

A) length of a shooter's hand in Craps Table
(probability of rolling a 7 on any roll = 6/36)

examples:
1) what is the probability of any shooter to not get past the 6th roll?
in other words, to 7out by the 6th roll (includes the 6th roill)
0.50278912957882

2) to 7out on the 3rd roll?
(the highest probability of any one roll to 7out on. roll #2 is second)
0.116769547

3) to Survive the 30th roll or the 50th?
30: 0.014315113 or 1 in 69.86
50: 0.000742575 or 1 in 1,346.67

4) get past the 153rd roll? (to Survive the 153rd roll)
1 in 5,590,264,071.83

5) to 7out on exactly your 154th roll?
1 in 40,648,590,642.69

RollSurvival by1 in Survival7out byRoll7out on1 in 7out on
111.000100.00
20.8888888891.130.1111111111111120.1111111119.00
30.7721193421.300.2278806584362130.1167695478.56
40.6673525381.500.3326474622770940.1047668049.55
50.5761289091.740.4238710911700550.09122362910.96
60.497210872.010.5027891295788260.07891803812.67
70.4290441072.330.5709558933747970.06816676414.67
80.3701913492.700.6298086514588380.05885275816.99
90.3193906993.130.6806093013484090.0508006519.68
100.2755465623.630.72445343801271100.04384413722.81
110.2377104264.210.76228957403871110.03783613626.43
120.2050619254.880.79493807470694120.03264850130.63
130.1768919035.650.82310809653915130.02817002235.50
140.1525875696.550.84741243116016140.02430433541.14
150.131619567.600.86838043965154150.02096800847.69
160.1135307038.810.88646929664857160.01808885755.28
170.09792624910.210.90207375103577170.01560445464.08
180.0844654111.840.91553458977339180.01346083974.29
190.07285402913.730.92714597073443190.01161138186.12
200.06283822915.910.93716177107751200.010015899.84
210.0541989218.450.94580108000490210.008639309115.75
220.04674705121.390.95325294882548220.007451869134.19
230.04031950324.800.95968049700960230.006427548155.58
240.0347755428.760.96522446029318240.005543963180.38
250.02999374433.340.97000625573677250.004781795209.13
260.02586937138.660.97413062884098260.004124373242.46
270.02231206144.820.97768793922773270.00355731281.11
280.01924386651.960.98075613388823280.003068195325.92
290.0165975560.250.98340245045075290.002646317377.88
300.01431511369.860.98568488722231300.002282437438.13
310.01234652880.990.98765347180503310.001968585507.98
320.01064864493.910.98935135578848320.001697884588.97
330.009184241108.880.99081575929113330.001464404682.87
340.007921214126.240.99207878589382340.001263027791.75
350.006831874146.370.99316812571178350.00108934917.99
360.005892338169.710.99410766193198360.0009395361,064.35
370.005082006196.770.99491799405020370.0008103321,234.06
380.004383111228.150.99561688923312380.0006988951,430.83
390.003780328264.530.99621967166785390.0006027821,658.97
400.003260442306.710.99673955841081400.0005198871,923.50
410.002812051355.610.99718794908172410.0004483912,230.20
420.002425324412.320.99757467574136420.0003867272,585.81
430.002091782478.060.99790821842246430.0003335432,998.12
440.001804109554.290.99819589103257440.0002876733,476.17
450.001555998642.670.99844400169998450.0002481114,030.46
460.001342009745.150.99865799107506460.0002139894,673.13
470.001157448863.970.99884255161671470.0001845615,418.28
480.000998271,001.730.99900173047753480.0001591796,282.24
490.0008609821,161.460.99913901824259490.0001372887,283.97
500.0007425751,346.670.99925742546618500.0001184078,445.43
510.0006404511,561.400.99935954868441510.0001021239,792.09
520.0005523731,810.370.99944762735040528.80787E-0511,353.49
530.0004764072,099.050.99952359294022537.59656E-0513,163.85
540.0004108892,433.750.99958911130615546.55184E-0515,262.90
550.0003543812,821.820.99964561920559555.65079E-0517,696.64
560.0003056443,271.780.99969435580674564.87366E-0520,518.46
570.000263613,793.480.99973638986160574.20341E-0523,790.23
580.0002273574,398.370.99977264314214583.62533E-0527,583.71
590.0001960895,099.720.99980391065356593.12675E-0531,982.08
600.0001691225,912.890.99983087806775602.69674E-0537,081.79
610.0001458636,855.740.99985413675932612.32587E-0542,994.68
620.0001258037,948.920.99987419677374622.006E-0549,850.41
630.0001085029,216.420.99989149801220631.73012E-0557,799.33
649.35801E-0510,686.030.99990641987813641.49219E-0567,015.75
658.07104E-0512,389.980.99991928959722651.28697E-0577,701.77
666.96106E-0514,365.630.99993038939317661.10998E-0590,091.75
676.00373E-0516,656.310.99993996267658679.57328E-06104,457.37
685.17806E-0519,312.250.99994821938281688.25671E-06121,113.67
694.46594E-0522,391.690.99995534057563697.12119E-06140,425.91
703.85176E-0525,962.170.99996148241783706.14184E-06162,817.60
713.32204E-0530,101.980.99996677959575715.29718E-06188,779.76
722.86517E-0534,901.910.99997134827283724.56868E-06218,881.74
732.47114E-0540,467.210.99997528863701733.94036E-06253,783.65
742.13129E-0546,919.940.99997868709779743.39846E-06294,250.86
751.83818E-0554,401.580.99998161818107752.93108E-06341,170.79
761.58538E-0563,076.220.99998414616352762.52798E-06395,572.37
771.36735E-0573,134.070.99998632648207772.18032E-06458,648.58
781.17931E-0584,795.700.99998820694961781.88047E-06531,782.64
791.01712E-0598,316.850.99998982880353791.62185E-06616,578.34
808.77239E-06113,994.020.99999122760997801.39881E-06714,895.19
817.56596E-06132,171.000.99999243404383811.20643E-06828,889.20
826.52544E-06153,246.400.99999347456137821.04052E-06961,060.20
835.62802E-06177,682.400.99999437198045838.97419E-071,114,306.60
844.85402E-06206,014.840.99999514598085847.74E-071,291,988.99
854.18646E-06238,865.060.99999581353588856.67555E-071,498,003.84
863.61072E-06276,953.420.99999638928458865.75749E-071,736,868.89
873.11415E-06321,115.190.99999688585272874.96568E-072,013,822.31
882.68587E-06372,318.800.99999731412971884.28277E-072,334,937.50
892.31649E-06431,687.110.99999768350737893.69378E-072,707,256.29
901.99791E-06500,522.020.99999800208591903.18579E-073,138,943.40
911.72315E-06580,333.050.99999827685154912.74766E-073,639,465.41
921.48617E-06672,870.390.99999851382968922.36978E-074,219,798.46
931.28178E-06780,163.320.99999871821711932.04387E-074,892,668.84
941.1055E-06904,564.710.99999889449590941.76279E-075,672,832.16
959.53468E-071,048,802.600.99999904653173951.52036E-076,577,396.87
968.22341E-071,216,040.020.99999917765864961.31127E-077,626,199.47
977.09248E-071,409,944.380.99999929075217971.13094E-078,842,239.48
986.11708E-071,634,767.870.99999938829236989.75402E-0810,252,183.86
995.27582E-071,895,440.720.99999947241822998.41259E-0811,886,951.72
1004.55025E-072,197,679.310.999999544974561007.25563E-0813,782,392.46
1013.92447E-072,548,111.530.999999607552501016.25779E-0815,980,071.74
1023.38476E-072,954,422.120.999999661524331025.39718E-0818,528,183.29
1032.91926E-073,425,521.200.999999708073621034.65493E-0821,482,605.41
1042.51779E-073,971,739.660.999999748221161044.01475E-0824,908,126.61
1052.17153E-074,605,055.690.999999782847361053.46262E-0828,879,866.26
1061.87288E-075,339,357.490.999999812711551062.98642E-0833,484,921.92
1071.61531E-076,190,747.810.999999838468631072.57571E-0838,824,279.47
1081.39317E-077,177,897.070.999999860683431082.22148E-0845,015,027.15
1091.20157E-078,322,452.770.999999879843121091.91597E-0852,192,924.42
1101.03632E-079,649,514.270.999999896367841101.65247E-0860,515,377.07
1118.938E-0811,188,183.120.999999910619981111.42521E-0870,164,891.60
1127.70879E-0812,972,201.300.999999922912081121.22921E-0881,353,074.42
1136.64863E-0815,040,691.120.999999933513691131.06016E-0894,325,275.81
1145.73427E-0817,439,013.170.999999942657311149.14361E-09109,365,966.74
1154.94566E-0820,219,761.050.999999950543431157.88613E-09126,804,979.46
1164.2655E-0823,443,914.680.999999957345011166.80158E-09147,024,741.85
1173.67888E-0827,182,177.590.999999963211191175.86618E-09170,468,654.74
1183.17294E-0831,516,527.360.999999968270621185.05943E-09197,650,832.47
1192.73658E-0836,542,013.360.999999972634241194.36362E-09229,167,361.69
1202.36023E-0842,368,841.130.999999976397751203.76351E-09265,709,376.56
1212.03563E-0849,124,789.070.999999979643681213.24593E-09308,078,214.04
1221.75568E-0856,958,010.570.999999982443211222.79953E-09357,203,007.84
1231.51423E-0866,040,282.920.999999984857731232.41452E-09414,161,006.84
1241.30598E-0876,570,774.240.999999986940191242.08246E-09480,201,304.48
1251.12637E-0888,780,411.100.999999988736251251.79607E-09556,772,080.02
1269.71469E-09102,936,942.640.999999990285321261.54906E-09645,552,466.57
1278.37866E-09119,350,812.050.999999991621341271.33602E-09748,489,447.15
1287.22638E-09138,381,964.470.999999992773631281.15229E-09867,840,236.02
1296.23256E-09160,447,740.230.999999993767441299.93816E-101,006,222,112.75
1305.37542E-09186,032,026.970.999999994624581308.5714E-101,166,670,067.35
1314.63616E-09215,695,870.880.999999995363841317.39261E-101,352,701,845.36
1323.99856E-09250,089,780.080.999999996001441326.37593E-101,568,397,883.09
1333.44866E-09289,967,989.870.999999996551341335.49908E-101,818,487,443.33
1342.97438E-09336,205,002.540.999999997025621344.74281E-102,108,455,911.43
1352.56532E-09389,814,764.670.999999997434681354.09055E-102,444,660,285.98
1362.21252E-09451,972,902.270.999999997787481363.52799E-102,834,475,948.16
1371.90824E-09524,042,501.470.999999998091761373.0428E-103,286,447,400.40
1381.64581E-09607,604,000.070.999999998354191382.62433E-103,810,492,076.38
1391.41947E-09704,489,845.520.999999998580531392.26342E-104,418,094,044.28
1401.22425E-09816,824,679.210.999999998775751401.95214E-105,122,584,572.95
1411.05589E-09947,071,928.430.999999998944111411.68367E-105,939,410,552.58
1429.10674E-101,098,087,827.730.999999999089331421.45212E-106,886,480,147.42
1437.85432E-101,273,184,054.140.999999999214571431.25242E-107,984,567,754.96
1446.77415E-101,476,200,350.090.999999999322591441.08018E-109,257,751,028.58
1455.84253E-101,711,588,726.320.999999999415751459.31623E-1110,733,960,793.66
1465.03902E-101,984,511,091.530.999999999496101468.03501E-1112,445,541,431.59
1474.34603E-102,300,952,449.520.999999999565401476.92998E-1114,430,058,546.81
1483.74833E-102,667,852,146.330.999999999625171485.97693E-1116,730,997,177.96
1493.23284E-103,093,256,045.410.999999999676721495.15494E-1119,398,856,069.45
1502.78824E-103,586,492,968.000.999999999721181504.446E-1122,492,132,184.84
1512.40478E-104,158,379,267.890.999999999759521513.83457E-1126,078,570,573.71
1522.07406E-104,821,456,026.790.999999999792591523.30721E-1130,236,966,550.21
1531.78882E-105,590,264,071.830.999999999821121532.85237E-1135,058,517,488.94
1541.54281E-106,481,662,846.050.999999999845721542.46011E-1140,648,590,642.69
1551.33064E-107,515,200,124.740.999999999866941552.12177E-1147,130,474,563.30
1561.14764E-108,713,540,684.890.999999999885241561.82998E-1154,645,387,700.91
1579.89809E-1110,102,963,328.600.999999999901021571.5783E-1163,359,143,891.37
1588.53684E-1111,713,937,159.430.999999999914631581.36124E-1173,462,191,132.38
1597.3628E-1113,581,789,749.420.999999999926371591.17404E-1185,176,071,932.72
1606.35022E-1115,747,481,848.920.999999999936501601.01258E-1198,757,735,373.51
1615.4769E-1118,258,505,628.280.999999999945231618.73324E-12114,505,088,285.84
1624.72368E-1121,169,926,149.240.999999999952761627.5322E-12132,763,387,399.64
1634.07405E-1124,545,588,904.600.999999999959261636.49625E-12153,935,010,249.71
1643.51376E-1128,459,519,906.980.999999999964861645.60285E-12178,480,546,402.35
1653.03053E-1132,997,549,029.440.999999999969701654.83236E-12206,938,364,534.78
1662.61375E-1138,259,192,196.810.999999999973861664.16778E-12239,936,048,341.53
1672.25429E-1144,359,833,703.000.999999999977461673.59457E-12278,197,462,851.44
1681.94427E-1151,433,256,510.880.999999999980561683.1003E-12322,549,659,972.82
1691.67688E-1159,634,576,022.670.999999999983231692.67386E-12373,991,000,445.98
1701.44626E-1169,143,641,656.270.999999999985541702.30616E-12433,622,147,830.78
1711.24737E-1180,168,980,822.010.999999999987531711.98896E-12502,774,169,954.84
1721.07582E-1192,952,371,788.450.999999999989241721.71552E-12582,914,784,800.74
1739.27866E-12107,774,145,717.030.999999999990721731.47948E-12675,911,695,538.12
1748.0026E-12124,959,334,135.890.999999999992001741.27609E-12783,643,575,321.12
1756.90204E-12144,884,796,662.480.999999999993101751.10056E-12908,624,962,649.15
1765.95282E-12167,987,485,281.420.999999999994051769.49241E-131,053,473,597,045.73
1775.13415E-12194,774,026,407.440.999999999994871778.18678E-131,221,480,777,697.45
1784.42807E-12225,831,830,861.770.999999999995571787.05991E-131,416,449,010,023.74
1793.8191E-12261,841,975,396.100.999999999996181796.09068E-131,641,851,851,028.25
1803.29387E-12303,594,138,247.500.999999999996711805.25135E-131,904,270,455,547.78
1812.84088E-12352,003,916,250.680.999999999997161814.53082E-132,207,105,918,828.96
1822.45018E-12408,132,903,260.490.999999999997551823.90687E-132,559,590,581,057.40
1832.11322E-12473,211,970,190.720.999999999997891833.36953E-132,967,775,701,726.85
1841.82259E-12548,668,257,184.990.999999999998181842.90656E-133,440,488,638,174.56
1851.57194E-12636,156,469,839.690.999999999998431852.50577E-133,990,783,896,650.86
1861.35576E-12737,595,165,784.210.999999999998641862.1616E-134,626,193,762,065.22
1871.16931E-12855,208,827,358.680.999999999998831871.86517E-135,361,428,127,822.02
1881.00849E-12991,576,643,014.740.999999999998991881.6076E-136,220,441,474,268.64
1898.698E-131,149,689,067,182.670.999999999999131891.38778E-137,205,759,403,792.79
1907.5018E-131,333,013,398,924.630.999999999999251901.19571E-138,363,230,505,794.79
1916.47011E-131,545,569,817,469.840.999999999999351911.0314E-139,695,585,850,097.95
1925.5803E-131,792,019,542,039.740.999999999999441928.90399E-1411,230,921,764,016.20
1934.81286E-132,077,767,049,248.810.999999999999521937.67164E-1413,035,020,629,147.60
1944.15096E-132,409,078,589,639.830.999999999999591946.61693E-1415,112,750,427,417.80
1953.5801E-132,793,219,602,341.500.999999999999641955.70655E-1417,523,733,958,640.10
1963.08774E-133,238,614,041,259.330.999999999999691964.92939E-1420,286,484,807,975.20
1972.6631E-133,755,029,106,716.040.999999999999731974.24105E-1423,579,055,640,683.20
1982.29685E-134,353,789,433,581.830.999999999999771983.66374E-1427,294,543,196,184.80
1991.98097E-135,048,025,432,896.400.999999999999801993.16414E-1431,604,207,911,371.90
2001.70854E-135,852,961,232,947.040.999999999999832002.72005E-1436,764,078,590,779.60
length of a shooter's hand table above created with the Wizard's recursive formulas
(can actually be done also by a Markov chain or SN Ethier's closed form formula)

Here is a table from the famous Zumma Craps system tester
(35,097 actual casino dice rolls)
4,183 shooter hands
LengthCountFreq%or lesscount
244810.71%10.71%448
352012.43%23.14%968
443210.33%33.47%1400
542410.14%43.61%1824
63337.96%51.57%2157
72706.45%58.02%2427
82415.76%63.78%2668
92054.90%68.68%2873
101844.40%73.08%3057
111593.80%76.88%3216
121423.39%80.28%3358
131152.75%83.03%3473
14982.34%85.37%3571
15972.32%87.69%3668
16791.89%89.58%3747
17581.39%90.96%3805
18441.05%92.02%3849
19370.88%92.90%3886
20390.93%93.83%3925
21431.03%94.86%3968
22240.57%95.43%3992
23280.67%96.10%4020
24210.50%96.61%4041
25210.50%97.11%4062
26150.36%97.47%4077
27190.45%97.92%4096
2880.19%98.11%4104
2990.22%98.33%4113
3090.22%98.54%4122
3180.19%98.73%4130
3260.14%98.88%4136
3370.17%99.04%4143
3460.14%99.19%4149
3560.14%99.33%4155
3670.17%99.50%4162
3700.00%99.50%4162
3860.14%99.64%4168
3900.00%99.64%4168
4020.05%99.69%4170
4140.10%99.78%4174
4210.02%99.81%4175
4310.02%99.83%4176
4400.00%99.83%4176
4510.02%99.86%4177
4620.05%99.90%4179
4720.05%99.95%4181
4800.00%99.95%4181
4900.00%99.95%4181
5010.02%99.98%4182
5100.00%99.98%4182
5200.00%99.98%4182
5300.00%99.98%4182
5400.00%99.98%4182
5510.02%100.00%4183

Comments

odiousgambit
odiousgambit Sep 11, 2010

not sure how the "one hour" thing works out. Do the percentages change with more trials?

teddys
teddys Sep 12, 2010

That's interesting. So for a hour's play you actually have a better than 50% chance of leaving with the same money you came in with. Pass line is a great bet for the casual short-term player. I wonder at which point the edge kicks in and you have a >50% chance of losing.

7craps
7craps Sep 15, 2010

9-15-2001

I have more information and tables coming. Just finishing a large unrelated musical project that has been slowing me down.



"I wonder at which point the edge kicks in and you have a >50% chance of losing."

I was also surprised at seeing that information when I made the table.



The answer is:

70 pass line wagers have a 50.03% chance of being even or ahead

at 72 wagers it drops to 49.89% of winning and a 50.11% chance or better of losing.

Up to 70 wagers one needs to make an even number of bets to have the chance of coming out even or ahead.

At an odd number of bets like 69 bets, one has a 45.31% chance of being ahead and an odd number of equal wagers can not end in an even outcome.



The same exists in the game of Baccarat.

Player bet is 74 hands ( about the same bets in a full shoe) at 50.09% of being even or ahead.

Player at 76 hands drops to 49.97% coming out even or ahead



Banker bet is 76 hands at 50.03% to be ahead (only by 25 cents when paying 5% commission on a banker win)

78 hands at 50.15% to be even or ahead



a Baccarat table is coming soon

Zcore13
Zcore13 Apr 11, 2013

I'm obviously way late to this party, but what if you place one additional bet of double odds on every passline bet when the point is established? From what I understand, the odds help the player. So if it's 50/50 with just a passline bet after an hour of play, wouldn't it be better than 50/50 if you place odds?



ZCore13

7craps
7craps Aug 27, 2013

but what if you place one additional bet of double odds on every passline bet when the point is established?



From what I understand, the odds help the player.



So if it's 50/50 with just a passline bet after an hour of play,

wouldn't it be better than 50/50 if you place odds?



ZCore13



nice question

the odds bet reduces the combined house edge per $ bet

but still needs time to play out



some data (calculated)

flat bet pass $5 / $5 with $10 odds



30 wagers

prob loss: 45.859956% / 51.203797%

70 wagers

prob loss: 49.974513% / 51.731364%

100 wagers

prob loss: 51.669330% / 52.039478%



110 wagers

52.128743 / 52.132462



120 wagers

52.552143 / 52.221542

130 wagers

52.945653 / 52.307289

140 wagers

53.313939 / 52.389974

150 wagers

53.660638 / 52.469867

200 wagers

prob loss: 55.154561% / 52.835661%

500 wagers

prob loss: 60.706249% / 54.433524%



a bit more than 110 wagers does the 2X odds bettor

has a lower net losing probability

7craps
Posted by 7craps
Aug 27, 2010

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