Balloon Game
Introduction
The Balloon Game is a keno-based game found on multi-game machines made by U1 Gaming. I have seen such machines at the Las Vegas Club, Rampart, and Dotty's casinos in Las Vegas. Balloon Game is similar to Caveman Keno, except it uses five balloons instead of three eggs.
All games by U1 feature random bonuses in addition to the base game. These random bonuses evidently add 0.5% to the total return. I can tell because in all but one case, my return is 0.5% less than the advertised return of the game. This page endeavors to only analyze the base game, and ignores the random bonuses.
Rules
- Player picks 2 to 10 numbers from 1 to 80.
- The game will pick 5 numbers from the remaining numbers and mark them with balloons.
- The game will pick 20 numbers from 1 to 80. As the game picks numbers, it will count the number that match the player's picks as well as the balloons. When the game picks a number marked with a balloon, that balloon will pop.
- The player is paid according to the number of player numbers caught and balloons popped.
Odds
Following is an analysis of the game according to how many numbers the player chooses, from 2 to 10. Rather than repeat the same table introductions for each number of picks, let me explain them here.
Pay Table: How much each win pays. These wins are based on a maximum $2 bet as found at the Rampart casino. As the player bets less, the pay table will be depressed.
Combinations: Number of combinations for each win, according to the number of catches and balloons popped. Please note that Excel, where I did the math, can handle only 15 significant digits. Should anyone at Microsoft read this, please do something about this.
Probabilities: Probability of each win, according to the number of catches and balloons popped.
Return: Contribution to the return for each win, according to the number of catches and balloons popped. The lower image--rightell shows the overall return of the game.
Pick 2
Pick 2 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
2 |
7 |
14 |
30 |
120 |
530 |
1 |
0 |
1 |
2 |
10 |
80 |
0 |
0 |
0 |
0 |
3.5 |
60 |
Pick 2 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
2 |
143,371,172,961,555,000 |
52,717,590,634,746,100 |
14,542,783,623,378,200 |
1,848,658,935,175,200 |
86,270,750,308,176 |
212,566,476,905,162,000 |
1 |
868,289,728,101,701,000 |
353,517,960,727,121,000 |
105,435,181,269,492,000 |
14,542,783,623,378,200 |
739,463,574,070,080 |
1,342,525,117,295,760,000 |
0 |
1,225,735,666,170,230,000 |
549,916,827,797,744,000 |
176,758,980,363,561,000 |
26,358,795,317,373,100 |
1,454,278,362,337,820 |
1,980,224,548,011,250,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 2 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
2 |
0.0405539892882 |
0.0149117047851 |
0.0041135737338 |
0.0005229119153 |
0.0000244025560 |
0.0601265822785 |
1 |
0.2456045494020 |
0.0999961379708 |
0.0298234095702 |
0.0041135737338 |
0.0002091647661 |
0.3797468354430 |
0 |
0.3467117555725 |
0.1555495479546 |
0.0499980689854 |
0.0074558523926 |
0.0004113573734 |
0.5601265822785 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 2 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
2 |
0.283878 |
0.208764 |
0.123407 |
0.062749 |
0.012933 |
0.691732 |
1 |
0.000000 |
0.099996 |
0.059647 |
0.041136 |
0.016733 |
0.217512 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.026095 |
0.024681 |
0.050777 |
Total |
0.283878 |
0.308760 |
0.183054 |
0.129981 |
0.054348 |
0.960021 |
Pick 3
Pick 3 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
3 |
20 |
50 |
120 |
305 |
1,000 |
2 |
1 |
2 |
10 |
30 |
100 |
1 |
- |
- |
2 |
6 |
80 |
0 |
- |
- |
- |
4 |
60 |
Pick 3 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
3 |
34,141,118,125,016,500 |
11,554,540,413,095,000 |
2,988,243,210,283,200 |
354,537,330,033,600 |
15,363,284,301,456 |
49,053,802,362,729,800 |
2 |
327,690,164,509,615,000 |
123,489,150,664,953,000 |
34,663,621,239,285,100 |
4,482,364,815,424,800 |
212,722,398,020,160 |
490,538,023,627,298,000 |
1 |
974,744,427,642,937,000 |
406,787,790,425,728,000 |
123,489,150,664,953,000 |
17,331,810,619,642,600 |
896,472,963,084,960 |
1,523,249,652,316,350,000 |
0 |
900,820,856,955,922,000 |
414,320,897,655,834,000 |
135,595,930,141,909,000 |
20,581,525,110,825,500 |
1,155,454,041,309,500 |
1,472,474,663,905,800,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 3 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
3 |
0.0096571612698 |
0.0032683188570 |
0.0008452548768 |
0.0001002844769 |
0.0000043456607 |
0.0138753651412 |
2 |
0.0926904840551 |
0.0349301577843 |
0.0098049565710 |
0.0012678823152 |
0.0000601706861 |
0.1387536514119 |
1 |
0.2757163400479 |
0.1150640491719 |
0.0349301577843 |
0.0049024782855 |
0.0002535764630 |
0.4308666017527 |
0 |
0.2548063088899 |
0.1171948648973 |
0.0383546830573 |
0.0058216929641 |
0.0003268318857 |
0.4165043816943 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 3 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
3 |
0.193143 |
0.163416 |
0.101431 |
0.030587 |
0.004346 |
0.492922 |
2 |
0.092690 |
0.069860 |
0.098050 |
0.038036 |
0.006017 |
0.304654 |
1 |
0.000000 |
0.000000 |
0.069860 |
0.029415 |
0.020286 |
0.119561 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.023287 |
0.019610 |
0.042897 |
Total |
0.285834 |
0.233276 |
0.269340 |
0.121325 |
0.050259 |
0.960034 |
Pick 4
Pick 4 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
4 |
45 |
100 |
200 |
500 |
2,400 |
3 |
4 |
10 |
20 |
60 |
200 |
2 |
1 |
2 |
4 |
10 |
100 |
1 |
- |
- |
1 |
4 |
60 |
0 |
- |
- |
- |
3 |
80 |
Pick 4 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
4 |
7,775,242,819,645,210 |
2,407,195,919,394,800 |
581,047,290,888,400 |
64,013,684,589,400 |
2,560,547,383,576 |
10,830,060,261,901,400 |
3 |
105,463,501,221,485,000 |
36,589,377,974,801,000 |
9,628,783,677,579,200 |
1,162,094,581,776,800 |
51,210,947,671,520 |
152,894,968,403,314,000 |
2 |
497,185,077,187,001,000 |
192,094,234,367,705,000 |
54,884,066,962,201,400 |
7,221,587,758,184,400 |
348,628,374,533,040 |
751,733,594,649,625,000 |
1 |
968,202,518,732,581,000 |
414,320,897,655,834,000 |
128,062,822,911,803,000 |
18,294,688,987,400,500 |
962,878,367,757,920 |
1,529,843,806,655,380,000 |
0 |
658,770,227,272,777,000 |
310,740,673,241,876,000 |
103,580,224,413,959,000 |
16,007,852,863,975,400 |
914,734,449,370,024 |
1,090,013,712,241,960,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 4 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
4 |
0.0021993062309 |
0.0006808997619 |
0.0001643551149 |
0.0000181069194 |
0.0000007242768 |
0.0030633923039 |
3 |
0.0298314201557 |
0.0103496763805 |
0.0027235990475 |
0.0003287102299 |
0.0000144855356 |
0.0432478913492 |
2 |
0.1406338378768 |
0.0543358009978 |
0.0155245145708 |
0.0020426992856 |
0.0000986130690 |
0.2126354658000 |
1 |
0.2738658948127 |
0.1171948648973 |
0.0362238673319 |
0.0051748381903 |
0.0002723599048 |
0.4327318251369 |
0 |
0.1863398351867 |
0.0878961486730 |
0.0292987162243 |
0.0045279834165 |
0.0002587419095 |
0.3083214254100 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 4 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
4 |
0.098969 |
0.068090 |
0.032871 |
0.009053 |
0.001738 |
0.210722 |
3 |
0.119326 |
0.103497 |
0.054472 |
0.019723 |
0.002897 |
0.299914 |
2 |
0.140634 |
0.108672 |
0.062098 |
0.020427 |
0.009861 |
0.341692 |
1 |
0.000000 |
0.000000 |
0.036224 |
0.020699 |
0.016342 |
0.073265 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.013584 |
0.020699 |
0.034283 |
Total |
0.358928 |
0.280258 |
0.185665 |
0.083486 |
0.051538 |
0.959876 |
Pick 5
Pick 5 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
5 |
200 |
400 |
1,000 |
2,000 |
5,000 |
4 |
15 |
30 |
60 |
200 |
500 |
3 |
2 |
5 |
13 |
35 |
200 |
2 |
- |
1 |
2 |
5 |
100 |
1 |
- |
- |
- |
2 |
60 |
0 |
- |
- |
- |
3 |
80 |
Pick 5 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
5 |
1,687,749,477,006,660 |
474,658,350,303,200 |
106,388,940,585,200 |
10,819,214,296,800 |
396,704,524,216 |
2,280,012,686,716,080 |
4 |
30,437,466,713,192,700 |
9,662,687,845,458,000 |
2,373,291,751,516,000 |
265,972,351,463,000 |
10,819,214,296,800 |
42,750,237,875,926,500 |
3 |
202,783,819,627,327,000 |
72,148,069,246,086,400 |
19,325,375,690,916,000 |
2,373,291,751,516,000 |
106,388,940,585,200 |
296,736,945,256,431,000 |
2 |
625,857,975,684,341,000 |
248,008,988,033,422,000 |
72,148,069,246,086,400 |
9,662,687,845,458,000 |
474,658,350,303,200 |
956,152,379,159,611,000 |
1 |
897,324,160,573,556,000 |
393,896,628,053,082,000 |
124,004,494,016,711,000 |
18,037,017,311,521,600 |
966,268,784,545,800 |
1,434,228,568,739,420,000 |
0 |
479,305,395,158,066,000 |
231,961,347,631,259,000 |
78,779,325,610,616,400 |
12,400,449,401,671,100 |
721,480,692,460,864 |
803,167,998,494,073,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 5 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
5 |
0.0004773970443 |
0.0001342619249 |
0.0000300931901 |
0.0000030603244 |
0.0000001122119 |
0.0006449246956 |
4 |
0.0086095459328 |
0.0027331891850 |
0.0006713096244 |
0.0000752329751 |
0.0000030603244 |
0.0120923380417 |
3 |
0.0573594585237 |
0.0204078125813 |
0.0054663783700 |
0.0006713096244 |
0.0000300931901 |
0.0839350522895 |
2 |
0.1770302712709 |
0.0701518557484 |
0.0204078125813 |
0.0027331891850 |
0.0001342619249 |
0.2704573907106 |
1 |
0.2538172328804 |
0.1114176532474 |
0.0350759278742 |
0.0051019531453 |
0.0002733189185 |
0.4056860860658 |
0 |
0.1355763886107 |
0.0656126180235 |
0.0222835306495 |
0.0035075927874 |
0.0002040781258 |
0.2271842081969 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 5 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
5 |
0.095479 |
0.053705 |
0.030093 |
0.006121 |
0.000561 |
0.185959 |
4 |
0.129143 |
0.081996 |
0.040279 |
0.015047 |
0.001530 |
0.267994 |
3 |
0.114719 |
0.102039 |
0.068330 |
0.023496 |
0.006019 |
0.314602 |
2 |
0.000000 |
0.070152 |
0.040816 |
0.013666 |
0.013426 |
0.138060 |
1 |
0.000000 |
0.000000 |
0.000000 |
0.010204 |
0.016399 |
0.026603 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.010523 |
0.016326 |
0.026849 |
Total |
0.339342 |
0.307891 |
0.179517 |
0.079056 |
0.054261 |
0.960067 |
Pick 6
Pick 6 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
6 |
500 |
1,200 |
2,500 |
6,000 |
15,000 |
5 |
22 |
50 |
111 |
475 |
1,500 |
4 |
5 |
10 |
20 |
50 |
300 |
3 |
2 |
4 |
8 |
20 |
200 |
2 |
- |
- |
2 |
6 |
100 |
1 |
- |
- |
- |
3 |
60 |
0 |
- |
- |
- |
5 |
80 |
Pick 6 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
6 |
347,856,762,436,488 |
88,150,836,484,880 |
18,238,104,100,320 |
1,700,162,246,640 |
56,672,074,888 |
456,002,537,343,216 |
5 |
8,039,356,287,421,060 |
2,319,045,082,909,920 |
528,905,018,909,280 |
54,714,312,300,960 |
2,040,194,695,968 |
10,944,060,896,237,200 |
4 |
71,214,009,421,025,500 |
23,190,450,829,099,200 |
5,797,612,707,274,800 |
661,131,273,636,600 |
27,357,156,150,480 |
100,890,561,387,187,000 |
3 |
310,615,626,693,288,000 |
113,375,537,386,707,000 |
30,920,601,105,465,600 |
3,865,075,138,183,200 |
176,301,672,969,760 |
458,953,141,996,613,000 |
2 |
705,825,243,506,547,000 |
286,981,829,010,103,000 |
85,031,653,040,030,400 |
11,595,225,414,549,600 |
579,761,270,727,480 |
1,090,013,712,241,960,000 |
1 |
794,458,895,285,649,000 |
357,883,222,059,657,000 |
114,792,731,604,041,000 |
17,006,330,608,006,100 |
927,618,033,163,968 |
1,285,068,797,590,520,000 |
0 |
346,895,579,277,124,000 |
172,314,143,954,650,000 |
59,647,203,676,609,600 |
9,566,060,967,003,420 |
566,877,686,933,536 |
588,989,865,562,320,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 6 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
6 |
0.0000983948107 |
0.0000249343575 |
0.0000051588326 |
0.0000004809081 |
0.0000000160303 |
0.0001289849391 |
5 |
0.0022740134019 |
0.0006559654044 |
0.0001496061449 |
0.0000154764977 |
0.0000005770897 |
0.0030956385387 |
4 |
0.0201436042935 |
0.0065596540440 |
0.0016399135110 |
0.0001870076811 |
0.0000077382489 |
0.0285379177784 |
3 |
0.0878607779894 |
0.0320694197707 |
0.0087462053920 |
0.0010932756740 |
0.0000498687150 |
0.1298195475411 |
2 |
0.1996498234143 |
0.0811757187946 |
0.0240520648280 |
0.0032798270220 |
0.0001639913511 |
0.3083214254100 |
1 |
0.2247207500907 |
0.1012308963791 |
0.0324702875178 |
0.0048104129656 |
0.0002623861618 |
0.3634947331150 |
0 |
0.0981229302622 |
0.0487408019603 |
0.0168718160632 |
0.0027058572932 |
0.0001603470989 |
0.1666017526777 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 6 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
6 |
0.049197 |
0.029921 |
0.012897 |
0.002885 |
0.000240 |
0.095142 |
5 |
0.050028 |
0.032798 |
0.016606 |
0.007351 |
0.000866 |
0.107650 |
4 |
0.100718 |
0.065597 |
0.032798 |
0.009350 |
0.002321 |
0.210785 |
3 |
0.175722 |
0.128278 |
0.069970 |
0.021866 |
0.009974 |
0.405808 |
2 |
0.000000 |
0.000000 |
0.048104 |
0.019679 |
0.016399 |
0.084182 |
1 |
0.000000 |
0.000000 |
0.000000 |
0.014431 |
0.015743 |
0.030174 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.013529 |
0.012828 |
0.026357 |
Total |
0.375665 |
0.256594 |
0.180375 |
0.089092 |
0.058371 |
0.960098 |
Pick 7
Pick 7 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
7 |
2,500 |
5,000 |
10,000 |
20,000.0 |
25,000 |
6 |
110 |
220 |
500 |
1,000 |
4,000 |
5 |
10 |
20 |
55 |
120 |
500 |
4 |
2 |
6 |
15 |
50 |
300 |
3 |
1 |
2 |
4 |
10 |
200 |
2 |
- |
- |
2 |
5 |
100 |
1 |
- |
- |
- |
3 |
60 |
0 |
- |
- |
- |
6 |
80 |
Pick 7 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
7 |
67,778,853,872,488 |
15,330,580,258,240 |
2,907,523,842,080 |
246,400,325,600 |
7,392,009,768 |
86,270,750,308,176 |
6 |
1,960,545,359,948,000 |
509,741,793,586,480 |
107,314,061,807,680 |
10,176,333,447,280 |
344,960,455,840 |
2,588,122,509,245,280 |
5 |
22,256,110,926,129,700 |
6,587,432,409,425,280 |
1,529,225,380,759,440 |
160,971,092,711,520 |
6,105,800,068,368 |
30,539,845,609,094,300 |
4 |
129,072,503,772,177,000 |
43,131,997,918,856,000 |
10,979,054,015,708,800 |
1,274,354,483,966,200 |
53,657,030,903,840 |
184,511,567,221,611,000 |
3 |
414,504,842,941,077,000 |
155,275,192,507,882,000 |
43,131,997,918,856,000 |
5,489,527,007,854,400 |
254,870,896,793,240 |
618,656,431,272,462,000 |
2 |
739,452,435,144,519,000 |
308,609,445,109,415,000 |
93,165,115,504,728,900 |
12,939,599,375,656,800 |
658,743,240,942,528 |
1,154,825,338,375,260,000 |
1 |
680,384,566,118,417,000 |
314,660,610,699,795,000 |
102,869,815,036,472,000 |
15,527,519,250,788,200 |
862,639,958,377,120 |
1,114,305,151,063,850,000 |
0 |
249,697,784,117,350,000 |
127,362,628,140,393,000 |
44,951,515,814,256,500 |
7,347,843,931,176,540 |
443,643,407,165,376 |
429,803,415,410,342,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 7 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
7 |
0.0000191719357 |
0.0000043364100 |
0.0000008224226 |
0.0000000696968 |
0.0000000020909 |
0.0000244025560 |
6 |
0.0005545601245 |
0.0001441856324 |
0.0000303548700 |
0.0000028784790 |
0.0000000975756 |
0.0007320766814 |
5 |
0.0062953665332 |
0.0018633220183 |
0.0004325568971 |
0.0000455323050 |
0.0000017270874 |
0.0086385048410 |
4 |
0.0365094657960 |
0.0122003227389 |
0.0031055366972 |
0.0003604640809 |
0.0000151774350 |
0.0521909667479 |
3 |
0.1172468956855 |
0.0439211618599 |
0.0122003227389 |
0.0015527683486 |
0.0000720928162 |
0.1749932414489 |
2 |
0.2091616153688 |
0.0872933091965 |
0.0263526971159 |
0.0036600968217 |
0.0001863322018 |
0.3266540507047 |
1 |
0.1924536699829 |
0.0890049427101 |
0.0290977697322 |
0.0043921161860 |
0.0002440064548 |
0.3151925050659 |
0 |
0.0706295488361 |
0.0360258101446 |
0.0127149918157 |
0.0020784121237 |
0.0001254890339 |
0.1215742519540 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 7 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
7 |
0.047930 |
0.021682 |
0.008224 |
0.001394 |
0.000052 |
0.079282 |
6 |
0.061002 |
0.031721 |
0.015177 |
0.002878 |
0.000390 |
0.111169 |
5 |
0.062954 |
0.037266 |
0.023791 |
0.005464 |
0.000864 |
0.130338 |
4 |
0.073019 |
0.073202 |
0.046583 |
0.018023 |
0.004553 |
0.215380 |
3 |
0.117247 |
0.087842 |
0.048801 |
0.015528 |
0.014419 |
0.283837 |
2 |
0.000000 |
0.000000 |
0.052705 |
0.018300 |
0.018633 |
0.089639 |
1 |
0.000000 |
0.000000 |
0.000000 |
0.013176 |
0.014640 |
0.027817 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.012470 |
0.010039 |
0.022510 |
Total |
0.362151 |
0.251714 |
0.195282 |
0.087234 |
0.063591 |
0.959972 |
Pick 8
Pick 8 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
8 |
6,000 |
12,000 |
25,000 |
25,000 |
25,000 |
7 |
400 |
1,200 |
2,400 |
5,000.0 |
10,000 |
6 |
60 |
120 |
240 |
500 |
1,000 |
5 |
6 |
15 |
30 |
60 |
400 |
4 |
2 |
4 |
8 |
18 |
200 |
3 |
- |
1 |
2 |
5 |
100 |
2 |
- |
- |
1 |
3 |
80 |
1 |
- |
- |
- |
4 |
60 |
0 |
- |
- |
- |
7 |
100 |
Pick 8 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
8 |
12,422,279,003,368 |
2,479,946,806,480 |
427,577,035,600 |
32,611,807,800 |
869,648,208 |
15,363,284,301,456 |
7 |
442,852,598,952,960 |
102,805,067,614,080 |
19,839,574,451,840 |
1,710,308,142,400 |
52,178,892,480 |
567,259,728,053,760 |
6 |
6,292,197,343,456,640 |
1,679,149,437,696,640 |
359,817,736,649,280 |
34,719,255,290,720 |
1,197,215,699,680 |
8,367,080,988,792,960 |
5 |
46,765,234,449,432,600 |
14,208,187,549,740,800 |
3,358,298,875,393,280 |
359,817,736,649,280 |
13,887,702,116,288 |
64,705,426,313,332,200 |
4 |
199,688,464,482,562,000 |
68,503,761,400,536,000 |
17,760,234,437,176,000 |
2,098,936,797,120,800 |
89,954,434,162,320 |
288,141,351,551,558,000 |
3 |
503,456,977,119,673,000 |
193,637,298,892,182,000 |
54,803,009,120,428,800 |
7,104,093,774,870,400 |
335,829,887,539,328 |
759,337,208,794,693,000 |
2 |
734,208,091,632,856,000 |
314,660,610,699,795,000 |
96,818,649,446,090,900 |
13,700,752,280,107,200 |
710,409,377,487,040 |
1,160,098,513,436,340,000 |
1 |
567,808,620,811,661,000 |
269,709,094,885,539,000 |
89,903,031,628,513,000 |
13,831,235,635,155,800 |
782,900,130,291,840 |
942,034,883,091,160,000 |
0 |
178,721,706,515,893,000 |
93,648,991,279,701,000 |
33,713,636,860,692,400 |
5,618,939,476,782,060 |
345,780,890,878,896 |
312,049,055,023,947,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 8 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
0 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
0.0000000000000 |
8 |
0.0000035137675 |
0.0000007014781 |
0.0000001209445 |
0.0000000092246 |
0.0000000002460 |
0.0000043456607 |
7 |
0.0001252653458 |
0.0000290794553 |
0.0000056118247 |
0.0000004837780 |
0.0000000147593 |
0.0001604551631 |
6 |
0.0017798117878 |
0.0004749644360 |
0.0001017780934 |
0.0000098206932 |
0.0000003386446 |
0.0023667136551 |
5 |
0.0132280205131 |
0.0040189298434 |
0.0009499288721 |
0.0001017780934 |
0.0000039282773 |
0.0183025855993 |
4 |
0.0564839059507 |
0.0193769831735 |
0.0050236623042 |
0.0005937055450 |
0.0000254445234 |
0.0815037014968 |
3 |
0.1424079083362 |
0.0547722724370 |
0.0155015865388 |
0.0020094649217 |
0.0000949928872 |
0.2147862251209 |
2 |
0.2076781996570 |
0.0890049427101 |
0.0273861362185 |
0.0038753966347 |
0.0002009464922 |
0.3281456217125 |
1 |
0.1606104229356 |
0.0762899508944 |
0.0254299836315 |
0.0039123051741 |
0.0002214512363 |
0.2664641138718 |
0 |
0.0505532459691 |
0.0264895662828 |
0.0095362438618 |
0.0015893739770 |
0.0000978076294 |
0.0882662377200 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 8 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
8 |
0.021083 |
0.008418 |
0.003024 |
0.000231 |
0.000006 |
0.032761 |
7 |
0.050106 |
0.034895 |
0.013468 |
0.002419 |
0.000148 |
0.101036 |
6 |
0.106789 |
0.056996 |
0.024427 |
0.004910 |
0.000339 |
0.193460 |
5 |
0.079368 |
0.060284 |
0.028498 |
0.006107 |
0.001571 |
0.175828 |
4 |
0.112968 |
0.077508 |
0.040189 |
0.010687 |
0.005089 |
0.246441 |
3 |
0.000000 |
0.054772 |
0.031003 |
0.010047 |
0.009499 |
0.105322 |
2 |
0.000000 |
0.000000 |
0.027386 |
0.011626 |
0.016076 |
0.055088 |
1 |
0.000000 |
0.000000 |
0.000000 |
0.015649 |
0.013287 |
0.028936 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.011126 |
0.009781 |
0.020906 |
Total |
0.370313 |
0.292873 |
0.167995 |
0.072802 |
0.055795 |
0.959779 |
Pick 9
Pick 9 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
9 |
8,000 |
16,000 |
25,000 |
25,000 |
25,000 |
8 |
2,000 |
4,000 |
8,000 |
16,000 |
25,000 |
7 |
150 |
300 |
600 |
1,200.0 |
4,000 |
6 |
20 |
42 |
100 |
200 |
600 |
5 |
4 |
8 |
19 |
44 |
300 |
4 |
1 |
3 |
7 |
15 |
200 |
3 |
- |
- |
2 |
5 |
100 |
2 |
- |
- |
1 |
3 |
80 |
1 |
- |
- |
- |
4 |
60 |
0 |
- |
- |
- |
8 |
100 |
Pick 9 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
9 |
2,128,985,542,008 |
370,141,314,400 |
57,435,721,200 |
3,893,947,200 |
90,858,768 |
2,560,547,383,576 |
8 |
92,639,641,152,240 |
18,988,249,428,720 |
3,331,271,829,600 |
258,460,745,400 |
7,009,104,960 |
115,224,632,260,920 |
7 |
1,622,278,130,679,360 |
386,669,806,548,480 |
75,952,997,714,880 |
6,662,543,659,200 |
206,768,596,320 |
2,091,770,247,198,240 |
6 |
15,091,276,392,118,100 |
4,135,218,764,476,800 |
902,229,548,613,120 |
88,611,830,667,360 |
3,109,187,040,960 |
20,220,445,722,916,300 |
5 |
82,584,862,923,046,200 |
25,765,593,840,201,600 |
6,202,828,146,715,200 |
676,672,161,459,840 |
26,583,549,200,208 |
115,256,540,620,623,000 |
4 |
276,854,373,145,566,000 |
97,541,176,680,763,200 |
25,765,593,840,201,600 |
3,101,414,073,357,600 |
135,334,432,291,968 |
403,397,892,172,181,000 |
3 |
570,615,883,582,465,000 |
225,428,497,217,764,000 |
65,027,451,120,508,800 |
8,588,531,280,067,200 |
413,521,876,447,680 |
870,073,885,077,252,000 |
2 |
699,432,167,706,901,000 |
307,951,429,234,981,000 |
96,612,213,093,327,400 |
13,934,453,811,537,600 |
736,159,824,005,760 |
1,118,666,423,670,750,000 |
1 |
463,926,656,486,393,000 |
226,434,874,437,486,000 |
76,987,857,308,745,200 |
12,076,526,636,665,900 |
696,722,690,576,880 |
780,122,637,559,867,000 |
0 |
127,174,300,239,627,000 |
68,489,560,786,647,000 |
25,159,430,493,054,000 |
4,277,103,183,819,180 |
268,367,258,592,576 |
225,368,761,961,739,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 9 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
9 |
0.0000006022051 |
0.0000001046982 |
0.0000000162463 |
0.0000000011014 |
0.0000000000257 |
0.0000007242768 |
8 |
0.0000262040614 |
0.0000053710188 |
0.0000009422840 |
0.0000000731082 |
0.0000000019826 |
0.0000325924550 |
7 |
0.0004588778105 |
0.0001093734735 |
0.0000214840752 |
0.0000018845680 |
0.0000000584866 |
0.0005916784138 |
6 |
0.0042687204722 |
0.0011696885365 |
0.0002552047716 |
0.0000250647544 |
0.0000008794651 |
0.0057195579998 |
5 |
0.0233599654461 |
0.0072880593429 |
0.0017545328048 |
0.0001914035787 |
0.0000075194263 |
0.0326014805987 |
4 |
0.0783110652651 |
0.0275905103694 |
0.0072880593429 |
0.0008772664024 |
0.0000382807157 |
0.1141051820955 |
3 |
0.1614044856609 |
0.0637647350759 |
0.0183936735796 |
0.0024293531143 |
0.0001169688537 |
0.2461092162844 |
2 |
0.1978414771329 |
0.0871071827376 |
0.0273277436040 |
0.0039415014813 |
0.0002082302669 |
0.3164261352227 |
1 |
0.1312263565193 |
0.0640493990718 |
0.0217767956844 |
0.0034159679505 |
0.0001970750741 |
0.2206655943001 |
0 |
0.0359725396892 |
0.0193729663859 |
0.0071165998969 |
0.0012098219825 |
0.0000759103989 |
0.0637478383534 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 9 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
9 |
0.004818 |
0.001675 |
0.000406 |
0.000028 |
0.000001 |
0.006927 |
8 |
0.052408 |
0.021484 |
0.007538 |
0.001170 |
0.000050 |
0.082650 |
7 |
0.068832 |
0.032812 |
0.012880 |
0.002261 |
0.000234 |
0.117019 |
6 |
0.085374 |
0.049127 |
0.025520 |
0.005013 |
0.000527 |
0.165562 |
5 |
0.093440 |
0.058304 |
0.033336 |
0.008422 |
0.002256 |
0.195758 |
4 |
0.078311 |
0.082772 |
0.051016 |
0.013159 |
0.007656 |
0.232914 |
3 |
0.000000 |
0.000000 |
0.036787 |
0.012147 |
0.011697 |
0.060631 |
2 |
0.000000 |
0.000000 |
0.027328 |
0.011825 |
0.016658 |
0.055811 |
1 |
0.000000 |
0.000000 |
0.000000 |
0.013664 |
0.011825 |
0.025488 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.009679 |
0.007591 |
0.017270 |
Total |
0.383183 |
0.246174 |
0.194812 |
0.077366 |
0.058494 |
0.960030 |
Pick 10
Pick 10 Pay Table
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
10 |
10,000 |
20,000 |
25,000 |
25,000 |
25,000 |
9 |
3,000 |
6,000 |
12,000 |
25,000 |
25,000 |
8 |
300 |
600 |
1,200 |
2,500 |
5,000 |
7 |
60 |
125 |
300 |
599.5 |
2,000 |
6 |
7 |
15 |
35 |
100 |
500 |
5 |
3 |
6 |
12 |
30 |
300 |
4 |
1 |
2 |
4 |
8 |
200 |
3 |
- |
- |
2 |
6 |
100 |
2 |
- |
- |
1 |
4 |
80 |
1 |
- |
- |
- |
5 |
60 |
0 |
- |
- |
- |
10 |
100 |
Pick 10 CombinationsExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
10 |
338,847,548,728 |
50,473,815,600 |
6,961,905,600 |
412,994,400 |
8,259,888 |
396,704,524,216 |
9 |
17,901,379,932,800 |
3,196,674,988,000 |
504,738,156,000 |
34,809,528,000 |
825,988,800 |
21,638,428,593,600 |
8 |
382,641,996,063,600 |
80,556,209,697,600 |
14,385,037,446,000 |
1,135,660,851,000 |
31,328,575,200 |
478,750,232,633,400 |
7 |
4,387,215,112,761,600 |
1,074,082,795,968,000 |
214,816,559,193,600 |
19,180,049,928,000 |
605,685,787,200 |
5,695,900,203,638,400 |
6 |
30,050,564,532,962,400 |
8,458,402,018,247,990 |
1,879,644,892,944,000 |
187,964,489,294,400 |
6,713,017,474,800 |
40,583,288,950,923,600 |
5 |
129,109,048,406,537,000 |
41,381,105,258,505,600 |
10,150,082,421,897,600 |
1,127,786,935,766,400 |
45,111,477,430,656 |
181,813,134,500,138,000 |
4 |
353,833,081,570,496,000 |
128,084,373,419,184,000 |
34,484,254,382,088,000 |
4,229,201,009,124,000 |
187,964,489,294,400 |
520,818,874,870,186,000 |
3 |
612,975,215,648,952,000 |
248,849,639,785,843,000 |
73,191,070,525,248,000 |
9,852,644,109,168,000 |
483,337,258,185,600 |
945,351,907,327,397,000 |
2 |
644,424,503,765,270,000 |
291,620,671,624,035,000 |
93,318,614,919,691,200 |
13,723,325,723,484,000 |
738,948,308,187,600 |
1,043,826,064,340,670,000 |
1 |
372,268,617,481,488,000 |
186,789,711,236,310,000 |
64,804,593,694,230,000 |
10,368,734,991,076,800 |
609,925,587,710,400 |
634,841,582,990,815,000 |
0 |
89,947,438,491,477,900 |
49,810,589,663,016,000 |
18,678,971,123,631,000 |
3,240,229,684,711,500 |
207,374,699,821,536 |
161,884,603,662,658,000 |
Total |
2,237,396,567,233,490,000 |
956,152,379,159,611,000 |
296,736,945,256,431,000 |
42,750,237,875,926,500 |
2,280,012,686,716,080 |
3,535,316,142,212,170,000 |
Pick 10 ProbabilitiesExpand
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
10 |
0.0000000958465 |
0.0000000142770 |
0.0000000019692 |
0.0000000001168 |
0.0000000000023 |
0.0000001122119 |
9 |
0.0000050635867 |
0.0000009042119 |
0.0000001427703 |
0.0000000098462 |
0.0000000002336 |
0.0000061206488 |
8 |
0.0001082341665 |
0.0000227861403 |
0.0000040689536 |
0.0000003212332 |
0.0000000088616 |
0.0001354193553 |
7 |
0.0012409682575 |
0.0003038152043 |
0.0000607630409 |
0.0000054252715 |
0.0000001713244 |
0.0016111430985 |
6 |
0.0085001067300 |
0.0023925447338 |
0.0005316766075 |
0.0000531676608 |
0.0000018988450 |
0.0114793945770 |
5 |
0.0365198028162 |
0.0117050650052 |
0.0028710536805 |
0.0003190059645 |
0.0000127602386 |
0.0514276877050 |
4 |
0.1000852730950 |
0.0362299631113 |
0.0097542208377 |
0.0011962723669 |
0.0000531676608 |
0.1473188970716 |
3 |
0.1733862520327 |
0.0703896426163 |
0.0207028360636 |
0.0027869202393 |
0.0001367168419 |
0.2674023677939 |
2 |
0.1822820019038 |
0.0824878624409 |
0.0263961159811 |
0.0038817817619 |
0.0002090190179 |
0.2952567811057 |
1 |
0.1052999512651 |
0.0528353628707 |
0.0183306360980 |
0.0029329017757 |
0.0001725236339 |
0.1795713756432 |
0 |
0.0254425445627 |
0.0140894300988 |
0.0052835362871 |
0.0009165318049 |
0.0000586580355 |
0.0457907007890 |
Total |
0.6328702942627 |
0.2704573907106 |
0.0839350522895 |
0.0120923380417 |
0.0006449246956 |
1.0000000000000 |
Pick 10 Returns
Balloons |
Catch |
0 or 1 |
2 |
3 |
4 |
5 |
Total |
10 |
0.000958 |
0.000286 |
0.000049 |
0.000003 |
0.000000 |
0.001296 |
9 |
0.015191 |
0.005425 |
0.001713 |
0.000246 |
0.000006 |
0.022581 |
8 |
0.032470 |
0.013660 |
0.004883 |
0.000803 |
0.000044 |
0.051861 |
7 |
0.074458 |
0.037977 |
0.018229 |
0.003252 |
0.000343 |
0.134259 |
6 |
0.059501 |
0.035888 |
0.018609 |
0.005317 |
0.000949 |
0.120264 |
5 |
0.109559 |
0.070230 |
0.034453 |
0.009570 |
0.003828 |
0.227641 |
4 |
0.100085 |
0.072460 |
0.039017 |
0.009570 |
0.010634 |
0.231766 |
3 |
0.000000 |
0.000000 |
0.041406 |
0.016722 |
0.013672 |
0.071799 |
2 |
0.000000 |
0.000000 |
0.026396 |
0.015527 |
0.016722 |
0.058645 |
1 |
0.000000 |
0.000000 |
0.000000 |
0.014665 |
0.010351 |
0.025016 |
0 |
0.000000 |
0.000000 |
0.000000 |
0.009165 |
0.005866 |
0.015031 |
Total |
0.392223 |
0.235926 |
0.184754 |
0.084840 |
0.062414 |
0.960158 |

Summary
Here is the return for picking 2 to 10 numbers, again according to a $2 bet made at the Rampart casino.
Summary
Pick |
Return |
2 |
96.00% |
3 |
96.00% |
4 |
95.99% |
5 |
96.01% |
6 |
96.01% |
7 |
96.00% |
8 |
95.98% |
9 |
96.00% |
10 |
96.02% |
For more information about returns for bet amounts other than exactly $2, please visit my page on U1 Gaming theoretical returns.
Written by:
Michael Shackleford