Roulette Up

Introduction

Roulette Up is a side bet in roulette that wins if the outcome of future spins are increasing for at least three consecutive spins. The bet is offered by Galaxy Gaming.

 

Rules

1. The version of this side bet I saw at the Global Gaming Expo was based on a double-zero wheel.
2. The cost of the side bet is $5.
3. For purposes of the side bet, the order of the numbers is 00,0,1,2,3,...,36.
4. After the side bet is made, a count is made of the number of spins where each outcome is greater than the last.
5. An electronic sign is used to keep track of the different players and when they made the bet.
6. The pay table is as follows:
   • Streak of 8 or more -- Pays Jackpot
   • Streak of 7 -- Pays $1,000
   • Streak of 6 -- Pays $300
   • Streak of 5 -- Pays $100
   • Streak of 4 -- Pays $50
   • Streak of 3 -- Pays $10
7. The sign for the game also indicates a mystery jackpot, that hits randomly, with a "must hit by" limit of $1,250.

Examples:

• 10-20-30-25 -- Streak of 3, because the 25 is lower than 30
• 5-10-15-20-35-35 -- Streak of 5, because the second 35 is not greater than the first 35.

Analysis

The following table shows my analysis. The lower right cell shows that the fixed wins have an expected win of $3.52.

The value per $10,000 in the jackpot meter is 2.25%.

The breakeven jackpot, assuming no value in the Mystery Jackpot, is $131,624.57.

I do not know the reseed nor contribution rate of the Mystery Jackpot, thus I cannot analyze that.

 

The next table shows the exact number of permutations for all streaks of length 1 to 38.

Streak	Permutations
38	1
37	1,443
36	1,013,688
35	461,885,060
34	153,451,413,648
33	39,617,544,382,416
32	8,272,463,408,821,248
31	1,435,641,707,832,666,048
30	211,178,264,119,901,844,480
29	26,719,525,403,200,321,522,688
28	2,940,990,520,241,911,251,738,624
27	284,111,142,659,992,946,052,698,112
26	24,258,181,020,203,842,159,264,940,032
25	1,840,894,506,414,877,370,961,969,561,600
24	124,717,972,960,313,063,486,429,206,413,312
23	7,569,688,081,063,445,658,829,106,000,363,520
22	412,712,558,854,502,645,920,508,648,889,384,960
21	20,253,813,650,308,934,661,029,453,854,855,004,160
20	895,882,974,161,813,194,530,191,715,484,591,718,400
19	35,745,730,669,056,346,461,754,649,447,835,209,564,160
18	1,286,846,304,086,028,472,623,167,380,122,067,544,309,760
17	41,785,056,974,475,961,568,721,577,840,259,939,256,238,080
16	1,222,715,677,884,130,811,251,574,726,962,044,853,530,132,480
15	32,195,964,452,981,596,633,227,606,261,582,104,974,747,238,400
14	761,255,692,843,831,529,283,426,068,051,630,215,402,912,481,280
13	16,116,870,525,636,547,519,971,963,326,464,513,988,958,804,246,528
12	304,408,584,129,182,601,678,997,082,473,814,962,442,346,172,514,304
11	5,105,420,512,833,266,226,924,907,858,526,884,277,505,275,004,452,864
10	75,586,745,254,934,071,411,615,518,944,424,000,991,636,539,026,964,480
9	980,542,536,720,903,367,760,336,490,582,493,419,760,471,240,756,690,944
8	11,040,182,635,672,393,474,042,307,153,225,111,096,562,342,858,890,149,888
7	106,573,375,926,611,733,777,650,335,987,181,112,762,783,261,307,189,592,064
6	867,811,775,402,409,832,189,438,450,181,331,918,211,235,127,787,115,249,664
5	5,829,240,713,561,641,802,080,571,407,783,694,198,085,569,292,711,430,717,440
4	31,272,161,945,695,396,020,573,418,375,874,877,109,729,642,323,251,910,672,384
3	127,322,373,636,045,540,940,906,060,530,347,713,946,756,400,887,525,636,308,992
2	358,388,903,568,128,189,315,142,985,196,534,305,924,203,202,498,220,309,610,496
1	552,112,635,226,575,859,215,220,274,491,958,255,072,421,149,794,555,612,102,656
Total	1,075,911,801,979,993,982,060,429,252,856,123,779,115,487,368,830,416,064,610,304

 

I would like to thank ThatDonGuy for confirming the permutations and for the many significant digits you see above. I was restricted to about 15 in Excel.

External Links

Discussion about Roulette Up in my forum at Wizard of Vegas.

Written by: Michael Shackleford