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Roulette Up
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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
- The version of this side bet I saw at the Global Gaming Expo was based on a double-zero wheel.
- The cost of the side bet is $5.
- For purposes of the side bet, the order of the numbers is 00,0,1,2,3,...,36.
- After the side bet is made, a count is made of the number of spins where each outcome is greater than the last.
- An electronic sign is used to keep track of the different players and when they made the bet.
- 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
- 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.
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Analysis
The following table shows my analysis. The lower right cell shows that the fixed wins have an expected win of $3.52.
Roulette Up Analysis
| Event | Pays | Probability | Return |
|---|---|---|---|
| 8+ | ? | 0.000011 | ? |
| 7 | $1,000 | 0.000099 | 0.099054 |
| 6 | $300 | 0.000807 | 0.241975 |
| 5 | $100 | 0.005418 | 0.541795 |
| 4 | $50 | 0.029066 | 1.453287 |
| 3 | $10 | 0.118339 | 1.183390 |
| 1 or 2 | 0 | 0.846260 | 0.000000 |
| Total+ | 1.000000 | 3.519501 |
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.
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External Links
Discussion about Roulette Up in my forum at Wizard of Vegas.