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Roulette Up

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Introduction

The Roulette Up side bet is a unique wager in roulette that pays out when the results of subsequent spins increase for at least three spins in a row. This option is provided by Galaxy Gaming.

Rules

  1. At the recent Global Gaming Expo, I encountered this specific side bet which operates on a double-zero roulette wheel.
  2. The cost of the side bet is $5.
  3. For this side bet, the sequence of numbers is set as follows: 00, 0, 1, 2, 3,..., 36.
  4. Once the side bet is placed, the game counts how many times the outcome of each spin exceeds that of the one before it.
  5. An electronic display keeps track of the various players and the timing of their bets.
  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. In addition to tracking players, the game display also highlights a mystery jackpot that activates unpredictably, with a 'must hit by' threshold set at $1,250.

Examples:

  • For instance, the sequence 10-20-30-25 is considered a streak of 3, as the number 25 is lower than 30.
  • In the series 5-10-15-20-35-35, we see a streak of 5, since the second occurrence of 35 does not surpass the first 35.

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Analysis

The table below presents the findings of my analysis. The cell in the lower-right corner indicates that the fixed wins have an expected value 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 there is no value assigned to the Mystery Jackpot, is calculated to be $131,624.57.

I'm unsure about the reseed amount or the rate of contribution for the Mystery Jackpot, hence I'm unable to provide an analysis on that.

The subsequent table illustrates the precise number of permutations for streaks ranging in length from 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 want to express my gratitude to ThatDonGuy for validating the permutations and providing the numerous significant digits you see above. My analysis in Excel was limited to about 15.

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External Links

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