Roulette Up

I noticed a mathematically interesting side bet at the Global Gaming Expo called Roulette Up. It pays based on the how many spins since the bet is made the outcome keeps increasing. For purposes of this bet, the rank of the numbers goes 00,0,1,2,3,...,38.

To start, I calculated the number of ways for any length streak from 1 to 38. Here are those results. My usual apologies that Excel can handle only about 16 significant digits.

Streak	Combinations	Probability
38	1	0.00000000000000000000000000000000000000000000000000000000000092944
37	1,443	0.00000000000000000000000000000000000000000000000000000000134118800
36	1,013,688	0.00000000000000000000000000000000000000000000000000000094216644723
35	461,885,060	0.00000000000000000000000000000000000000000000000000042929639692584
34	153,451,413,648	0.00000000000000000000000000000000000000000000000014262452867010500
33	39,617,544,382,416	0.00000000000000000000000000000000000000000000003682229743135830000
32	8,272,463,408,821,250	0.00000000000000000000000000000000000000000000768879325758625000000
31	1,435,641,707,832,670,000	0.00000000000000000000000000000000000000000133434887989021000000000
30	211,178,264,119,902,000,000	0.00000000000000000000000000000000000000019627841588062500000000000
29	26,719,525,403,200,300,000,000	0.00000000000000000000000000000000000002483430830857000000000000000
28	2,940,990,520,241,910,000,000,000	0.00000000000000000000000000000000000273348662486054000000000000000
27	284,111,142,659,993,000,000,000,000	0.00000000000000000000000000000000026406545790941700000000000000000
26	24,258,181,020,203,800,000,000,000,000	0.00000000000000000000000000000002254662601113000000000000000000000
25	1,840,894,506,414,880,000,000,000,000,000	0.00000000000000000000000000000171100874906948000000000000000000000
24	124,717,972,960,313,000,000,000,000,000,000	0.00000000000000000000000000011591839845124400000000000000000000000
23	7,569,688,081,063,450,000,000,000,000,000,000	0.00000000000000000000000000703560279488802000000000000000000000000
22	412,712,558,854,503,000,000,000,000,000,000,000	0.00000000000000000000000038359330020824200000000000000000000000000
21	20,253,813,650,308,900,000,000,000,000,000,000,000	0.00000000000000000000001882478992519270000000000000000000000000000
20	895,882,974,161,813,000,000,000,000,000,000,000,000	0.00000000000000000000083267324748471500000000000000000000000000000
19	35,745,730,669,056,300,000,000,000,000,000,000,000,000	0.00000000000000000003322366257464010000000000000000000000000000000
18	1,286,846,304,086,030,000,000,000,000,000,000,000,000,000	0.00000000000000000119605185268704000000000000000000000000000000000
17	41,785,056,974,476,000,000,000,000,000,000,000,000,000,000	0.00000000000000003883687947058410000000000000000000000000000000000
16	1,222,715,677,884,130,000,000,000,000,000,000,000,000,000,000	0.00000000000000113644601317132000000000000000000000000000000000000
15	32,195,964,452,981,600,000,000,000,000,000,000,000,000,000,000	0.00000000000002992435290116860000000000000000000000000000000000000
14	761,255,692,843,832,000,000,000,000,000,000,000,000,000,000,000	0.00000000000070754469970763200000000000000000000000000000000000000
13	16,116,870,525,636,500,000,000,000,000,000,000,000,000,000,000,000	0.00000000001497973207095300000000000000000000000000000000000000000
12	304,408,584,129,183,000,000,000,000,000,000,000,000,000,000,000,000	0.00000000028293079745847300000000000000000000000000000000000000000
11	5,105,420,512,833,270,000,000,000,000,000,000,000,000,000,000,000,000	0.00000000474520355984365000000000000000000000000000000000000000000
10	75,586,745,254,934,100,000,000,000,000,000,000,000,000,000,000,000,000	0.00000007025366309378910000000000000000000000000000000000000000000
9	980,542,536,720,903,000,000,000,000,000,000,000,000,000,000,000,000,000	0.00000091135958813391300000000000000000000000000000000000000000000
8	11,040,182,635,672,400,000,000,000,000,000,000,000,000,000,000,000,000,000	0.00001026123388121150000000000000000000000000000000000000000000000
7	106,573,375,926,612,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.00009905400770814610000000000000000000000000000000000000000000000
6	867,811,775,402,410,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.00080658263419490400000000000000000000000000000000000000000000000
5	5,829,240,713,561,640,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.00541795405797587000000000000000000000000000000000000000000000000
4	31,272,161,945,695,400,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.02906573000514110000000000000000000000000000000000000000000000000
3	127,322,373,636,046,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.11833904359236000000000000000000000000000000000000000000000000000
2	358,388,903,568,128,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.33310249307479200000000000000000000000000000000000000000000000000
1	552,112,635,226,576,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000	0.51315789473684200000000000000000000000000000000000000000000000000
Total	1,075,911,801,979,990,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000	1.00000000000000000000000000000000000000000000000000000000000000000

Does anyone agree or disagree thus far?



The question for the poll is would you make this side bet? Multiple votes allowed.

Quote: Wizard

To start, I calculated the number of ways for any length streak from 1 to 38. Here are those results. My usual apologies that Excel can handle only about 16 significant digits.
link to original post

Challenge accepted!

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

Mike -
I REALLY feel like I mentioned Roulette Up and/or pointed it out to you a few years ago. Whatever. Roulette Up is not all that new. I first saw it at G2E in 2019.

It is distributed by Galaxy Gaming - the same company that I had a contract with to distribute my roulette side bet, Poker For Roulette. That contract ran from 3/31/15 to 3/31/18, with no results.

At each successive G2E (including last week), I mentioned to the Galaxy staff that know me that I think PFR is better, and I’m not holding any grudges if they want to renew the distribution deal.

For info about my games, go to: http://www.davemillergaming.com/pfr/index.html
For a WoV post detailing my story and history with Galaxy, go to: https://wizardofvegas.com/forum/gaming-business/game-inventors/35477-my-experiences-with-galaxy-gaming/

Anyway, I’m obviously biased, and I’m really not holding a grudge, but I truly think Poker For Roulette is better. Hell, I think the Touchtown Roulette that I saw on a machine some years ago at G2E and didn’t care for, is better than Roulette Up. Here’s a Wizard article about it: https://wizardofodds.com/games/touchdown-roulette/

For what it’s worth, when you place the Roulette Up bet, the next spin is your starting point, and the spin after that must be higher, the one ofter that higher still, and finally one more that’s higher in order to get paid. No indication if a repeat is a push or a loss. I assume it’s a loss.

That’s four spins before you even think about getting paid. And if the first spin is a high number, your chances are slim!

By contrast, with Poker For Roulette, it’s just three spins. And since a 0 and 00 (and 000) are wild, if that comes out first, you know you’re gonna get a wild pair at the minumum. So you often know immediately that you’ll win something. Similarly, if the zeros comes out second or third, even if the other numbers are meaningless, you still know you're gonna win.

Anyway, here’s Galaxy’s brief web page about Roulette Up: https://www.galaxygaming.com/products/roulette-up
Note: I had to do a specific Google search to find it. I couldn’t find a link on Galaxy’s own home page.

Thanks DJ.
I was really struggling to understand how this bet worked.

How do they handle the progressive payout when multiple players hit it at the same time? Is each player awarded the full amount? Or is it the current amount + seed amount for every player beyond the first, then split evenly?

Quote: zbrownson

How do they handle the progressive payout when multiple players hit it at the same time? Is each player awarded the full amount? Or is it the current amount + seed amount for every player beyond the first, then split evenly?
link to original post

I believe the game publisher insures them against that. Not sure though.

Quote: zbrownson

How do they handle the progressive payout when multiple players hit it at the same time? Is each player awarded the full amount? Or is it the current amount + seed amount for every player beyond the first, then split evenly?
link to original post

I wondered about that myself since my Poker For Roulette and Pick A Card games have progressive elements which would be shared.

While adding the seed value or having a minimum wasn't mentioned, I WAS told that having it be shared by those players who played it on that round was an acceptable way of handling it.

But for the record, because regulations dictate that progressives MUST be paid out, field trials never have progressive options - instead they merely pay high, static numbers that make calculating the edge simple. Therefore, I get the feeling that the progressive math would be ironed out after a successful field trial and before the progressive option was added.

Quote: ThatDonGuy

Challenge accepted!
link to original post

Thank you for the confirmation! How did you get so many significant digits?

Quote: zbrownson

How do they handle the progressive payout when multiple players hit it at the same time? Is each player awarded the full amount? Or is it the current amount + seed amount for every player beyond the first, then split evenly?
link to original post

They probably just split the current jackpot among the winners. No, they would not add the seed to each win. That is a problem with bets like this where when it hits, multiple players are likely to have to split the jackpot.

My page is up on Roulette Up at WoO. I welcome all comments.

Bottom line is the fixed wins are worth $3.52 and the value per $10,000 in the jackpot is 2.25%. The cost of the bet is $5. Breakeven jackpot is $131,624.57. This ignores the Mystery Jackpot, which I don't have enough information about to analyze.

There would also be a reduction in the expected value if other players made that bet at the same time as you, resulting in jackpot sharing, which I loathe to see in game design.

Quote: Wizard

Quote: ThatDonGuy

Challenge accepted!
link to original post

Thank you for the confirmation! How did you get so many significant digits?
link to original post

Using .NET's BigInteger class.

Did somebody say "significant digits"? Here are the fractional values, to 51 significant digits:

1	0.513157894736842105263157894736842105263157894736842
2	0.333102493074792243767313019390581717451523545706371
3	0.118339043592360402391019098994022452252514943869369
4	0.0290657300051411514644608313318651637111440213012485
5	0.00541795405797587253175256724387837481457728467238184
6	8.06582634194904331794743093449562566380678470023763 x 10-4
7	9.90540077081461460098807307745076835906096366695849 x 10-5
8	1.02612338812114637470553137978604450837390099808091 x 10-5
9	9.11359588133912898587149580731026372568925228558705 x 10-7
10	7.02536630937891389128850022360440319098852515369550 x 10-8
11	4.74520355984365236516854839664507934829926698977678 x 10-9
12	2.82930797458473199542622318828304326251189272117718 x 10-10
13	1.49797320709529983467115200131527039901162239937012 x 10-11
14	7.07544699707631500856819433819628393595233252064160 x 10-13
15	2.99243529011686255061624760544015767967908800215105 x 10-14
16	1.13644601317131622149306410609079259661703238884581 x 10-15
17	3.88368794705840887096496688302226271139227077328520 x 10-17
18	1.19605185268704460911256108993190101426289583860339 x 10-18
19	3.32236625746401280309044747203305837295248844056498 x 10-20
20	8.32673247484714988243219917802771522043230185605258 x 10-22
21	1.88247899251927192318144215866894518739438403205016 x 10-23
22	3.83593300208242181142998456653691565917783386720476 x 10-25
23	7.03560279488801448667381539316978151204865860811080 x 10-27
24	1.15918398451244174608813434395474661068078585762924 x 10-28
25	1.71100874906947794842631165816532267939555942210794 x 10-30
26	2.25466260111299628291654323766034723444716992075042 x 10-32
27	2.64065457909416857889300176764731240587363741441272 x 10-34
28	2.73348662486053613732286262161515164686791800644995 x 10-36
29	2.48343083085700338290610952465035707265568991814062 x 10-38
30	1.96278415880624938055339140464725838539030583074167 x 10-40
31	1.33434887989021339467445468298388179708551492879368 x 10-42
32	7.68879325758624788823063870423392299601675526186612 x 10-45
33	3.68222974313582885514141462712441165153666201105237 x 10-47
34	1.42624528670105013755762243474857594158403404392550 x 10-49
35	4.29296396925840684679366917923977966593061502729554 x 10-52
36	9.42166447225986465055306383576297914896375580060798 x 10-55
37	1.34118800197605029266875716344733082683771531479877 x 10-57
38	9.29444214813617666437115151384151647150183863339408 x 10-61

Quote: WoO article

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.

While the web page doesn’t specify, I agree that a duplicate should end the streak. But it’s my understanding that the first number after making the bet is the starting point. IE. A ‘streak’ of zero. Your examples would be streaks of 2 and 4.

Quote: Galaxy’s web page

DETAILS
The first spin establishes the starting number and the wager is active for as long as each subsequent spin lands on a greater number than the previous spin. The streak length is tracked on the Up Streak tracker after each increasing number is spun.

https://www.galaxygaming.com/products/roulette-up

Quote: DJTeddyBear

While the web page doesn’t specify, I agree that a duplicate should end the streak. But it’s my understanding that the first number after making the bet is the starting point. IE. A ‘streak’ of zero. Your examples would be streaks of 2 and 4.
link to original post

Hmmm. If this were true, the return on the fixed pays would be only 13.7% of money bet. The math works out nicely according to my interpretation. I'll ask them about this the next time I speak with someone at Galaxy.

There is a close to ZERO% chance I’d play if I get X for the bonus, but 1/2X if there are two of us betting it, 1/3 X if three of us, etc….