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Wizard
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Wizard
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October 15th, 2024 at 3:04:24 PM permalink
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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October 15th, 2024 at 5:50:00 PM permalink
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!
381
371,443
361,013,688
35461,885,060
34153,451,413,648
3339,617,544,382,416
328,272,463,408,821,248
311,435,641,707,832,666,048
30211,178,264,119,901,844,480
2926,719,525,403,200,321,522,688
282,940,990,520,241,911,251,738,624
27284,111,142,659,992,946,052,698,112
2624,258,181,020,203,842,159,264,940,032
251,840,894,506,414,877,370,961,969,561,600
24124,717,972,960,313,063,486,429,206,413,312
237,569,688,081,063,445,658,829,106,000,363,520
22412,712,558,854,502,645,920,508,648,889,384,960
2120,253,813,650,308,934,661,029,453,854,855,004,160
20895,882,974,161,813,194,530,191,715,484,591,718,400
1935,745,730,669,056,346,461,754,649,447,835,209,564,160
181,286,846,304,086,028,472,623,167,380,122,067,544,309,760
1741,785,056,974,475,961,568,721,577,840,259,939,256,238,080
161,222,715,677,884,130,811,251,574,726,962,044,853,530,132,480
1532,195,964,452,981,596,633,227,606,261,582,104,974,747,238,400
14761,255,692,843,831,529,283,426,068,051,630,215,402,912,481,280
1316,116,870,525,636,547,519,971,963,326,464,513,988,958,804,246,528
12304,408,584,129,182,601,678,997,082,473,814,962,442,346,172,514,304
115,105,420,512,833,266,226,924,907,858,526,884,277,505,275,004,452,864
1075,586,745,254,934,071,411,615,518,944,424,000,991,636,539,026,964,480
9980,542,536,720,903,367,760,336,490,582,493,419,760,471,240,756,690,944
811,040,182,635,672,393,474,042,307,153,225,111,096,562,342,858,890,149,888
7106,573,375,926,611,733,777,650,335,987,181,112,762,783,261,307,189,592,064
6867,811,775,402,409,832,189,438,450,181,331,918,211,235,127,787,115,249,664
55,829,240,713,561,641,802,080,571,407,783,694,198,085,569,292,711,430,717,440
431,272,161,945,695,396,020,573,418,375,874,877,109,729,642,323,251,910,672,384
3127,322,373,636,045,540,940,906,060,530,347,713,946,756,400,887,525,636,308,992
2358,388,903,568,128,189,315,142,985,196,534,305,924,203,202,498,220,309,610,496
1552,112,635,226,575,859,215,220,274,491,958,255,072,421,149,794,555,612,102,656
Total1,075,911,801,979,993,982,060,429,252,856,123,779,115,487,368,830,416,064,610,304
DJTeddyBear
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Dieter
October 15th, 2024 at 6:01:17 PM permalink
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.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Dieter
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October 15th, 2024 at 6:04:51 PM permalink
Thanks DJ.
I was really struggling to understand how this bet worked.
May the cards fall in your favor.
zbrownson
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October 15th, 2024 at 6:05:53 PM permalink
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?
AutomaticMonkey
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October 15th, 2024 at 6:17:48 PM permalink
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.
DJTeddyBear
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October 15th, 2024 at 6:19:48 PM permalink
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.
Last edited by: DJTeddyBear on Oct 16, 2024
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Wizard
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October 15th, 2024 at 7:29:08 PM permalink
Quote: ThatDonGuy


Challenge accepted!
link to original post



Thank you for the confirmation! How did you get so many significant digits?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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zbrownson
October 15th, 2024 at 7:32:40 PM permalink
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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October 16th, 2024 at 2:06:46 PM permalink
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
ThatDonGuy
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October 16th, 2024 at 3:27:03 PM permalink
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:
10.513157894736842105263157894736842105263157894736842
20.333102493074792243767313019390581717451523545706371
30.118339043592360402391019098994022452252514943869369
40.0290657300051411514644608313318651637111440213012485
50.00541795405797587253175256724387837481457728467238184
68.06582634194904331794743093449562566380678470023763 x 10-4
79.90540077081461460098807307745076835906096366695849 x 10-5
81.02612338812114637470553137978604450837390099808091 x 10-5
99.11359588133912898587149580731026372568925228558705 x 10-7
107.02536630937891389128850022360440319098852515369550 x 10-8
114.74520355984365236516854839664507934829926698977678 x 10-9
122.82930797458473199542622318828304326251189272117718 x 10-10
131.49797320709529983467115200131527039901162239937012 x 10-11
147.07544699707631500856819433819628393595233252064160 x 10-13
152.99243529011686255061624760544015767967908800215105 x 10-14
161.13644601317131622149306410609079259661703238884581 x 10-15
173.88368794705840887096496688302226271139227077328520 x 10-17
181.19605185268704460911256108993190101426289583860339 x 10-18
193.32236625746401280309044747203305837295248844056498 x 10-20
208.32673247484714988243219917802771522043230185605258 x 10-22
211.88247899251927192318144215866894518739438403205016 x 10-23
223.83593300208242181142998456653691565917783386720476 x 10-25
237.03560279488801448667381539316978151204865860811080 x 10-27
241.15918398451244174608813434395474661068078585762924 x 10-28
251.71100874906947794842631165816532267939555942210794 x 10-30
262.25466260111299628291654323766034723444716992075042 x 10-32
272.64065457909416857889300176764731240587363741441272 x 10-34
282.73348662486053613732286262161515164686791800644995 x 10-36
292.48343083085700338290610952465035707265568991814062 x 10-38
301.96278415880624938055339140464725838539030583074167 x 10-40
311.33434887989021339467445468298388179708551492879368 x 10-42
327.68879325758624788823063870423392299601675526186612 x 10-45
333.68222974313582885514141462712441165153666201105237 x 10-47
341.42624528670105013755762243474857594158403404392550 x 10-49
354.29296396925840684679366917923977966593061502729554 x 10-52
369.42166447225986465055306383576297914896375580060798 x 10-55
371.34118800197605029266875716344733082683771531479877 x 10-57
389.29444214813617666437115151384151647150183863339408 x 10-61
DJTeddyBear
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October 16th, 2024 at 3:34:20 PM permalink
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
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Wizard
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October 16th, 2024 at 4:52:26 PM permalink
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.
Last edited by: Wizard on Oct 17, 2024
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
SOOPOO
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October 17th, 2024 at 11:53:43 AM permalink
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….
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