I like playing it when the jackpot reaches the break even threshold and the machine has over 100% RTP.

It’s a $1 machine so you need to bet $5 per hand in order for the jackpot to be live and right now with the current progressive the payable is this:

Roughly $8800 Royal (resets at $4000 after being hit)

$250 Straight flush

$125 Quads

$40 Full house

$25 Flush

$20 Straight

$15 3 of a kind

$10 2 pair

$5 Jacks or better

With this current progressive and this payable the RTP is 100.08% if you play only 1 hand at a time and use an optimal strategy but that’s where my question comes in.

This machine gives you the option to play 1/3/5/10/25/50/100 hands at once and I am curious how playing more than one hand affects the RTP.

Of course the EV changes because if you play 100 hands at once and are dealt 4 to a royal for example and are lucky enough to hit multiple royals in one spin the progressive is only paid out for the first royal and after that the next royals are paid out $4000 for each…

Does anyone know how to solve this and figure out how much EV is being lost by playing multiple hands ? I just want to know if it’s still profitable to play 10 or even more hands at once as the progressive gets higher.

The base RTP when the royal flush resets to $4000 is 97.3% and with the progressive at $8800 it's about 100.08% RTP with an optimized strategy. With where it sits now how much EV do you lose by playing 10 or 25 hands and if it gets higher like maybe it reaches 100.50% rtp does it ever become worth it to play 100 hands at once or is the EV loss too much still??

Sorry for the long winded question, I know this is probably pretty simple to solve but for me it feels so complicated :')

Thanks for any help!

But, the easiest way I know to get a good answer to the general question you raise is via Monte Carlo simulation. I am already set up to do that for any number of hands, N. I just set N in my program and it produces a histogram for me.

0, 0.262005440638

1, 0.155447378952

2, 0.159159837012

3, 0.137299893034

4, 0.074138424601

5, 0.074141206483

6, 0.062010007849

7, 0.008590770924

8, 0.009769134577

9, 0.016852575646

10, 0.007190726291

11, 0.002677551790

12, 0.015184046696

13, 0.000482877766

14, 0.003293729030

15, 0.002148855696

16, 0.000064460400

17, 0.000029404069

18, 0.000965624711

19, 0.000226371318

20, 0.000000003848

21, 0.000000007695

24, 0.001474893804

25, 0.001299542894

26, 0.000083556500

27, 0.001116373472

28, 0.000640660110

29, 0.000267622434

30, 0.000128101240

31, 0.002214177979

32, 0.000000126974

33, 0.000034448395

34, 0.000015956383

35, 0.000011189091

36, 0.000302040047

37, 0.000000003848

41, 0.000010207929

50, 0.000156778096

51, 0.000029942746

52, 0.000010365685

53, 0.000106627266

54, 0.000023274694

55, 0.000043894481

56, 0.000003043525

57, 0.000000277034

58, 0.000008761197

59, 0.000004609536

60, 0.000004120879

61, 0.000000003848

75, 0.000241642811

100, 0.000003062764

101, 0.000000138517

102, 0.000000007695

104, 0.000000427094

105, 0.000000673346

150, 0.000013890171

800, 0.000026387478

801, 0.000020946840

802, 0.000006298673

803, 0.000001523686

804, 0.000003101240

805, 0.000006845046

806, 0.000002235510

807, 0.000000088497

808, 0.000000207775

809, 0.000000607935

810, 0.000000700280

826, 0.000000003848

850, 0.000000092345

851, 0.000000053868

854, 0.000000015391

855, 0.000000015391

1600, 0.000000303968

1601, 0.000000134669

1604, 0.000000050020

1605, 0.000000069258

1650, 0.000000007695

2400, 0.000001539077

The spoiler contains the output of my MC program for the base game strategy for N=3. The first column is the payoff and the second column is the probability of that payoff. For example, the 2400:1 payoff is the case of a dealt RF. The 1600:1 payoff is for two RFs and no win on the other line. The 1650:1 payoff is for holding TJQK and hitting two RFs and a SF, etc.

If you copy these results into a spreadsheet, you should be able to add formulas to sum the probabilities of all RFs. Hint: multiply the probability for all payoffs 16XX by two before summing. You should be able to create a second sum for the probabilities of RFs beyond one RF in a given hand. You can then convert that number into lost EV due to being paid only 800:1 for those RFs.

If you make strategy adjustments for the jackpot, then the number of RFs from holding zero to three cards will increase. The number of RFs from holding four to a RF will not change at all. Likewise for dealt RFs. So, I will not redo the calculations with different values for the RF jackpot. There would be trivial differences due to multiple RFRs holding three or fewer cards.

I did the MC calculation for 100 play and saw a number of hands hit nine RFs. This output is too large to fit in a spoiler (almost 4000 lines). I doubt that you will be playing much 100-play at $500 per hand just to win a $8000 jackpot. Here are the results for 10-play.

0, 0.025684870102

1, 0.030150521747

2, 0.075132472220

3, 0.085339889802

4, 0.101253951581

5, 0.103167259211

6, 0.078546457044

7, 0.065313086773

8, 0.055454928125

9, 0.035141194940

10, 0.039539773602

11, 0.033059381445

12, 0.035825053098

13, 0.032867870225

14, 0.028334172130

15, 0.026177798042

16, 0.018975640256

17, 0.011339581987

18, 0.007546418567

19, 0.005394269246

20, 0.025363941731

21, 0.003798211592

22, 0.002278957737

23, 0.001364834395

24, 0.000866392711

25, 0.001362052513

26, 0.018746621726

27, 0.001121456275

28, 0.000832406039

29, 0.000901629883

30, 0.008310174070

31, 0.000834864715

32, 0.008431695755

33, 0.000746263890

34, 0.000663115246

35, 0.005670398929

36, 0.000899609844

37, 0.000851840736

38, 0.002666751316

39, 0.000551555237

40, 0.005747922246

41, 0.000249669098

42, 0.000158982824

43, 0.000127231662

44, 0.000399471327

45, 0.000335118663

46, 0.000044987226

47, 0.000026225875

48, 0.000014898267

49, 0.000009084403

50, 0.002079043156

51, 0.000047888386

52, 0.003417043741

53, 0.000045187306

54, 0.000074075784

55, 0.000116381168

56, 0.000053725336

57, 0.002106534922

58, 0.000041358851

59, 0.000066457352

60, 0.000076130452

61, 0.000030943146

62, 0.000584422230

63, 0.000028665312

64, 0.000040423862

65, 0.000033836612

66, 0.000010646566

67, 0.000098004586

68, 0.000014144119

69, 0.000017464678

70, 0.000011627728

71, 0.000003666851

72, 0.000013043679

73, 0.000005113584

74, 0.000722866070

75, 0.000002885770

76, 0.000001046572

77, 0.000001608336

78, 0.000001204328

79, 0.000390637024

80, 0.001441184166

81, 0.000000242405

82, 0.000000257795

83, 0.000000250100

84, 0.000092875612

85, 0.000000165451

86, 0.000000069258

87, 0.000000042325

88, 0.000000023086

89, 0.000012939791

90, 0.000000023086

91, 0.000000015391

93, 0.000000003848

94, 0.000001065811

96, 0.000089851325

99, 0.000000053868

100, 0.000004140118

101, 0.000043436605

102, 0.000000688737

103, 0.000000353988

104, 0.000003843845

105, 0.000007087450

106, 0.000010500354

107, 0.000000900360

108, 0.000002100840

109, 0.000006063964

110, 0.000006237110

111, 0.000002501000

112, 0.000001058116

113, 0.000002627974

114, 0.000004159356

115, 0.000003274387

116, 0.000000796472

117, 0.000000834949

118, 0.000008968972

119, 0.000001689137

120, 0.000000954228

121, 0.000000330902

122, 0.000000300120

123, 0.000003470619

124, 0.000000450180

125, 0.000000188537

126, 0.000000069258

127, 0.000000050020

128, 0.000000654108

129, 0.000000050020

130, 0.000000015391

131, 0.000000007695

132, 0.000000003848

133, 0.000000034629

134, 0.000000003848

140, 0.000000346292

145, 0.000000150060

150, 0.000000411703

151, 0.000000057715

152, 0.000000026934

153, 0.000000011543

154, 0.000000461723

155, 0.000000696432

156, 0.000000119278

157, 0.000000046172

158, 0.000000250100

159, 0.000000477114

160, 0.000000523286

161, 0.000000076954

162, 0.000000065411

163, 0.000000277034

164, 0.000000373226

165, 0.000000215471

166, 0.000000030782

167, 0.000000061563

168, 0.000000107735

169, 0.000000107735

170, 0.000000080802

171, 0.000000023086

172, 0.000000015391

173, 0.000000042325

174, 0.000000023086

175, 0.000000007695

200, 0.000000034629

201, 0.000000007695

204, 0.000000038477

205, 0.000000057715

206, 0.000000007695

207, 0.000000003848

208, 0.000000019238

209, 0.000000019238

210, 0.000000034629

212, 0.000000003848

213, 0.000000019238

214, 0.000000026934

215, 0.000000011543

218, 0.000000003848

250, 0.000240099886

254, 0.000000003848

260, 0.000000003848

500, 0.000013851695

800, 0.000004147813

801, 0.000013336104

802, 0.000021497060

803, 0.000023301628

804, 0.000021643273

805, 0.000019634777

806, 0.000018576661

807, 0.000016768246

808, 0.000012555022

809, 0.000008795826

810, 0.000009015145

811, 0.000008868932

812, 0.000006683443

813, 0.000004513344

814, 0.000003616831

815, 0.000004455628

816, 0.000004101641

817, 0.000002916551

818, 0.000001900760

819, 0.000001754548

820, 0.000001985410

821, 0.000001542925

822, 0.000000923446

823, 0.000000577154

824, 0.000000607935

825, 0.000000588697

826, 0.000000357835

827, 0.000000230862

828, 0.000000157755

829, 0.000000084649

830, 0.000000096192

831, 0.000000073106

832, 0.000000023086

833, 0.000000019238

834, 0.000000019238

835, 0.000000007695

850, 0.000000042325

851, 0.000000080802

852, 0.000000069258

853, 0.000000073106

854, 0.000000069258

855, 0.000000180842

856, 0.000000153908

857, 0.000000161603

858, 0.000000126974

859, 0.000000100040

860, 0.000000211623

861, 0.000000207775

862, 0.000000150060

863, 0.000000080802

864, 0.000000130822

865, 0.000000173146

866, 0.000000119278

867, 0.000000069258

868, 0.000000046172

869, 0.000000088497

870, 0.000000042325

871, 0.000000038477

872, 0.000000015391

873, 0.000000019238

874, 0.000000019238

875, 0.000000023086

876, 0.000000007695

878, 0.000000007695

901, 0.000000003848

902, 0.000000007695

903, 0.000000007695

905, 0.000000007695

906, 0.000000023086

907, 0.000000015391

908, 0.000000003848

909, 0.000000011543

910, 0.000000038477

911, 0.000000007695

912, 0.000000007695

913, 0.000000003848

914, 0.000000015391

916, 0.000000011543

917, 0.000000003848

918, 0.000000003848

919, 0.000000007695

920, 0.000000003848

973, 0.000000003848

1600, 0.000000073106

1601, 0.000000219318

1602, 0.000000261643

1603, 0.000000203928

1604, 0.000000180842

1605, 0.000000300120

1606, 0.000000484809

1607, 0.000000469419

1608, 0.000000380922

1609, 0.000000330902

1610, 0.000000519439

1611, 0.000000542525

1612, 0.000000438637

1613, 0.000000234709

1614, 0.000000261643

1615, 0.000000373226

1616, 0.000000319359

1617, 0.000000176994

1618, 0.000000092345

1619, 0.000000115431

1620, 0.000000192385

1621, 0.000000111583

1622, 0.000000065411

1623, 0.000000030782

1624, 0.000000053868

1625, 0.000000053868

1626, 0.000000023086

1627, 0.000000007695

1628, 0.000000003848

1629, 0.000000011543

1651, 0.000000003848

1652, 0.000000003848

1654, 0.000000007695

1656, 0.000000023086

1657, 0.000000019238

1658, 0.000000007695

1659, 0.000000015391

1660, 0.000000007695

1661, 0.000000015391

1662, 0.000000007695

1664, 0.000000011543

1666, 0.000000003848

1667, 0.000000003848

1670, 0.000000003848

1676, 0.000000003848

1712, 0.000000003848

1718, 0.000000003848

2400, 0.000000003848

2401, 0.000000030782

2402, 0.000000007695

2403, 0.000000015391

2404, 0.000000007695

2405, 0.000000023086

2406, 0.000000042325

2407, 0.000000050020

2408, 0.000000019238

2409, 0.000000015391

2410, 0.000000038477

2411, 0.000000030782

2412, 0.000000019238

2413, 0.000000007695

2414, 0.000000011543

2415, 0.000000019238

2416, 0.000000015391

2417, 0.000000011543

2418, 0.000000003848

2420, 0.000000003848

2421, 0.000000007695

2422, 0.000000003848

2425, 0.000000003848

2455, 0.000000007695

2456, 0.000000003848

2458, 0.000000003848

2459, 0.000000003848

2460, 0.000000003848

3206, 0.000000003848

3209, 0.000000003848

3215, 0.000000003848

8000, 0.000001539077

Here's how I calculated it:

Using the Wizard's VP strategy calculator, I set it to 8/5 Jacks or Better with a Royal payout of 1760 (representing a payout of 8800 on a bet of 5).

It came up with these numbers:

The probability of a Royal using modified basic strategy is 1 / 32,576

A non-Royal has an ER of 0.946793

One Royal will add 1760 / N to the EV

Each additional Royal adds 800 / N to the EV

Based on that, I calculated the total ER of an N-hand game as:

EV for 0 Royals = (32,575 / 32,576)^N x 0.946793

EV for 1 Royal = C(N,1) x 32,575^(N-1) / 32,576^N x (0.946793 + 1760 / N)

EV for 2 Royals = C(N,2) x 32,575^(N-2) / 32,576^N x (0.946793 + (1760 + 800) / N)

EV for 3 Royals = C(N,3) x 32,575^(N-3) / 32,576^N x (0.946793 + (1760 + 800 x 2) / N)

...

EV for N Royals = C(N,N) x 1 / 32,576^N x (0.946793 + (1760 + 800 x (N - 1) / N)

There may or may not be an "easy way" to calculate a closed-form solution, given that combinations are involved; I just plugged numbers into Excel.

'# Extra' is the number of extra RFs after you have already hit the first RF on the multi-play hand.

'Hands w/ RF' is the number of hands that result in at least one RF.

'Total # RF' is the total number of RF in the simulation.

'Cycle' is just the RF cycle in the simulation. It is a sanity check.

'% Extra' is the percentage of RFs that are paid out at the 800:1 payoff.

The first table is for the base game strategy with the jackpot at the 800:1 reset value.

# Hands | # Extra | Hands w/ RF | Total # RF | Cycle | % Extra |
---|---|---|---|---|---|

1 | 0 | 6506 | 6506 | 39947 | 0.0000% |

3 | 927 | 18372 | 19299 | 40400 | 4.8034% |

10 | 5518 | 59304 | 64822 | 40094 | 8.5125% |

25 | 20977 | 140476 | 161453 | 40243 | 12.9926% |

50 | 60526 | 263106 | 323632 | 40153 | 18.7021% |

The percentage of extra RFs is the important result. If 10% of the RFs pay 800:1 instead of 1760:1, then you need to adjust the effective value of the jackpot to be 96 units lower than it actually is. After making this adjustment, you can just get the effective EV from any VP analyzer.

The second table is for the modified optimal strategy for the jackpot at the 1760:1 value.

# Hands | # Extra | Hands w/ RF | Total # RF | Cycle | % Extra |
---|---|---|---|---|---|

1 | 0 | 7900 | 7900 | 32898 | 0.00% |

3 | 949 | 23244 | 24193 | 32228 | 3.92% |

10 | 5567 | 73945 | 79512 | 32686 | 7.00% |

25 | 21456 | 177994 | 199450 | 32577 | 10.76% |

50 | 62026 | 337971 | 399997 | 32487 | 15.51% |

When you use the modified strategy, you get more single royals because you hold more singletons and two-card holds.

You can estimate the number of extra RFs just from dealt Royals. Let us say you are using a strategy that puts the RF cycle at 33,000 hands. If you play 100-play, then you will be dealt a RF every 649,740 starting hands or 99 extra RF every 649740*100 total hands. You expect to get 649740*100/33000 = 1969 RFs in this number of hands. This amounts about 5% extra RFs just from dealt RFs. If you add in the draws, the effective RF jackpot has to be significantly reduced already at 100 play.Quote:ThatDonGuyI get 1850 hands as the point where EV drops below 100%.

Here's how I calculated it:

Using the Wizard's VP strategy calculator, I set it to 8/5 Jacks or Better with a Royal payout of 1760 (representing a payout of 8800 on a bet of 5).

It came up with these numbers:

The probability of a Royal using modified basic strategy is 1 / 32,576

A non-Royal has an ER of 0.946793

One Royal will add 1760 / N to the EV

Each additional Royal adds 800 / N to the EV

Based on that, I calculated the total ER of an N-hand game as:

EV for 0 Royals = (32,575 / 32,576)^N x 0.946793

EV for 1 Royal = C(N,1) x 32,575^(N-1) / 32,576^N x (0.946793 + 1760 / N)

EV for 2 Royals = C(N,2) x 32,575^(N-2) / 32,576^N x (0.946793 + (1760 + 800) / N)

EV for 3 Royals = C(N,3) x 32,575^(N-3) / 32,576^N x (0.946793 + (1760 + 800 x 2) / N)

...

EV for N Royals = C(N,N) x 1 / 32,576^N x (0.946793 + (1760 + 800 x (N - 1) / N)

There may or may not be an "easy way" to calculate a closed-form solution, given that combinations are involved; I just plugged numbers into Excel.

link to original post

The fraction of extra RFs on a 1850-play game would be rather large, so the effective RF payoff would be pretty low.

Twice, I hit two RFs from a 3-card hold on a 10-play machine. Once, I hit 4 RFs from a 4-card hold on a 10-play machine.