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Last Updated: December 25, 2018

Number Bonus

Introduction

Number Bonus is a video poker game that offers premium pays if a predetermined rank is pertinent part of certain hands. The only provider of this game, as far as I know, is Red Rake Gaming, a provider of software for Internet casinos.

Rules

The game plays like standard video poker, except as follows.

  1. Every day there will be a Bonus Number, which can be anything from 2 to 10. This number will be disclosed to the player upon loading the game.
  2. The lowest paying hand is for jacks or better or a pair of the rank of the Bonus Number.
  3. The Bonus Double Pair is a two pair including a pair of the rank of the Bonus Number.
  4. The Bonus Three of a Kind is a three of a kind of the rank of the Bonus Number.
  5. The Bonus Flush is a flush including the rank of the Bonus Number.
  6. The Bonus Full House includes the rank of the Bonus Number in either the pair or three of a kind.
  7. The Bonus Four of a Kind is all four suits of the rank of the Bonus Number.

Please note that a singleton of the rank of the Bonus Number only helps improve the rank of the flush.

Bonus Number 2

Bonus Number 2

Hand Payoff Permutations Probability Return
Royal flush 600 437,702,508 0.000022 0.013175
Straight flush 80 2,202,313,404 0.000110 0.008839
Bonus four of a kind 40 4,124,113,488 0.000207 0.008276
Four of a kind 20 39,526,088,136 0.001983 0.039658
Bonus full house 12 53,204,115,432 0.002669 0.032029
Full house 10 172,705,830,864 0.008664 0.086642
Bonus flush 6 106,565,595,192 0.005346 0.032077
Flush 5 132,753,224,616 0.006660 0.033299
Straight 4 214,551,649,512 0.010764 0.043054
Bonus three of a kind 5 143,611,593,528 0.007205 0.036023
Three of a kind 2 1,271,260,177,140 0.063776 0.127552
Two pair including Bonus Pair 3 677,132,041,104 0.033970 0.101910
Two pair 2 1,919,655,989,316 0.096304 0.192609
Pair jacks or better of Bonus Pair 1 4,933,455,828,408 0.247499 0.247499
Nothing 0 10,262,044,254,552 0.514821 0.000000
Total 19,933,230,517,200 1.000000 1.002643

Bonus Number 3

Hand Payoff Permutations Probability Return
Royal flush 600 436,265,808 0.000022 0.013132
Straight flush 80 2,252,140,020 0.000113 0.009039
Bonus four of a kind 40 4,114,175,844 0.000206 0.008256
Four of a kind 20 39,523,503,492 0.001983 0.039656
Bonus full house 12 53,034,864,960 0.002661 0.031928
Full house 10 172,755,436,344 0.008667 0.086667
Bonus flush 6 107,609,349,912 0.005398 0.032391
Flush 5 132,391,036,140 0.006642 0.033209
Straight 4 217,770,985,548 0.010925 0.043700
Bonus three of a kind 5 143,144,865,300 0.007181 0.035906
Three of a kind 2 1,270,707,534,540 0.063748 0.127496
Two pair including Bonus Pair 3 674,785,107,144 0.033852 0.101557
Two pair 2 1,919,771,281,800 0.096310 0.192620
Pair jacks or better of Bonus Pair 1 4,934,629,515,528 0.247558 0.247558
Nothing 0 10,260,304,454,820 0.514734 0.000000
Total 19,933,230,517,200 1.000000 1.003114

Bonus Number 4

Hand Payoff Permutations Probability Return
Royal flush 600 435,749,916 0.000022 0.013116
Straight flush 80 2,307,285,216 0.000116 0.009260
Bonus four of a kind 40 4,099,682,952 0.000206 0.008227
Four of a kind 20 39,521,914,728 0.001983 0.039654
Bonus full house 12 52,835,597,832 0.002651 0.031808
Full house 10 172,821,474,888 0.008670 0.086700
Bonus flush 6 108,637,732,740 0.005450 0.032700
Flush 5 132,221,366,148 0.006633 0.033166
Straight 4 221,031,645,876 0.011089 0.044354
Bonus three of a kind 5 142,401,163,548 0.007144 0.035720
Three of a kind 2 1,270,286,761,512 0.063727 0.127454
Two pair including Bonus Pair 3 671,689,293,840 0.033697 0.101091
Two pair 2 1,920,435,060,060 0.096343 0.192687
Pair jacks or better of Bonus Pair 1 4,935,888,338,436 0.247621 0.247621
Nothing 0 10,258,617,449,508 0.514649 0.000000
Total 19,933,230,517,200 1.000000 1.003559

Bonus Number 5

Hand Payoff Permutations Probability Return
Royal flush 600 434,676,972 0.000022 0.013084
Straight flush 80 2,361,556,512 0.000118 0.009478
Bonus four of a kind 40 4,087,427,436 0.000205 0.008202
Four of a kind 20 39,519,652,068 0.001983 0.039652
Bonus full house 12 52,650,782,112 0.002641 0.031696
Full house 10 172,877,949,024 0.008673 0.086729
Bonus flush 6 109,659,011,244 0.005501 0.033008
Flush 5 131,973,008,652 0.006621 0.033104
Straight 4 224,167,709,172 0.011246 0.044984
Bonus three of a kind 5 141,791,093,136 0.007113 0.035567
Three of a kind 2 1,269,786,331,296 0.063702 0.127404
Two pair including Bonus Pair 3 668,945,869,416 0.033559 0.100678
Two pair 2 1,920,805,182,216 0.096362 0.192724
Pair jacks or better of Bonus Pair 1 4,936,685,046,048 0.247661 0.247661
Nothing 0 10,257,485,221,896 0.514592 0.000000
Total 19,933,230,517,200 1.000000 1.003970

Bonus Number 6

Hand Payoff Permutations Probability Return
Royal flush 600 434,392,416 0.000022 0.013075
Straight flush 80 2,362,662,336 0.000119 0.009482
Bonus four of a kind 40 4,078,757,604 0.000205 0.008185
Four of a kind 20 39,507,780,972 0.001982 0.039640
Bonus full house 12 52,549,322,556 0.002636 0.031635
Full house 10 172,835,949,588 0.008671 0.086707
Bonus flush 6 113,189,380,332 0.005678 0.034071
Flush 5 132,550,710,876 0.006650 0.033249
Straight 4 223,483,091,232 0.011212 0.044846
Bonus three of a kind 5 141,272,315,172 0.007087 0.035436
Three of a kind 2 1,269,074,951,484 0.063666 0.127333
Two pair including Bonus Pair 3 667,540,443,384 0.033489 0.100466
Two pair 2 1,919,875,836,168 0.096315 0.192631
Pair jacks or better of Bonus Pair 1 4,923,433,843,956 0.246996 0.246996
Nothing 0 10,271,041,079,124 0.515272 0.000000
Total 19,933,230,517,200 1.000000 1.003753

Bonus Number 7

Hand Payoff Permutations Probability Return
Royal flush 600 435,043,512 0.000022 0.013095
Straight flush 80 2,360,195,616 0.000118 0.009472
Bonus four of a kind 40 4,090,566,264 0.000205 0.008209
Four of a kind 20 39,517,372,896 0.001982 0.039650
Bonus full house 12 52,668,958,728 0.002642 0.031707
Full house 10 172,863,236,832 0.008672 0.086721
Bonus flush 6 109,643,443,524 0.005501 0.033003
Flush 5 131,981,923,608 0.006621 0.033106
Straight 4 224,288,317,848 0.011252 0.045008
Bonus three of a kind 5 141,967,317,456 0.007122 0.035611
Three of a kind 2 1,269,644,877,120 0.063695 0.127390
Two pair including Bonus Pair 3 669,366,300,024 0.033580 0.100741
Two pair 2 1,920,432,324,744 0.096343 0.192687
Pair jacks or better of Bonus Pair 1 4,935,583,927,332 0.247606 0.247606
Nothing 0 10,258,386,711,696 0.514637 0.000000
Total 19,933,230,517,200 1.000000 1.004005

Bonus Number 8

Hand Payoff Permutations Probability Return
Royal flush 600 438,179,628 0.000022 0.013189
Straight flush 80 2,376,005,004 0.000119 0.009536
Bonus four of a kind 40 4,103,888,352 0.000206 0.008235
Four of a kind 20 39,551,806,092 0.001984 0.039684
Bonus full house 12 52,787,329,128 0.002648 0.031778
Full house 10 172,974,724,308 0.008678 0.086777
Bonus flush 6 105,931,687,740 0.005314 0.031886
Flush 5 131,473,316,628 0.006596 0.032978
Straight 4 224,768,855,640 0.011276 0.045104
Bonus three of a kind 5 142,772,527,200 0.007163 0.035813
Three of a kind 2 1,271,083,800,912 0.063767 0.127534
Two pair including Bonus Pair 3 671,292,736,488 0.033677 0.101031
Two pair 2 1,922,086,440,144 0.096426 0.192852
Pair jacks or better of Bonus Pair 1 4,947,013,305,144 0.248179 0.248179
Nothing 0 10,244,575,914,792 0.513945 0.000000
Total 19,933,230,517,200 1.000000 1.004579

Bonus Number 9

Hand Payoff Permutations Probability Return
Royal flush 600 441,654,600 0.000022 0.013294
Straight flush 80 2,374,788,948 0.000119 0.009531
Bonus four of a kind 40 4,083,773,640 0.000205 0.008195
Four of a kind 20 39,595,445,760 0.001986 0.039728
Bonus full house 12 52,890,365,352 0.002653 0.031841
Full house 10 173,075,776,368 0.008683 0.086828
Bonus flush 6 100,979,683,956 0.005066 0.030395
Flush 5 130,224,824,136 0.006533 0.032665
Straight 4 228,066,620,580 0.011442 0.045766
Bonus three of a kind 5 142,193,442,828 0.007133 0.035667
Three of a kind 2 1,273,358,812,200 0.063881 0.127762
Two pair including Bonus Pair 3 672,655,795,992 0.033745 0.101236
Two pair 2 1,924,258,514,292 0.096535 0.193070
Pair jacks or better of Bonus Pair 1 4,972,964,455,332 0.249481 0.249481
Nothing 0 10,216,066,563,216 0.512514 0.000000
Total 19,933,230,517,200 1.000000 1.005461

Bonus Number 10

Hand Payoff Permutations Probability Return
Royal flush 600 475,610,700 0.000024 0.014316
Straight flush 80 2,279,289,192 0.000114 0.009148
Bonus four of a kind 40 4,027,338,204 0.000202 0.008082
Four of a kind 20 39,653,297,100 0.001989 0.039786
Bonus full house 12 52,938,047,256 0.002656 0.031869
Full house 10 173,157,535,200 0.008687 0.086869
Bonus flush 6 91,832,489,568 0.004607 0.027642
Flush 5 130,898,009,520 0.006567 0.032834
Straight 4 237,309,887,580 0.011905 0.047621
Bonus three of a kind 5 140,523,781,416 0.007050 0.035249
Three of a kind 2 1,275,918,398,100 0.064010 0.128019
Two pair including Bonus Pair 3 674,980,528,536 0.033862 0.101586
Two pair 2 1,924,510,105,548 0.096548 0.193096
Pair jacks or better of Bonus Pair 1 5,021,493,555,924 0.251916 0.251916
Nothing 0 10,163,232,643,356 0.509864 0.000000
Total 19,933,230,517,200 1.000000 1.008032

The following table summarizes the return by Bonus Number.

Return Summary

Bonus
Number
Expected
Return
2 100.26%
3 100.31%
4 100.36%
5 100.40%
6 100.38%
7 100.40%
8 100.46%
9 100.55%
10 100.80%
Average 100.43%

Strategy

Sorry, you're on your own with that.


Written by: Michael Shackleford

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