Last Updated: June 13, 2013

No Risk Double Up

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Introduction

I first played No Risk Double Up on the day it premiered, Feb. 1, 2013, at the Red Rock. It is one of various games available on the WMS My Poker machines. The thrust of the game is that sometimes on a winning hand the player plays a bonus game in which the player may double his win up to four times, or to a multiplier of 24=16. There is "no risk," because the worst that can happen in the bonus is the player gets paid the base amount for his hand. However, the player pays for the bonus feature via a non-refundable fee equal to his video poker wager.

Rules

  1. Player makes a 10-coin bet. Five coins pay for the standard video poker hand and five enable the No Risk Double Up feature.
  2. The player plays his hand according to standard video poker rules.
  3. If the player gets any paying hand on the draw, then he will have a specified chance of playing the Double Up feature.
  4. This probability depends on the poker hand.
  5. In the Double Up feature, the player will first pick one of five face-down cards. Four are aces and one is a joker, and the goal is to pick an ace. If the player picks the joker, then his multiplier is 1x. Otherwise, see rule 6.
  6. In the next stage, there are three aces and two jokers. If the player picks a joker, his multiplier is 2x. Otherwise, see rule 7.
  7. In the next stage, there are two aces and three jokers. If the player picks the joker, then his multiplier is 4x. Otherwise see rule 8.
  8. In the next stage, there is one ace and four jokers. If the player picks a joker, then his multiplier is 8x. If the player picks the ace, his multiplier is 16x.
  9. Player is paid according to his poker hand and any multiplier earned.

Here is an example, in pictures, of the bonus game.

First I got a four of a kind on the draw. The probability of the bonus feature with a four of a kind is 100%, as seen in the table to the right of the pay table.


Then I was given five cards and challenged to pick one of the four aces.

It isn't clear which card I chose from the picture, but I did pick one of the aces.

Next, I was asked to picked one of three aces in the next set of five cards.

I must have picked one of the jokers, which ended the bonus, giving me a multiplier of 2x.

Odds

The following tables show the probability and return for the pay tables I noticed at the Red Rock. The "bonus prob." column refers to the probability of playing the bonus feature with that hand. The "adjusted pay" column refers to the average win for that hand, considering the probability of playing the bonus and the average bonus multiplier.

55-9-5 Jacks or Better

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 50,841,598 0.000031 0.046954
Straight flush 55 1.000000 105.47 214,210,910 0.000129 0.013601
Four of a kind 25 1.000000 47.94 3,914,082,611 0.002356 0.112962
Full house 9 1.000000 17.26 19,051,457,919 0.011469 0.197939
Flush 5 0.333333 4.86 19,370,987,397 0.011662 0.056706
Straight 4 0.333333 3.89 20,771,970,996 0.012505 0.048646
Three of a kind 3 0.200000 2.35 122,823,581,699 0.073941 0.173803
Two pair 2 0.166667 1.47 212,898,461,571 0.128167 0.188730
Jacks or better 1 0.166667 0.74 334,272,435,996 0.201235 0.148163
Loser 0 0.000000 0.00 927,734,512,403 0.558505 0.000000
Total 1,661,102,543,100 1.000000 0.987504

55-7-5 Jacks or Better

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 50,824,583 0.000031 0.046938
Straight flush 55 1.000000 105.47 214,585,611 0.000129 0.013625
Four of a kind 25 1.000000 47.94 3,892,982,511 0.002344 0.112353
Full house 7 1.000000 13.42 18,929,401,539 0.011396 0.152967
Flush 5 0.500000 6.04 24,123,066,721 0.014522 0.087773
Straight 4 0.250000 3.42 17,575,843,366 0.010581 0.036161
Three of a kind 3 0.200000 2.35 121,993,405,530 0.073441 0.172628
Two pair 2 0.200000 1.57 211,800,539,664 0.127506 0.199807
Jacks or better 1 0.166667 0.74 321,989,453,811 0.193841 0.142719
Loser 0 0.000000 0.00 940,532,439,764 0.566210 0.000000
Total 1,661,102,543,100 1.000000 0.964970

55-7-5 Bonus Poker

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 50,833,965 0.000031 0.046947
Straight flush 55 1.000000 105.47 210,409,105 0.000127 0.013359
Four aces 80 1.000000 153.41 344,139,578 0.000207 0.031782
Four 2-4 40 1.000000 76.70 875,353,709 0.000527 0.040421
Four 5-K 25 1.000000 47.94 2,685,202,897 0.001617 0.077496
Full house 7 0.500000 8.46 18,770,201,496 0.011300 0.095615
Flush 5 0.500000 6.04 22,907,520,905 0.013791 0.083350
Straight 4 0.333333 3.89 19,616,676,850 0.011809 0.045940
Three of a kind 3 0.250000 2.56 122,108,491,916 0.073511 0.188422
Two pair 2 0.250000 1.71 211,395,173,364 0.127262 0.217465
Jacks or better 1 0.166667 0.74 321,751,591,491 0.193698 0.142613
Loser 0 0.000000 0.00 940,386,947,824 0.566122 0.000000
Total 0.000000 1,661,102,543,100 1.000000 0.983411

55-8-5 Bonus Poker

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 51,279,913 0.000031 0.047359
Straight flush 55 1.000000 105.47 204,623,113 0.000123 0.012992
Four aces 80 1.000000 153.41 339,803,845 0.000205 0.031382
Four 2-4 40 1.000000 76.70 887,030,961 0.000534 0.040960
Four 5-K 25 1.000000 47.94 2,706,328,195 0.001629 0.078106
Full house 8 0.500000 9.67 19,146,735,969 0.011527 0.111466
Flush 5 0.250000 4.27 18,359,113,789 0.011052 0.047216
Straight 4 0.250000 3.42 17,807,967,546 0.010721 0.036639
Three of a kind 3 0.250000 2.56 124,025,547,128 0.074665 0.191380
Two pair 2 0.250000 1.71 215,245,052,118 0.129580 0.221426
Jacks or better 1 0.250000 0.85 341,447,589,567 0.205555 0.175626
Loser 0 0.000000 0.00 920,881,470,956 0.554380 0.000000
Total 1,661,102,543,100 1.000000 0.994551

80-9-6 Double Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 50,848,370 0.000031 0.046960
Straight flush 80 1.000000 153.41 232,091,773 0.000140 0.021434
Four aces 160 1.000000 306.82 381,850,707 0.000230 0.070530
Four 2-4 80 1.000000 153.41 899,534,501 0.000542 0.083075
Four 5-K 50 1.000000 95.88 2,684,977,620 0.001616 0.154979
Full house 9 0.250000 7.69 17,359,094,436 0.010450 0.080359
Flush 6 0.250000 5.13 19,625,454,642 0.011815 0.060567
Straight 5 0.200000 3.92 21,636,064,393 0.013025 0.051027
Three of a kind 3 0.200000 2.35 124,196,495,645 0.074768 0.175746
Two pair 1 0.166667 0.74 202,195,087,155 0.121723 0.089621
Jacks or better 1 0.166667 0.74 339,388,020,489 0.204315 0.150430
Loser 0 0.000000 0.00 932,453,023,369 0.561346 0.000000
Total 1.000000 0.984728

55-9-7 Double Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 49,449,663 0.000030 0.045668
Straight flush 55 1.000000 105.47 220,904,899 0.000133 0.014026
Four aces 160 1.000000 306.82 377,831,669 0.000227 0.069788
Four 2-4 80 0.500000 96.70 875,147,954 0.000527 0.050948
Four 5-K 50 0.500000 60.44 2,658,484,847 0.001600 0.096730
Full house 9 0.333333 8.75 17,707,138,842 0.010660 0.093304
Flush 7 0.333333 6.81 24,672,674,798 0.014853 0.101117
Straight 4 0.333333 3.89 20,525,941,554 0.012357 0.048070
Three of a kind 3 0.333333 2.92 122,197,922,340 0.073564 0.214631
Two pair 1 0.200000 0.78 199,755,347,184 0.120255 0.094222
Jacks or better 1 0.200000 0.78 324,521,368,260 0.195365 0.153072
Loser 0 0.000000 0.00 947,540,331,090 0.570429 0.000000
Total 1,661,102,543,100 1.000000 0.981576

55-9-5 Double Double Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 48,363,447 0.000029 0.044665
Straight flush 55 1.000000 105.47 212,523,804 0.000128 0.013494
Four aces + 2-4 400 1.000000 767.04 102,642,886 0.000062 0.047397
Four 2-4 + A-4 160 1.000000 306.82 287,007,958 0.000173 0.053012
Four aces + 5-K 160 1.000000 306.82 289,445,734 0.000174 0.053462
Four 2-4 + 5-K 80 0.500000 96.70 532,887,662 0.000321 0.031023
Four 5-K 50 0.500000 60.44 2,697,263,322 0.001624 0.098141
Full house 9 0.333333 8.75 17,464,609,326 0.010514 0.092026
Flush 5 0.333333 4.86 19,018,885,704 0.011450 0.055675
Straight 4 0.250000 3.42 20,272,323,417 0.012204 0.041709
Three of a kind 3 0.250000 2.56 125,397,768,299 0.075491 0.193498
Two pair 1 0.250000 0.85 203,984,111,961 0.122800 0.104921
Jacks or better 1 0.166667 0.74 345,489,472,116 0.207988 0.153135
Loser 0 0.000000 0.00 925,305,237,464 0.557043 0.000000
Total 0.00 1,661,102,543,100 1.000000 0.982158

55-9-6 Double Double Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 28,668,371 0.000017 0.026476
Straight flush 55 1.000000 105.47 211,274,677 0.000127 0.013414
Four aces + 2-4 400 1.000000 767.04 103,310,572 0.000062 0.047705
Four 2-4 + A-4 160 1.000000 306.82 287,043,734 0.000173 0.053019
Four aces + 5-K 160 1.000000 306.82 288,541,935 0.000174 0.053295
Four 2-4 + 5-K 80 0.500000 96.70 531,884,343 0.000320 0.030965
Four 5-K 50 0.500000 60.44 2,679,069,506 0.001613 0.097479
Full house 9 0.333333 8.75 17,337,699,378 0.010437 0.091357
Flush 6 0.333333 5.84 25,108,867,497 0.015116 0.088204
Straight 4 0.250000 3.42 19,915,596,512 0.011989 0.040975
Three of a kind 3 0.250000 2.56 123,946,114,922 0.074617 0.191258
Two pair 1 0.250000 0.85 201,287,917,422 0.121177 0.103534
Jacks or better 1 0.166667 0.74 330,338,086,155 0.198867 0.146419
Loser 0 0.000000 0.00 939,038,468,076 0.565310 0.000000
Total 1,661,102,543,100 1.000000 0.984100

55-8-5 Double Double Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 48,356,129 0.000029 0.044658
Straight flush 55 1.000000 105.47 212,963,213 0.000128 0.013522
Four aces + 2-4 400 1.000000 767.04 102,638,278 0.000062 0.047395
Four 2-4 + A-4 160 1.000000 306.82 287,016,086 0.000173 0.053014
Four aces + 5-K 160 1.000000 306.82 289,422,478 0.000174 0.053458
Four 2-4 + 5-K 80 0.500000 96.70 532,877,126 0.000321 0.031022
Four 5-K 50 0.500000 60.44 2,695,255,394 0.001623 0.098068
Full house 8 0.333333 7.78 17,457,361,686 0.010510 0.081767
Flush 5 0.333333 4.86 19,023,273,263 0.011452 0.055688
Straight 4 0.250000 3.42 20,353,545,582 0.012253 0.041876
Three of a kind 3 0.250000 2.56 125,317,814,777 0.075443 0.193374
Two pair 1 0.250000 0.85 203,878,772,595 0.122737 0.104867
Jacks or better 1 0.166667 0.74 345,691,511,217 0.208110 0.153224
Loser 0 0.000000 0.00 925,211,735,276 0.556987 0.000000
Total 0.000000 1,661,102,543,100 1.000000 0.971933

55-9-6 Triple Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 47,567,509 0.000029 0.043930
Straight flush 55 1.000000 105.47 229,865,632 0.000138 0.014595
Four aces + 2-4 800 1.000000 1534.08 119,239,081 0.000072 0.110121
Four 2-4 + A-4 400 0.500000 483.52 287,027,419 0.000173 0.083549
Four aces + 5-K 160 0.500000 193.41 231,530,280 0.000139 0.026958
Four 2-4 + 5-K 80 0.333333 77.80 531,240,135 0.000320 0.024882
Four 5-K 50 0.333333 48.63 2,622,157,200 0.001579 0.076760
Full house 9 0.250000 7.69 17,121,315,099 0.010307 0.079258
Flush 6 0.333333 5.84 23,153,412,754 0.013939 0.081334
Straight 4 0.333333 3.89 22,316,795,871 0.013435 0.052264
Three of a kind 2 0.333333 1.95 121,661,348,516 0.073241 0.142459
Two pair 1 0.200000 0.78 198,703,840,446 0.119622 0.093726
Jacks or better 1 0.200000 0.78 331,438,998,621 0.199530 0.156335
Loser 0 0.000000 0.00 942,638,204,537 0.567477 0.000000
Total 1,661,102,543,100 1.000000 0.986172

55-8-5 Triple Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 47,375,452 0.000029 0.043753
Straight flush 55 1.000000 105.47 220,869,185 0.000133 0.014024
Four aces + 2-4 800 1.000000 1534.08 119,312,469 0.000072 0.110189
Four 2-4 + A-4 400 0.500000 483.52 287,533,231 0.000173 0.083696
Four aces + 5-K 160 0.500000 193.41 231,639,169 0.000139 0.026971
Four 2-4 + 5-K 80 0.333333 77.80 532,444,734 0.000321 0.024939
Four 5-K 50 0.333333 48.63 2,658,246,670 0.001600 0.077817
Full house 8 0.333333 7.78 17,284,654,041 0.010406 0.080958
Flush 5 0.333333 4.86 19,735,896,528 0.011881 0.057774
Straight 4 0.333333 3.89 23,603,335,367 0.014209 0.055277
Three of a kind 2 0.333333 1.95 123,207,949,896 0.074172 0.144270
Two pair 1 0.200000 0.78 200,836,822,158 0.120906 0.094732
Jacks or better 1 0.166667 0.74 339,492,887,370 0.204378 0.150477
Loser 0 0.000000 0.00 932,843,576,830 0.561581 0.000000
Total 1,661,102,543,100 1.000000 0.964875

55-8-5 Triple Triple Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal Flush 800 1.000000 1534.08 48,199,494 0.000029 0.044514
Straight Flush 55 1.000000 105.47 233,880,851 0.000141 0.014850
Four Aces with any 2,3,4 800 1.000000 1534.08 119,863,933 0.000072 0.110698
Four 2s, 3s, 4s with an Ace 800 0.500000 967.04 130,893,766 0.000079 0.076202
Four 2s, 3s, 4s with any 2,3,4 400 0.500000 483.52 171,152,540 0.000103 0.049820
Four Aces 160 0.500000 193.41 233,038,056 0.000140 0.027133
Four 2s, 3s, 4s 80 0.333333 77.80 458,450,533 0.000276 0.021473
Four 5s thru Ks 50 0.333333 48.63 2,672,325,558 0.001609 0.078229
Full House 8 0.333333 7.78 17,353,094,178 0.010447 0.081278
Flush 5 0.333333 4.86 19,618,732,075 0.011811 0.057431
Straight 3 0.333333 2.92 17,791,107,475 0.010710 0.031249
Three of a Kind 2 0.250000 1.71 123,642,016,832 0.074434 0.127192
Two Pair 1 0.200000 0.78 205,006,847,508 0.123416 0.096699
Jacks or Better 1 0.200000 0.78 346,069,731,165 0.208337 0.163236
All Other 0 0.000000 0.00 927,553,209,136 0.558396 0.000000
Total 1,661,102,543,100 1.000000 0.980005

55-7-5 Triple Triple Bonus

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal Flush 800 1.000000 1534.08 48,166,386 0.000029 0.044483
Straight Flush 55 1.000000 105.47 234,023,229 0.000141 0.014859
Four Aces with any 2,3,4 800 1.000000 1534.08 119,858,237 0.000072 0.110693
Four 2s, 3s, 4s with an Ace 800 0.500000 967.04 130,780,910 0.000079 0.076136
Four 2s, 3s, 4s with any 2,3,4 400 0.500000 483.52 170,940,298 0.000103 0.049758
Four Aces 160 0.500000 193.41 232,984,197 0.000140 0.027127
Four 2s, 3s, 4s 80 0.333333 77.80 457,438,202 0.000275 0.021425
Four 5s thru Ks 50 0.333333 48.63 2,670,283,660 0.001608 0.078169
Full House 7 0.333333 6.81 17,337,031,320 0.010437 0.071053
Flush 5 0.333333 4.86 19,961,991,360 0.012017 0.058436
Straight 3 0.333333 2.92 17,767,538,673 0.010696 0.031207
Three of a Kind 2 0.250000 1.71 123,484,578,302 0.074339 0.127030
Two Pair 1 0.200000 0.78 204,761,498,130 0.123268 0.096583
Jacks or Better 1 0.200000 0.78 345,329,431,887 0.207892 0.162887
All Other 0 0.000000 0.00 928,395,998,309 0.558903 0.000000
Total 1,661,102,543,100 1.000000 0.969848

"Ugly Ducks" Deuces Wild

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 43,251,497 0.000026 0.039944
Four decues 200 1.000000 383.52 335,004,142 0.000202 0.077347
Wild royal 25 1.000000 47.94 3,511,011,126 0.002114 0.101329
Five of a kind 15 1.000000 28.76 5,201,941,178 0.003132 0.090078
Straight flush 9 0.500000 10.88 7,391,681,513 0.004450 0.048411
Four of a kind 4 0.250000 3.42 103,169,753,220 0.062109 0.212264
Full house 4 0.200000 3.13 43,687,254,000 0.026300 0.082427
Flush 3 0.200000 2.35 34,526,633,968 0.020785 0.048857
Straight 2 0.200000 1.57 78,437,312,310 0.047220 0.073996
Three of a kind 1 0.200000 0.78 455,582,791,984 0.274265 0.214892
Loser 0 0.000000 0.00 929,215,908,162 0.559397 0.000000
Total 1,661,102,543,100 1.000000 0.989545

16-13 Deuces Wild

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Royal flush 800 1.000000 1534.08 43,496,692 0.000026 0.040171
Four decues 200 1.000000 383.52 310,326,227 0.000187 0.071649
Wild royal 25 1.000000 47.94 3,428,050,502 0.002064 0.098935
Five of a kind 16 1.000000 30.68 5,062,837,638 0.003048 0.093514
Straight flush 13 0.500000 15.71 9,446,014,693 0.005687 0.089361
Four of a kind 4 0.250000 3.42 100,098,173,079 0.060260 0.205945
Full house 3 0.250000 2.56 42,934,498,656 0.025847 0.066251
Flush 2 0.250000 1.71 31,920,704,349 0.019217 0.032837
Straight 2 0.200000 1.57 88,851,336,959 0.053489 0.083820
Three of a kind 1 0.142857 0.70 443,197,694,512 0.266809 0.187437
Loser 0 0.000000 0.00 935,809,409,793 0.563366 0.000000
Total 1,661,102,543,100 1.000000 0.969920

940-17-7 Joker Wild

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Natural royal flush 940 1.000000 1802.54 55,190,603 0.000027 0.048590
Five of a kind 200 1.000000 383.52 188,141,951 0.000092 0.035243
Wild royal flush 100 1.000000 191.76 232,146,019 0.000113 0.021743
Straight flush 50 1.000000 95.88 1,465,910,588 0.000716 0.068649
Four of a kind 17 0.500000 20.55 17,153,441,573 0.008378 0.172167
Full house 7 0.500000 8.46 31,471,476,975 0.015371 0.130067
Flush 5 0.333333 4.86 37,332,583,750 0.018234 0.088666
Straight 3 0.250000 2.56 34,949,804,574 0.017070 0.043755
Three of a kind 2 0.200000 1.57 267,039,781,532 0.130428 0.204386
Two pair 1 0.166667 0.74 221,701,758,327 0.108284 0.079726
Kings or better 1 0.166667 0.74 259,310,127,713 0.126653 0.093250
Nothing 0 0.000000 0.00 1,176,505,096,495 0.574632 0.000000
Total 2,047,405,460,100 1.000000 0.986242

800-15-7 Joker Wild

Hand Pays Bonus
Prob.
Adjusted
Pay
Combinations Probability Return
Natural royal flush 800 1.000000 1534.08 54,663,353 0.000027 0.040958
Five of a kind 200 1.000000 383.52 187,905,361 0.000092 0.035198
Wild royal flush 100 1.000000 191.76 230,670,189 0.000113 0.021605
Straight flush 50 1.000000 95.88 1,473,681,154 0.000720 0.069012
Four of a kind 15 0.500000 18.13 17,119,418,143 0.008362 0.151611
Full house 7 0.500000 8.46 31,411,564,605 0.015342 0.129819
Flush 5 0.333333 4.86 37,565,266,344 0.018348 0.089219
Straight 3 0.200000 2.35 35,011,896,484 0.017101 0.040196
Three of a kind 2 0.200000 1.57 266,400,099,622 0.130116 0.203897
Two pair 1 0.200000 0.78 221,094,494,127 0.107988 0.084610
Kings or better 1 0.200000 0.78 261,766,601,769 0.127853 0.100175
Nothing 0 0.000000 0.00 1,175,089,198,949 0.573941 0.000000
Total 0.000000 0.00 2,047,405,460,100 1.000000 0.966301

The next table shows the Double Up feature probability for some of the above games, assuming optimal strategy.

Feature Probability

Game Pay Table Feature
Prob.
Jacks or Better 55-9-5 0.091729
Bonus Poker 55-7-5 0.101322
Bonus Poker 55-8-5 0.116178
Double Bonus 80-9-6 0.080023
Double Bonus 55-9-6 0.101723
Double Double Bonus 55-9-5 0.122966
Double Double Bonus 55-9-6 0.096522
Triple Triple Bonus 55-8-5 0.102925
Deuces Wild 25-15-9 0.096939
Joker Wild 940-17-7 0.088410

Finally, for those for whom an average return per hand won't do, here is the 55-9-5 Jacks or Better table broken down by hand and multiplier. This table allows us to see that the standard deviation is 12.09.

55-9-5 Jacks or Better — Detailed Table

Hand Bonus Pays Multiplier Total win Total Combinations Probability Return
Royal flush Yes 800 16 6400 73,211,901,120 0.000001 0.007522
Straight flush Yes 55 16 440 308,463,710,400 0.000005 0.002179
Four of a kind Yes 25 16 200 5,636,278,959,840 0.000090 0.018097
Full house Yes 9 16 72 27,434,099,403,360 0.000440 0.031710
Flush Yes 5 16 40 9,298,073,950,560 0.000149 0.005971
Straight Yes 4 16 32 9,970,546,078,080 0.000160 0.005122
Three of a kind Yes 3 16 24 35,373,191,529,312 0.000568 0.013629
Two pair Yes 2 16 16 51,095,630,777,040 0.000820 0.013124
Jacks or better Yes 1 16 8 80,225,384,639,040 0.001288 0.010303
Royal flush Yes 800 8 3200 292,847,604,480 0.000005 0.015044
Straight flush Yes 55 8 220 1,233,854,841,600 0.000020 0.004358
Four of a kind Yes 25 8 100 22,545,115,839,360 0.000362 0.036193
Full house Yes 9 8 36 109,736,397,613,440 0.001762 0.063420
Flush Yes 5 8 20 37,192,295,802,240 0.000597 0.011941
Straight Yes 4 8 16 39,882,184,312,320 0.000640 0.010244
Three of a kind Yes 3 8 12 141,492,766,117,248 0.002271 0.027258
Two pair Yes 2 8 8 204,382,523,108,160 0.003281 0.026249
Jacks or better Yes 1 8 4 320,901,538,556,160 0.005152 0.020606
Royal flush Yes 800 4 1600 549,089,258,400 0.000009 0.014104
Straight flush Yes 55 4 110 2,313,477,828,000 0.000037 0.004085
Four of a kind Yes 25 4 50 42,272,092,198,800 0.000679 0.033931
Full house Yes 9 4 18 205,755,745,525,200 0.003303 0.059456
Flush Yes 5 4 10 69,735,554,629,200 0.001120 0.011195
Straight Yes 4 4 8 74,779,095,585,600 0.001200 0.009604
Three of a kind Yes 3 4 6 265,298,936,469,840 0.004259 0.025554
Two pair Yes 2 4 4 383,217,230,827,800 0.006152 0.024608
Jacks or better Yes 1 4 2 601,690,384,792,800 0.009659 0.019319
Royal flush Yes 800 2 800 610,099,176,000 0.000010 0.007835
Straight flush Yes 55 2 55 2,570,530,920,000 0.000041 0.002270
Four of a kind Yes 25 2 25 46,968,991,332,000 0.000754 0.018851
Full house Yes 9 2 9 228,617,495,028,000 0.003670 0.033031
Flush Yes 5 2 5 77,483,949,588,000 0.001244 0.006219
Straight Yes 4 2 4 83,087,883,984,000 0.001334 0.005335
Three of a kind Yes 3 2 3 294,776,596,077,600 0.004732 0.014197
Two pair Yes 2 2 2 425,796,923,142,000 0.006836 0.013671
Jacks or better Yes 1 2 1 668,544,871,992,000 0.010733 0.010733
Royal flush Yes 800 1 400 381,311,985,000 0.000006 0.002449
Straight flush Yes 55 1 27.5 1,606,581,825,000 0.000026 0.000709
Four of a kind Yes 25 1 12.5 29,355,619,582,500 0.000471 0.005891
Full house Yes 9 1 4.5 142,885,934,392,500 0.002294 0.010322
Flush Yes 5 1 2.5 48,427,468,492,500 0.000777 0.001944
Straight Yes 4 1 2 51,929,927,490,000 0.000834 0.001667
Three of a kind Yes 3 1 1.5 184,235,372,548,500 0.002958 0.004436
Two pair Yes 2 1 1 266,123,076,963,750 0.004272 0.004272
Jacks or better Yes 1 1 0.5 417,840,544,995,000 0.006708 0.003354
Royal flush No 800 1 400 - 0.000000 0.000000
Straight flush No 55 1 27.5 - 0.000000 0.000000
Four of a kind No 25 1 12.5 - 0.000000 0.000000
Full house No 9 1 4.5 - 0.000000 0.000000
Flush No 5 1 2.5 484,274,684,925,000 0.007774 0.019436
Straight No 4 1 2 519,299,274,900,000 0.008337 0.016673
Three of a kind No 3 1 1.5 3,684,707,450,970,000 0.059153 0.088729
Two pair No 2 1 1 6,653,076,924,093,750 0.106806 0.106806
Jacks or better No 1 1 0.5 10,446,013,624,875,000 0.167696 0.083848
Loser No 0 1 0 34,790,044,215,112,500 0.558505 0.000000
Total 62,291,345,366,250,000 1.000000 0.987504

Analysis

This game was pretty easy to analyze. Here is how I did it.

  1. Determine the average multiplier, assuming the Double Up feature was won. It requires simple math to see the probability of a 1x multiplier is (1/5), 2x is (4/5)×(2/5), 4x is (4/5)×(3/5)×(3/5), 8x is (4/5)×(3/5)×(2/5)×(4/5), and 16x is (4/5)×(3/5)×(2/5)×(1/5). The following table shows the probability of each multiplier. The lower right cell shows the average multiplier earned is 3.8352.

    Multiplier Table

    Multiplier Combinations Probability Expected
    Multiplier
    1 125 0.2000 0.2000
    2 200 0.3200 0.6400
    4 180 0.2880 1.1520
    8 96 0.1536 1.2288
    16 24 0.0384 0.6144
    Total 625 1.0000 3.8352

  2. Determine the "adjusted pay" for each hand. This is how much the player can expect to win, on average, for each hand on the draw, relative to his total wager. This is defined as w*(p*3.8352 + (1-p)*1)/2 = w*(p*2.8352 + 1)/2, where w = base win for the hand and p=probability of bonus feature. The reason for dividing by 2 is the player must double his bet to enable the Double Up feature.

    For example, in 9-5 Jacks or Better the base win for a flush is 5, and the probability of the feature is 1/3. So the expected final win for a flush is 5×((1/3)×2.8352 + 1)/2 = 4.8627.

  3. Use my video poker return analyzer, putting the adjusted pays in the prize column. Note that the calculator doesn't accept decimals in that column. What I did was multiply the adjusted awards by 100 and rounded that product to the nearest integer.

  4. Use the resulting combinations to get the probability of each hand and create a return table.

If you encounter a pay table not on this page for this game you can use this method to find the return yourself. This method of calculating the adjusted win can also be used to create strategies for any game using my video poker strategy calculator.

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