Lucky Red Casino

Last Updated: November 05, 2006

Bonus Video Poker

Wizard Endorsed Internet Casinos

Bonus Video Poker is a video poker game found at Internet casinos using Cryptologic software. Unlike conventional video poker discarded cards are shuffled back into the deck. In addition if the player receives any card on the draw that he already discarded he will be awarded a bonus, which I call the "redraw bonus."

Games currently available are All American, Deuces Wild, Double Bonus, Jacks or Better, Joker Poker, Tens or Better, and Super Jackpot, which is a progressive Jacks or Better game. The player may play 3, 5, or 10 lines.

Not factored into this analysis is the fact that Cryptologic casinos offering 0.1% cash back in video poker.

The following table summarizes the return of the six games available, in order of highest to lowest return.

Bonus Video Poker Summary

Game Line Pays Redraw Bonus Total
Deuces Wild 0.942076 0.046275 0.988352
Joker Poker 0.945220 0.040411 0.985631
Double Bonus 0.951743 0.033694 0.985437
Tens or Better 0.949636 0.035232 0.984868
Jacks or Better 0.952642 0.032163 0.984805
All American 0.946660 0.035217 0.981877

The rest of this analysis is categorized by game.

Jacks or Better

The following table shows the return before considering the redraw bonus.

Jacks or Better Line Pays

Hand Pays Combinations Probability Return
Royal Flush 800 731391972 0.000022 0.017325
Straight Flush 40 3414244916 0.000101 0.004044
Four of a kind 20 74118447936 0.002195 0.043892
Full House 9 380509968384 0.011267 0.1014
Flush 6 366835148092 0.010862 0.065171
Straight 4 364150308936 0.010782 0.043129
Three of a kind 3 2422345886064 0.071724 0.215173
Two pair 2 4382137006416 0.129753 0.259506
Jacks or Better 1 6855990656340 0.203002 0.203002
Nonpaying hand 0 18922732348944 0.560292 0
Total 33772965408000 1 0.952642

The redraw bonus is 16%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 16% of the bet on that hand. The following table shows how much the bonus contributed to the total return. The pays column shows the average win, which is 0.16*n2/(47+n), where n is the number of discards.

Jacks or Better Redraw Bonus

Discards Pays Combinations Probability Return
5 0.076923 91128 0.035063 0.002697
4 0.050196 681288 0.262139 0.013158
3 0.0288 1374924 0.529029 0.015236
2 0.013061 137880 0.053052 0.000693
1 0.003333 294876 0.113459 0.000378
0 0 18864 0.007258 0
Total 2598960 1 0.032163

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game.

Jacks or Better Total Return

Type of Win Return
Line pays 0.952642
Bonus 0.032163
Total 0.984805

The next table shows the strategy in the Jacks or Better game. To use the strategy make the play with the highest expected value. For example if you had T♥ J♥ K♥ 4♥ 4♣ there are three viable plays as follows.

  • Keep T♥ J♥ K♥: The table shows three to a royal, king high, is worth 1.33194.
  • Keep T♥ J♥ K♥ 4♥: The table shows four to a flush with two high cards is worth 1.25333.
  • Keep 4♥ 4♣: The table shows a low pair is worth 0.81247.

So keeping the three to a royal is the best play.

Jacks or Better Strategy Table

Hand on Deal Expected Value
pat royal flush 800
pat straight flush 40
4 of a kind (discard 5th card) 20.0033
suited TJQK 19.0658
suited JQKA 18.17
suited TJQA, TJKA, TQKA 18.1075
pat full house 9
pat flush 6
3 of a kind 4.07429
pat straight 4
suited 9TJQ 3.17
suited 89TJ 3.1075
4 to outside straight flush, no high card 3.045
2 pairs 2.58667
suited 9JQK 2.27417
4 to inside straight flush, 2 high cards 2.21167
4 to inside straight flush, 1 high card 2.14917
4 to inside straight flush, no high card 2.08667
high pair (JJ-AA) 1.53084
suited JQK 1.42888
suited TJQ 1.41187
suited JQA, JKA, QKA 1.34895
suited TJK, TQK 1.33194
4 to a flush, 2 high cards 1.25333
suited TJA, TQA, TKA 1.25201
4 to a flush, 1 high card 1.19083
4 to a flush, no high card 1.12833
non-suited TJQK 0.8575
low pair (22-TT) 0.81247
non-suited 9TJQ 0.795
non-suited 89TJ 0.7325
suited 9JQ 0.68568
4 to an outside straight, no high card 0.67
suited 9TJ 0.66867
suited 9JK, 9QK, 8JQ 0.60574
suited JQ 0.594
suited 9TQ, 8TJ, 89J 0.58874
non-suited JQKA 0.58666
suited JK, QK 0.57941
3 consecutive suited cards except 234, no high card 0.57173
suited JA, QA, KA 0.56482
4 to an inside straight, 3 high cards 0.52416
3 to a straight flush, 1 high card, either spread 5 or any spread and containing A 0.50881
non-suited JQK 0.502
non-suited JQ 0.50012
3 to a straight flush, spread 4 or 234 0.4918
J 0.49063
non-suited QK 0.48706
Q 0.48641
K or A 0.4822
garbage, discard all 0.41245

Double Bonus

The following table shows the return before considering the redraw bonus.

Double Bonus Line Pays

Hand Pays Combinations Probability Return
Royal Flush 800 688175088 0.00002 0.016301
Straight Flush 50 3540194984 0.000105 0.005241
Four A 160 7086630444 0.00021 0.033573
Four 2-4 80 16459993008 0.000487 0.03899
Four 5-K 50 50547750564 0.001497 0.074835
Full House 9 354927965184 0.010509 0.094583
Flush 7 382557060388 0.011327 0.079291
Straight 5 497968441080 0.014745 0.073723
Three of a kind 3 2402407054944 0.071134 0.213402
Two pair 1 4097487996576 0.121324 0.121324
Jacks or Better 1 6770783660880 0.200479 0.200479
Nonpaying hand 0 19188510484860 0.568162 0
Total 33772965408000 1 0.951743

The redraw bonus is 18%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 18% of the bet on that hand. The following table shows how much the bonus contributed to the total return. The pays column shows the average win, which is 0.18*n2/(47+n), where n is the number of discards.

Double Bonus Redraw Bonus

Discards Pays Combinations Probability Return
5 0.086538 52812 0.02032 0.001758
4 0.056471 631716 0.243065 0.013726
3 0.0324 1344864 0.517462 0.016766
2 0.014694 154128 0.059304 0.000871
1 0.00375 396864 0.152701 0.000573
0 0 18576 0.007147 0
Total 2598960 1 0.033694

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game.

Double Bonus Total Return

Type of Win Return
Line pays 0.951743
Bonus 0.033694
Total 0.985437

Double Bonus Strategy Table

Hand on Deal Expected Value
pat royal flush 800
four A (discard 5th card) 160.004
four 2-4 (discard 5th card) 80.0037
four 5-K (discard 5th card) 50.0037
pat straight flush 50
suited TJQK 19.5454
suited JQKA 18.3996
suited TJQA, TJKA, TQKA 18.3371
three A 9.7902
pat full house 9
pat flush 7
three 2-4 6.5249
three 5-K 5.30041
pat straight 5
suited 9TJQ 3.85792
suited 89TJ 3.79542
4 to outside straight flush, no high cards 3.73292
suited 9JQK 2.71208
4 to inside straight flush, 2 high cards 2.64958
4 to inside straight flush, 1 high card 2.58708
4 to inside straight flush, no high cards 2.52458
pair of A 1.71567
2 pairs 1.67042
4 to a flush, 3 high cards 1.50375
suited TJQ 1.48153
suited JQK 1.47813
high pair (JJ-KK) 1.44628
4 to a flush, 2 high cards 1.44125
suited TJK, TQK 1.38119
4 to a flush, 1 high cards 1.37875
suited JQA, JKA, QKA 1.37779
4 to a flush, no high card 1.31625
suited TJA, TQA, TKA 1.28085
non-suited TJQK 1.02458
non-suited 9TJQ 0.962083
non-suited 89TJ 0.899583
4 to an outside straight, no high card 0.837083
pair 22-44 0.80138
suited 9TJ 0.746837
suited 9JQ 0.743435
pair 55-TT 0.72791
non-suited JQKA 0.670417
3 consecutive suited cards excluding 234, no high cards 0.649898
suited 9TQ, 8TJ, 89J 0.646497
suited 9JK, 9QK, 8JQ 0.643095
4 to an inside straight, 3 high cards 0.607917
suited JQ 0.579186
suited JK, QK 0.56092
3 to a straight flush, spread 4 or 234 0.549558
suited JA, QA, KA 0.548267
3 to a straight flush, 1 high card, either spread 5 or any spread and containing A 0.546156
4 to an inside straight, 2 high cards 0.545417
non-suited JQK 0.507891
4 to an inside straight, 1 high card 0.482917
non-suited TJQ 0.47898
non-suited JQ 0.476176
Suited TJ 0.475002
A 0.473681
J 0.463541
non-suited QK 0.459849
Q 0.458267
K 0.452993
3 to a straight flush, spread 5, no high card 0.449218
4 to an inside straight, no high card 0.420417

Tens or Better

The following table shows the return before considering the redraw bonus.

Tens or Better Line Pays

Hand Pays Combinations Probability Return
Royal Flush 800 801642672 0.000024 0.018989
Straight Flush 50 3015571940 0.000089 0.004464
Four of a kind 20 74177415936 0.002196 0.043927
Full House 6 380940153984 0.011279 0.067677
Flush 5 347882698108 0.010301 0.051503
Straight 4 384616044876 0.011388 0.045553
Three of a kind 3 2425921593264 0.07183 0.215491
Two pair 2 4388972240016 0.129955 0.25991
Tens or better 1 8177159043000 0.242121 0.242121
Nonpaying hand 0 17589479004204 0.520815 0
Total 33772965408000 1 0.949636

The redraw bonus in Tens or Better is 18%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 18% of the bet on that hand. The following table shows how much the bonus contributed to the total return. The pays column shows the average win, which is 0.18*n2/(47+n), where n is the number of discards.

Tens or Better Redraw Bonus

Discards Pays Combinations Probability Return
5 0.086538 35592 0.013695 0.001185
4 0.056471 682896 0.262757 0.014838
3 0.0324 1458792 0.561298 0.018186
2 0.014694 104760 0.040308 0.000592
1 0.00375 298056 0.114683 0.00043
0 0 18864 0.007258 0
Total 2598960 1 0.035232

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game.

Tens or Better Total Return

Type of Win Return
Line pays 0.949636
Bonus 0.035232
Total 0.984868

Tens or Better Strategy Table

Hand on Deal Expected Value
pat royal flush 800
pat straight flush 50
4 of a kind (discard 5th card) 20.0037
suited TJQK 19.1912
suited JQKA, TJQA, TJKA, TQKA 18.0037
pat full house 6
pat flush 5
pat straight 4
3 of a kind 3.89224
suited 9TJQ 3.50375
suited 89TJ 3.44125
suited 789T 3.37875
4 to outside straight flush, no high card 3.31625
2 pairs 2.33708
4 to inside straight flush, 3 high cards 2.31625
4 to inside straight flush, 2 high card 2.25375
4 to inside straight flush, 1 high card 2.19125
4 to inside straight flush, no high card 2.12875
high pair (TT-AA) 1.50505
suited TJQ 1.49684
suited JQK, TJK, TQK 1.40755
3 to a royal flush including A 1.31827
4 to a flush, 2 high cards 1.06625
4 to a flush, 1 high card 1.00375
4 to a flush, no high card 0.94125
non-suited TJQK 0.94125
non-suited 9TJQ 0.857917
non-suited 89TJ 0.795417
low pair (22-99) 0.786686
suited 9TJ 0.762143
non-suited 789T 0.732917
suited 9JQ, 9TQ, 8TJ 0.672857
4 to an outside straight, no high card 0.670417
suited 89T 0.665204
suited TJ 0.615002
suited JQ, TQ 0.599849
non-suited JQKA, TQKA, TJKA, TJQA 0.587083
suited TK, JK, QK 0.584696
suited 89J, 79T, 78T 0.575918
suited TA, JA, QA, KA 0.569543
3 consecutive suited cards, no high card, excluding 234 0.568265
non-suited TJQ 0.563163
non-suited TJ 0.526278
4 to an inside straight, 3 high cards 0.524583
T 0.516134
non-suited JQ 0.513216
J 0.511873
Q 0.507611
K or A 0.503349
3 to a straight flush, spread 4 or 234 0.47898
garbage, discard all 0.448423
High card means 10 or higher

For Tens or Better a "high card" is 10 or higher.

All American

The following table shows the return before considering the redraw bonus.

All American Line Pays

Hand Pays Combinations Probability Return
Royal Flush 800 718073112 0.000021 0.017009
Straight Flush 90 4092629516 0.000121 0.010906
Four of a kind 35 71009859024 0.002103 0.07359
Full House 8 365376291696 0.010819 0.086549
Flush 8 494311428412 0.014636 0.11709
Straight 8 599248763964 0.017743 0.141948
Three of a kind 3 2255801905656 0.066793 0.200379
Two pair 1 4085098962984 0.120958 0.120958
Jacks or Better 1 6019379397660 0.178231 0.178231
Nonpaying hand 0 19877928095976 0.588575 0
Total 33772965408000 1 0.94666

The redraw bonus in All American is 22%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 22% of the bet on that hand. The following table shows how much the bonus contributed to the total return. The pays column shows the average win, which is 0.22*n2/(47+n), where n is the number of discards.

All American Redraw Bonus

Discards Pays Combinations Probability Return
5 0.105769 52813 0.020321 0.002149
4 0.06902 400369 0.154049 0.010632
3 0.0396 1240117 0.477158 0.018895
2 0.017959 383965 0.147738 0.002653
1 0.004583 502837 0.193476 0.000887
0 0 18865 0.007259 0
Total 2598966 1 0.035217

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game.

All American Total Return

Type of Win Return
Line pays 0.94666
Bonus 0.035217
Total 0.981877

All American Strategy Table

Hand on Deal Expected Value
pat royal flush 800
pat straight flush 90
4 of a kind (discard 5th card) 35.0046
suited TJQK 20.9004
suited JQKA 18.7546
suited TJQA, TJKA, TQKA 18.6921
pat full house, flush or straight 8
suited 9TJQ 6.04625
suited 89TJ 5.98375
4 to outside straight flush, no high card 5.92125
3 of a kind 4.6302
suited 9JQK 3.90042
4 to inside straight flush, 2 high cards 3.83792
4 to inside straight flush, 1 high card 3.77542
4 to inside straight flush, no high card 3.71292
suited TJQ 1.70333
4 to a flush, 3 high cards 1.69208
4 to a flush, 2 high cards 1.62958
suited JQK 1.6285
2 pairs 1.58792
4 to a flush, 1 high card 1.56708
suited TJK, TQK 1.53156
non-suited TJQK 1.52542
4 to a flush, no high card 1.50458
non-suited 9TJQ 1.46292
suited JQA, JKA, QKA 1.45673
high pair (JJ-AA) 1.40695
non-suited 89TJ 1.40042
suited TJA, TQA, TKA 1.3598
4 to an outside straight, no high card 1.33792
suited 9TJ 1.00265
suited 9JQ 0.927823
non-suited JQKA 0.92125
3 consecutive suited cards excluding 234, no high cards 0.905714
4 to an inside straight, 3 high cards 0.85875
suited 9TQ, 8TJ, 89J 0.830884
4 to an inside straight, 2 high cards 0.79625
suited 9JK, 9QK, 8JQ 0.756054
3 to a straight flush, spread 4 or 234 0.733946
4 to an inside straight, 1 high card 0.73375
low pair (22-TT) 0.68858
4 to an inside straight, no high card 0.67125
3 to a straight flush, 1 high card, either spread 5 or any spread and containing A 0.659116
suited JQ 0.625212
non-suited TJQ 0.604694
suited JK, QK 0.595314
non-suited JQK 0.592789
3 to a flush, 2 high cards 0.584286
suited JA, QA, KA 0.565416
3 to a straight flush, spread 5, no high card 0.562177
suited TJ 0.532661
non-suited JQ 0.510314
non-suited 9TJ 0.507755
suited TQ 0.502763
non-suited TJK, TQK 0.49585
3 to a flush, 1 high card 0.487347
J 0.484938
non-suited QK 0.484192
Q 0.476447
suited TK 0.472865
K or A 0.467955
garbage, discard all 0.416241

Deuces Wild

The following table shows the return before considering the redraw bonus.

Deuces Wild Line Pays

Hand Pays Combinations Probability Return
Natural royal flush 800 669855940 0.00002 0.015867
Four deuces 200 5907527808 0.000175 0.034984
Wild royal flush 20 53637468560 0.001588 0.031764
Five of a kind 15 100903151232 0.002988 0.044815
Straight flush 9 151130978388 0.004475 0.040274
Four of a kind 4 2039227014032 0.06038 0.241522
Full house 4 887510010816 0.026279 0.105115
Flush 3 659309178424 0.019522 0.058565
Straight 2 1620038824248 0.047969 0.095937
Three of a kind 1 9227886409560 0.273233 0.273233
Nothing 0 19026744988992 0.563372 0
Total 33772965408000 1 0.942076

The redraw bonus in Deuces Wild is 19.5%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 19.5% of the bet on that hand. The following table shows how much the bonus contributed to the total return. The pays column shows the average win, which is 0.195*n2/(47+n), where n is the number of discards.

Deuces Wild Redraw Bonus

Discards Pays Combinations Probability Return
5 0.09375 655512 0.252221 0.023646
4 0.061176 373248 0.143614 0.008786
3 0.0351 789840 0.303906 0.010667
2 0.015918 451244 0.173625 0.002764
1 0.004063 264184 0.10165 0.000413
0 0 64932 0.024984 0
Total 2598960 1 0.046275

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game.

Deuces Wild Total Return

Type of Win Return
Line pays 0.942076
Bonus 0.046275
Total 0.988352

I'm sorry but I do not have a strategy table for deuces wild.

Joker Poker

The following table shows the return before considering the redraw bonus.

Joker Poker Line Pays

Hand Pays Combinations Probability Return
Natural royal flush 800 793158136 0.000019 0.01541
Five of a kind 200 3537943477 0.000086 0.017185
Wild royal flush 100 3646444268 0.000089 0.008856
Straight flush 50 21249566724 0.000516 0.025804
Four of a kind 18 332346489984 0.008071 0.145286
Full house 7 635253288552 0.015428 0.107996
Flush 5 594398884132 0.014436 0.072179
Straight 3 652570799016 0.015849 0.047546
Three of a kind 2 5389047502236 0.13088 0.26176
Two pair 1 4620724167456 0.11222 0.11222
Kings or better 1 5752097120292 0.139697 0.139697
Nothing 0 23169794631852 0.562709 0
Total 41175459996125 1 0.953939

The redraw bonus in Joker Poker is 18.5%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 18.5% of the bet on that hand. The following table shows how much the bonus contributed to the total return. The pays column shows the average win, which is 0.185*n2/(48+n), where n is the number of discards.

Joker Poker Redraw Bonus

Discards Pays Combinations Probability Return
5 0.087264 360336 0.125566 0.010957
4 0.056923 730944 0.254712 0.014499
3 0.032647 1141116 0.397645 0.012982
2 0.0148 306036 0.106644 0.001578
1 0.003776 299336 0.10431 0.000394
0 0 31917 0.011122 0
Total 2869685 1 0.040411

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game.

Joker Poker Total Return

Type of Win Return
Line pays 0.953939
Bonus 0.040411
Total 0.994349

Super Jackpot

Super Jackpot follows a 8/5 Jacks or Better pay table, except the royal flush win is progressive. The breakeven point is 1464 times the maximum bet, or 7320 coins. This would be $7320 for the $1 game and $1830 for the quarter game. The following return table is based on a meter at the breakeven point.

Super Jackpot Return Table

Hand Pays Combinations Probability Return
Royal Flush 1464 925757052 0.000027 0.04013
Straight Flush 50 3053170280 0.00009 0.00452
Four of a kind 25 73936828368 0.002189 0.054731
Full House 8 380066882832 0.011254 0.090029
Flush 5 356837431168 0.010566 0.052829
Straight 4 355884690588 0.010538 0.04215
Three of a kind 3 2417849218512 0.071591 0.214774
Two pair 2 4380633895248 0.129708 0.259417
Jacks or better 1 6764797393140 0.200302 0.200302
Nonpaying hand 0 19038980140812 0.563734 0
Total 33772965408000 1 0.958881

The redraw bonus in Super Jackpot is 20.0%. In other words for every card the player gets on the draw that he already discarded he will get a bonus of 20.0% of the bet on that hand. The following table shows how much the bonus contributes to the total return, assuming a meter of 7320 coins. The pays column shows the average win, which is 0.2*n2/(47+n), where n is the number of discards.

Super Jackpot Redraw Bonus

Discards Pays Combinations Probability Return
5 0.096154 91128 0.035063 0.003371
4 0.062745 741060 0.285137 0.017891
3 0.036 1350408 0.519596 0.018705
2 0.016327 110328 0.042451 0.000693
1 0.004167 287172 0.110495 0.00046
0 0 18864 0.007258 0
Total 2598960 1 0.041121

The next table shows how much the line pays and bonus contribute to the return, as well as the total return of the game, again assuming a meter of 7320 coins.

Joker Poker Total Return 7320 Coin Jackpot

Type of Win Return
Line pays 0.958881
Bonus 0.041121
Total 1.000003

Assuming no strategy changes for every additional $100 in the meter the return will go by 0.219% for quarters and 0.055% for dollars.

Super Jackpot Strategy Table 7320 Coin Jackpot

Hand on Deal Expected Value
pat royal flush 1463.91
pat straight flush 50
suited TJQK 32.9606
suited JQKA 31.8356
suited TJQA, TJKA, TQKA 31.7731
4 of a kind (discard 5th card) 25.0042
pat full house 8
pat flush 5
3 of a kind 4.22041
pat straight 4
suited 9TJQ 3.44167
suited 89TJ 3.37917
4 to outside straight flush, no high cards 3.31667
2 pairs 2.50417
suited 9JQK 2.31667
4 to inside straight flush, 2 high cards 2.25417
4 to inside straight flush, 1 high card 2.19167
4 to inside straight flush, no high cards 2.12917
suited JQK 1.96863
suited TJQ 1.96098
suited JQA, JKA, QKA 1.87934
suited TJK, TQK 1.87169
suited TJA, TQA, TKA 1.7824
high pair (JJ-AA) 1.54049
4 to a flush, 2 high cards 1.06667
4 to a flush, 1 high card 1.00417
4 to a flush, no high card 0.941667
non-suited TJQK 0.858333
low pair (22-TT) 0.822122
non-suited 9TJQ 0.795833
non-suited 89TJ 0.733333
4 to an outside straight, no high card 0.670833
suited 9JQ 0.669388
suited 9TJ 0.661735
suited JQ 0.627424
suited JK, QK 0.612271
suited JA, QA, KA 0.597118
non-suited JQKA 0.5875
suited 9TQ, 8TJ, 89J 0.572449
3 consecutive suited cards, no high cards, excluding 234 0.564796
4 to an inside straight, 3 high cards 0.525
suited TJ 0.520128
non-suited JQ 0.506918
suited TQ 0.504975
J 0.503757
Q 0.499495
K or A 0.495234
3 to a straight flush, spread 4 or 234 0.47551
garbage, discard all 0.430637

Acknowledgments

I would like to express my deep thanks to the great yet anonymous gaming mathematician G.M. for his contributions to this page. GM provided both the strategy tables as well as confirmed my results for the return tables.

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