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Bonus Video Poker
Introduction
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.