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Ultimate 4 of a Kind Bonus Poker
Introduction
Ultimate 4 of a Kind Bonus Poker is a video poker variant I noticed at the Red Rock casino in Las Vegas in June 2008. It is another in a rash of recent games that offers the player larger wins for four of a kinds for a sixth coin bet.
This page refers to the single-hand version of the game only. The bonus rules are a little different in the multi-hand version.
Rules
For 1 to 5 coins bet, the game plays like ordinary video poker. If the player bets a 6th coin, he will be eligible to play a bonus game if he gets any natural four of a kind on the draw.
In the bonus game, the player picks from 1 to 3 cards from a 53-card deck. Four aces will earn 3 picks, Four 2-4's will earn two picks, and four 5's to K's will earn one pick. If the player gets a four of a kind on the deal, then he will be awarded with an extra pick. The prizes associated with the 53-card bonus deck are as follows.
Joker: 3996
Aces: 400
2's-4's: 300
5's-K's: 200
When the joker is revealed, the player's total bonus win immediately jumps to 3996 credits and the bonus ends.
Bonus Analysis
The following table shows the possible outcomes of each bonus pick, assuming the player does not pick the joker. The lower right cell shows the average non-joker pick is worth 238.46 credits.
Bonus Probabilities — No Joker
| Card | Pays | Number | Probability | Return |
|---|---|---|---|---|
| Aces | 400 | 4 | 0.076923 | 30.769231 |
| 2 to 4 | 300 | 12 | 0.230769 | 69.230769 |
| 5 to K | 200 | 36 | 0.692308 | 138.461538 |
| Total | 52 | 1 | 238.461538 |
The expected win from p bonus picks is (p/53)×3996 + ((53-p)/53)×p×238.46. The next table shows this expected bonus win by number of picks.
Expected Bonus Win by Number of Picks
| Picks | Win |
|---|---|
| 4 | 1183.442671 |
| 3 | 901.079826 |
| 2 | 609.718433 |
| 1 | 309.358491 |
Bonus Poker Deluxe
The following table shows the wins return for Bonus Poker Deluxe. The "Base Pay" column shows the standard video poker win per coin bet, based on five coins bet. The "Bonus" column shows the bonus win, divided by 5, to be consistent with the Base Pay column. The return is the product of the total win, the probability, and 5/6. The reason for multiplying by 5/6 is because the player must bet a six coins to be eligible for the bonus. The lower right cell shows a return of 97.37%.
"6/5" Bonus Poker Deluxe
| Hand | Base Pay | Bonus | Total | Combinations | Probability | Return |
|---|---|---|---|---|---|---|
| Royal flush | 800 | 0 | 800 | 495429996 | 0.000025 | 0.01657 |
| Straight flush | 50 | 0 | 50 | 2054514540 | 0.000103 | 0.004295 |
| Four aces on deal | 80 | 236.69 | 316.69 | 4332670368 | 0.000018 | 0.004874 |
| Four 2-4 on deal | 80 | 180.22 | 260.22 | 9849862080 | 0.000055 | 0.012015 |
| Four 5-K on deal | 80 | 121.94 | 201.94 | 31215382332 | 0.000166 | 0.027973 |
| Four aces on draw | 80 | 180.22 | 260.22 | 165716748396 | 0.000217 | 0.047134 |
| Four 2-4 on draw | 80 | 121.94 | 201.94 | 201525295044 | 0.000494 | 0.083158 |
| Four 5-K on draw | 80 | 61.87 | 141.87 | 249481016712 | 0.001566 | 0.185142 |
| Full house | 6 | 0 | 6 | 165716748396 | 0.008314 | 0.041568 |
| Flush | 5 | 0 | 5 | 201525295044 | 0.01011 | 0.042125 |
| Straight | 4 | 0 | 4 | 249481016712 | 0.012516 | 0.041719 |
| Three of a kind | 3 | 0 | 3 | 1580289703032 | 0.079279 | 0.198198 |
| Two pair | 1 | 0 | 1 | 2199859576848 | 0.110361 | 0.091968 |
| Jacks or better | 1 | 0 | 1 | 4502373663204 | 0.225873 | 0.188227 |
| Nothing | 0 | 0 | 0 | 10981250764968 | 0.550902 | 0 |
| Total | 19933230517200 | 1 | 0.984965 |
The return for ordinary "6/5" Bonus Poker Deluxe is is 95.36%. So, the player should bet the full six coins.
Double Bonus
The following table shows the wins return for 9-5 Double Bonus. The "Base Pay" column shows the standard video poker win per coin bet, based on five coins bet. The "Bonus" column shows the bonus win, divided by 5, to be consistent with the Base Pay column. The return is the product of the total win, the probability, and 5/6. The reason for multiplying by 5/6 is because the player must bet a six coins to be eligible for the bonus. The lower right cell shows a return of 98.01%.
"9/5" Double Bonus
| Hand | Base Pay | Bonus | Total | Combinations | Probability | Return |
|---|---|---|---|---|---|---|
| Royal flush | 800 | 0 | 800 | 496337520 | 0.000025 | 0.0166 |
| Straight flush | 50 | 0 | 50 | 2005684116 | 0.000101 | 0.004193 |
| Four aces on deal | 160 | 236.69 | 396.69 | 4371289872 | 0.000018 | 0.006105 |
| Four 2-4 on deal | 80 | 180.22 | 260.22 | 9858654204 | 0.000055 | 0.012015 |
| Four 5-K on deal | 50 | 121.94 | 171.94 | 29300643588 | 0.000166 | 0.023817 |
| Four aces on draw | 160 | 180.22 | 340.22 | 211642918272 | 0.000219 | 0.062174 |
| Four 2-4 on draw | 80 | 121.94 | 201.94 | 204735812904 | 0.000495 | 0.083232 |
| Four 5-K on draw | 50 | 61.87 | 111.87 | 237125397372 | 0.00147 | 0.137037 |
| Full house | 9 | 0 | 9 | 211642918272 | 0.010618 | 0.079632 |
| Flush | 5 | 0 | 5 | 204735812904 | 0.010271 | 0.042796 |
| Straight | 4 | 0 | 4 | 237125397372 | 0.011896 | 0.039653 |
| Three of a kind | 3 | 0 | 3 | 1522028976792 | 0.076356 | 0.190891 |
| Two pair | 1 | 0 | 1 | 2478372668424 | 0.124334 | 0.103611 |
| Jacks or better | 1 | 0 | 1 | 4265356495356 | 0.213982 | 0.178318 |
| Nothing | 0 | 0 | 0 | 10963149749100 | 0.549994 | 0 |
| Total | 19933230517200 | 1 | 0.980074 |
The return for ordinary "9-5" Double Bonus is is 95.27%. So, the player should bet the full six coins.
Double Double Bonus
The following table shows the wins return for 7-5 Double Double Bonus. The "Base Pay" column shows the standard video poker win per coin bet, based on five coins bet. The "Bonus" column shows the bonus win, divided by 5, to be consistent with the Base Pay column. The return is the product of the total win, the probability, and 5/6. The reason for multiplying by 5/6 is because the player must bet a six coins to be eligible for the bonus. The lower right cell shows a return of 98.68%.
"7/5" Double Double Bonus
| Hand | Base Pay | Bonus | Total | Combinations | Probability | Return |
|---|---|---|---|---|---|---|
| Royal flush | 800 | 0 | 800 | 496286304 | 0.000025 | 0.016598 |
| Straight flush | 50 | 0 | 50 | 2011044216 | 0.000101 | 0.004204 |
| 4 aces + 2-4 on deal | 400 | 236.69 | 636.69 | 92036340 | 0.000005 | 0.00245 |
| 4 2-4 + A-4 on deal | 160 | 180.22 | 340.22 | 276109020 | 0.000014 | 0.003927 |
| 4 aces + 5-K on deal | 160 | 236.69 | 396.69 | 276109020 | 0.000014 | 0.004579 |
| 4 2-4 + 5-K on deal | 80 | 180.22 | 260.22 | 828327060 | 0.000042 | 0.009011 |
| 4 5-K on deal | 50 | 121.94 | 171.94 | 3313308240 | 0.000166 | 0.023817 |
| 4 aces + 2-4 on draw | 400 | 180.22 | 580.22 | 1148214852 | 0.000058 | 0.027852 |
| 4 2-4 + A-4 on draw | 160 | 121.94 | 281.94 | 2690934876 | 0.000135 | 0.031718 |
| 4 aces + 5-K on draw | 160 | 180.22 | 340.22 | 3223235496 | 0.000162 | 0.045845 |
| 4 2-4 + 5-K on draw | 80 | 121.94 | 201.94 | 7167109416 | 0.00036 | 0.060508 |
| 4 5-K on draw | 50 | 61.87 | 111.87 | 31153037664 | 0.001563 | 0.145701 |
| Full house | 7 | 0 | 7 | 165742198992 | 0.008315 | 0.048503 |
| Flush | 5 | 0 | 5 | 204735672540 | 0.010271 | 0.042796 |
| Straight | 4 | 0 | 4 | 239002991496 | 0.01199 | 0.039967 |
| Three of a kind | 3 | 0 | 3 | 1580975570820 | 0.079314 | 0.198284 |
| Two pair | 1 | 0 | 1 | 2202932423628 | 0.110516 | 0.092096 |
| Jacks or better | 1 | 0 | 1 | 4520003893488 | 0.226757 | 0.188964 |
| Nothing | 0 | 0 | 0 | 10967162013732 | 0.550195 | 0 |
| Total | 0 | 0 | 19933230517200 | 1 | 0.986821 |
The return for ordinary "7/5" Double Double Bonus is is 95.71%. So, the player should bet the full six coins.
Jacks or Better
The following table shows the wins return for 7-5 Jacks or Better. The "Base Pay" column shows the standard video poker win per coin bet, based on five coins bet. The "Bonus" column shows the bonus win, divided by 5, to be consistent with the Base Pay column. The return is the product of the total win, the probability, and 5/6. The reason for multiplying by 5/6 is because the player must bet a six coins to be eligible for the bonus. The lower right cell shows a return of 98.28%.
"7/5" Jacks or Better
| Hand | Base Pay | Bonus | Total | Combinations | Probability | Return |
|---|---|---|---|---|---|---|
| Royal flush | 800 | 0 | 800 | 497941608 | 0.000025 | 0.016654 |
| Straight flush | 50 | 0 | 50 | 1984110324 | 0.0001 | 0.004147 |
| Four aces on deal | 25 | 236.69 | 261.69 | 3930382320 | 0.000018 | 0.004028 |
| Four 2-4 on deal | 25 | 180.22 | 205.22 | 9859193424 | 0.000055 | 0.009475 |
| Four 5-K on deal | 25 | 121.94 | 146.94 | 29423360772 | 0.000166 | 0.020354 |
| Four aces on draw | 25 | 180.22 | 205.22 | 223027715844 | 0.000197 | 0.03372 |
| Four 2-4 on draw | 25 | 121.94 | 146.94 | 199818112788 | 0.000495 | 0.060567 |
| Four 5-K on draw | 25 | 61.87 | 86.87 | 217867866324 | 0.001476 | 0.106859 |
| Full house | 7 | 0 | 7 | 223027715844 | 0.011189 | 0.065268 |
| Flush | 5 | 0 | 5 | 199818112788 | 0.010024 | 0.041768 |
| Straight | 4 | 0 | 4 | 217867866324 | 0.01093 | 0.036433 |
| Three of a kind | 3 | 0 | 3 | 1512158573688 | 0.075861 | 0.189653 |
| Two pair | 2 | 0 | 2 | 2602718111808 | 0.130572 | 0.21762 |
| Jacks or better | 1 | 0 | 1 | 4216077070884 | 0.21151 | 0.176258 |
| Nothing | 0 | 0 | 0 | 10911082187736 | 0.547382 | 0 |
| Total | 19933230517200 | 1 | 0.982804 |
The return for ordinary "7/5" Jacks or Better is is 96.15%. So, the player should bet the full six coins.
Bonus Poker
The following table shows the wins return for 10-8 Bonus Poker. The "Base Pay" column shows the standard video poker win per coin bet, based on five coins bet. The "Bonus" column shows the bonus win, divided by 5, to be consistent with the Base Pay column. The return is the product of the total win, the probability, and 5/6. The reason for multiplying by 5/6 is because the player must bet a six coins to be eligible for the bonus. The lower right cell shows a return of 96.38%.
"10/8" Bonus Poker
| Hand | Base Pay | Bonus | Total | Combinations | Probability | Return |
|---|---|---|---|---|---|---|
| Royal flush | 800 | 0 | 800 | 397331376 | 0.00002 | 0.013289 |
| Straight flush | 50 | 0 | 50 | 2232922548 | 0.000112 | 0.004668 |
| Four aces on deal | 80 | 236.69 | 316.69 | 4116184116 | 0.000018 | 0.004874 |
| Four 2-4 on deal | 40 | 180.22 | 220.22 | 9677409204 | 0.000055 | 0.010168 |
| Four 5-K on deal | 25 | 121.94 | 146.94 | 28557904932 | 0.000166 | 0.020354 |
| Four aces on draw | 80 | 180.22 | 260.22 | 205672012524 | 0.000206 | 0.044779 |
| Four 2-4 on draw | 40 | 121.94 | 161.94 | 328137420456 | 0.000485 | 0.065519 |
| Four 5-K on draw | 25 | 61.87 | 86.87 | 280156665180 | 0.001433 | 0.103716 |
| Full house | 10 | 0 | 10 | 205672012524 | 0.010318 | 0.085984 |
| Flush | 8 | 0 | 8 | 328137420456 | 0.016462 | 0.109746 |
| Straight | 5 | 0 | 5 | 280156665180 | 0.014055 | 0.058561 |
| Three of a kind | 3 | 0 | 3 | 1460493243936 | 0.073269 | 0.183173 |
| Two pair | 1 | 0 | 1 | 2371585371048 | 0.118976 | 0.099147 |
| Jacks or better | 1 | 0 | 1 | 3822600300984 | 0.19177 | 0.159809 |
| Nothing | 0 | 0 | 0 | 11414817861216 | 0.572653 | 0 |
| Total | 19933230517200 | 1 | 0.963785 |
The return for ordinary "10/8" Bonus Poker is is 94.18%. So, the player should bet the full six coins.
Table of Returns
IGT, the game maker, was kind enough to provide me the list of all games, pay tables, and returns this game is available in. As usual, the return assumes optimal strategy. The following table summarizes this information.
Summary of Games
| Game | Pay Table | Return |
|---|---|---|
| Bonus Poker | 7-5-4-3-2 | 99.96% |
| Bonus Poker | 6-5-4-3-2 | 99.09% |
| Bonus Poker | 10-8-5-3-1 | 96.38% |
| Bonus Poker Deluxe | 8-5 | 99.88% |
| Bonus Poker Deluxe | 7-5 | 99.19% |
| Bonus Poker Deluxe | 6-5 | 98.50% |
| Super Deuces Wild | 25-16-10-4-4-3 | 99.73% |
| Super Deuces Wild | 25-15-9-4-4-3 | 99.10% |
| Super Deuces Wild | 20-12-10-4-4-3 | 97.93% |
| Super Deuces Wild | 25-16-13-4-3-2 | 97.80% |
| Super Deuces Wild | 20-12-9-4-4-3 | 97.54% |
| Super Deuces Wild | 20-10-8-4-4-3 | 96.66% |
| Super Deuces Wild | 25-15-10-4-3-2 | 96.30% |
| Deuces Wild Bonus | 9-4-4-3 | 99.65% |
| Deuces Wild Bonus | 13-4-3-3 | 99.42% |
| Deuces Wild Bonus | 10-4-3-3 | 98.30% |
| Deuces Wild Bonus | 12-4-3-2 | 97.50% |
| Deuces Wild Bonus | 10-4-3-2 | 96.79% |
| Double Bonus | 9-6 | 98.89% |
| Double Bonus | 9-5 | 98.01% |
| Double Bonus | 8-5 | 97.14% |
| Double Bonus | 7-5 | 96.45% |
| Double Double Bonus | 9-5 | 100.24% |
| Double Double Bonus | 8-5 | 99.38% |
| Double Double Bonus | 7-5 | 98.68% |
| Double Double Bonus | 6-5 | 97.99% |
| Jacks or Better | 9-5 | 100.15% |
| Jacks or Better | 8-6 | 100.09% |
| Jacks or Better | 8-5 | 99.21% |
| Jacks or Better | 7-5 | 98.28% |
| Jacks or Better | 6-5 | 97.41% |
| Joker Poker | 940-50-18-7-5 | 99.32% |
| Joker Poker | 940-50-17-7-5 | 98.59% |
| Joker Poker | 940-50-15-7-5 | 97.15% |
| Joker Poker | 800-50-15-7-5 | 96.89% |
| Joker Poker | 800-40-20-5-4 | 96.57% |