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Ultimate 4 of a Kind Bonus Poker
Introduction
I encountered the Ultimate 4 of a Kind Bonus Poker variant at the Red Rock Casino in Las Vegas back in June 2008. This game is part of a recent trend of variations offering players the chance to win more for achieving four of a kinds, provided they place a sixth coin bet.
This section is dedicated solely to the single-hand format of the game. The rules regarding bonuses differ slightly in this version. multi-hand version .
Rules
When betting between 1 and 5 coins, the gameplay resembles regular video poker. However, placing a 6th coin allows the player to participate in a bonus round by obtaining any natural four of a kind during the draw.
In this bonus game, players are given the option to choose between 1 and 3 cards from a 53-card deck. Achieving four aces provides three selections, while four 2s through 4s grant two, and four 5s to Kings allow for one card pick. Additionally, if the player is dealt a four of a kind, they receive an extra card selection. The associated prizes from the bonus deck are outlined as follows.
Joker: 3996
Aces: 400
2's-4's: 300
5's-K's: 200
If the joker is unveiled, the player's total bonus winnings instantly surge to 3996 credits, concluding the bonus round.
Bonus Analysis
The table below illustrates the potential outcomes for each bonus selection, assuming the joker is not chosen. The average value of a non-joker pick is indicated at 238.46 credits in the bottom right cell.
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 predicted winnings from p bonus selections can be calculated with the formula (p/53) × 3996 + ((53-p)/53) × p × 238.46. The table that follows provides an overview of expected bonus winnings based on the 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 table below exhibits the return rates for Bonus Poker Deluxe. The 'Base Pay' column indicates the regular winnings per coin bet when playing five coins. The 'Bonus' column reflects the bonus amount divided by 5, to align with the Base Pay column. The return is determined by multiplying the total winnings, the probability, and 5/6, with the latter factor reflecting the player's requirement to bet six coins for bonus eligibility. The lower right cell conveys a return rate 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 This equates to a return of 95.36%, suggesting players should ideally bet the full six coins.
Double Bonus
The upcoming table highlights the returns for the 9-5 Double Bonus variant. The 'Base Pay' indicates the regular winnings per coin, based on a five-coin bet, while the 'Bonus' shows the bonus sum divided by 5 for consistency. The return calculation is the same as before, yielding a lower right cell 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 This corresponds to a return of 95.27%, reinforcing the recommendation for players to place the full six-coin bet.
Double Double Bonus
The next table illustrates the return for the 7-5 Double Double Bonus format. The 'Base Pay' column represents the standard winnings per coin bet for five coins. The 'Bonus' column lists bonus winnings adjusted for the same column consistency. The calculated return shows 98.68% in the lower right cell.
"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 |
Jacks or Better
The subsequent table reveals the returns for 7-5 Jacks or Better. The 'Base Pay' details the normal winnings associated with a five-coin bet, while the 'Bonus' illustrates adjusted bonus returns. The overall return, based on calculations described earlier, amounts to 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 This results in a return rate of 96.15%, which suggests that players should opt to place the maximum bet of six coins.
Bonus Poker
The forthcoming table presents winnings for the 10-8 Bonus Poker variant. As in previous tables, the 'Base Pay' shows standard payouts based on a five-coin wager, with the 'Bonus' displaying corresponding figures. The calculated return stands at 96.38%, as depicted in the final cell.
'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 |
Table of Returns
IGT, the manufacturer of this game, graciously provided me with comprehensive details regarding all game variations, payout structures, and returns. As typical, these returns are based on the premise of optimal gameplay strategies. The following table summarizes this data.
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% |