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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

The return for ordinary '7/5' Double Double Bonus This indicates a return of 95.71%, further supporting the advice for players to make the complete six-coin wager.

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

The return for ordinary \"10/8\" Bonus Poker This translates to a 94.18% return, underscoring the recommendation for players to place a full six-coin bet.

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%

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Strategies

Full-Pay Jacks or Better:

Full-Pay Deuces Wild:

Quick Quads:

Other Strategies: