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# Lucky Stud Draw Poker

## Introduction

Lucky Stud Draw Poker is a video poker variant where the player plays one draw hand and five stud hands. If any stud hand wins, and hands underneath it on the screen earn a multiplier. The draw hand is on the bottom so it has a maximum multiplier of 5x.

The player has no control over the stud hands and they are dealt from separate decks, so the strategy is exactly the same as conventional video poker for the given draw poker game and pay table. I saw the game at the Palace Station in Las Vegas on May 31, 2017. It is located near the Irish pub.

## Rules

- The player must be in increments of ten coins, which are split between five poker hands. Wins for each hand are based on one coin.
- The five poker hands are shown in a five rows, with the draw poker hand at the bottom.
- After making a bet, the player will be given five cards to the draw poker hand and asked to hold the ones he wants, discarding the rest, as in conventional video poker.
- After pressing the "draw" button, the game will first deal four hands of stud poker above the draw hand. Each stud will be dealt from a separate 52-card deck.
- Starting with the top hand, each stud hand will be scored against the stud poker pay table. Each of these hands shall start with a multiplier of 1x
- If a stud poker hand pays anything, every multiplier below that hand will be incremented by one.
- Finally, the draw poker hand will get its replacement card and scored.

If that wasn't clear, here are links to the three rule screens: screen 1, screen 2, screen 3.

Following is an example of a set of pay tables. These were for 7-5 Bonus Poker. Wins are per coin bet (not counting the extra coin required to pay for the multipliers) based on a maximum-coin bet.

### 7-5 Bonus Poker Pay Table

Event | Stud Hand Pays | Draw Hand Pays |
---|---|---|

Royal flush | 5000 | 800 |

Straight flush | 1000 | 50 |

4 aces | 400 | 80 |

4 2-4 | 250 | 40 |

4 5-K | 200 | 25 |

Full house | 34 | 7 |

Flush | 22 | 5 |

Straight | 15 | 4 |

3 of a kind | 9 | 3 |

Two pair | 3 | 2 |

Pair: J-A | 1 | 1 |

Pair: 2-10 | 1 | 0 |

## Example

In the hand above I bet 50 credits. 25 of them were a fee to pay for the multiplier feature, which left a bet of five for each hand. Here is how they were scored:

- Level 1: I got a pair in the top hand which pays 1x my bet. The multiplier is always 1x for the top hand so that paid 5×1×1 = 5 credits. Every subsequent multiplier was incremented by one, to a total of two, because I had a paying hand.
- Level 2: I got a two pair in the second hand which pays 3x my bet. The multiplier was at 2x so I was paid 5×2×3 = 30 credits. Every subsequent multiplier was incremented by one, to a total of three, because I had a paying hand.
- Level 3: I got a pair in the third hand which pays 1x my bet. The multiplier was at 3x so I was paid 5×3×1 = 15 credits. Every subsequent multiplier was incremented by one, to a total of four, because I had a paying hand.
- Level 4: I got trash so won nothing. The multiplier on the level 5 hand remained at 4x because I didn't get a paying hand on level 4.
- Level 5: I ended up with a three of a kind on level 5, which pays 3x my bet. The multiplier was at 4x, thanks to three winning hands above it, so my win was 5×4×3 = 60 credits.
- My total win was thus 5+30+15+0+60 = 110 credits.

## 7-5 Bonus Poker

The following table shows the probability and contribution to the return for each stud hand in 7-5 Bonus Poker.

### 7-5 Bonus Poker Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Straight flush | 1000 | 36 | 0.000014 | 0.013852 |

4 aces | 400 | 48 | 0.000018 | 0.007388 |

4 2-4 | 250 | 144 | 0.000055 | 0.013852 |

4 5-K | 200 | 432 | 0.000166 | 0.033244 |

Full house | 34 | 3,744 | 0.001441 | 0.048980 |

Flush | 22 | 5,108 | 0.001965 | 0.043239 |

Straight | 15 | 10,200 | 0.003925 | 0.058870 |

3 of a kind | 9 | 54,912 | 0.021128 | 0.190156 |

Two pair | 3 | 123,552 | 0.047539 | 0.142617 |

Pair | 1 | 1,098,240 | 0.422569 | 0.422569 |

Nothing | 0 | 1,302,540 | 0.501177 | 0.000000 |

Total | 2,598,960 | 1.000000 | 0.982461 |

The probability of a winning stud poker hand is 0.498823. You can see from my Bonus Poker page that the return for the draw poker hand is 0.980147. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 98.06%.

### 7-5 Bonus Poker Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.982461 | 1.000000 | 0.098246 |

2 | 0.982461 | 1.498823 | 0.147253 |

3 | 0.982461 | 1.997645 | 0.196261 |

4 | 0.982461 | 2.496468 | 0.245268 |

5 | 0.980147 | 2.995290 | 0.293582 |

Total | 0.980611 |

## 9-5 Double Double Bonus

The following table shows the probability and contribution to the return for each stud hand in 9-5 Double Double Bonus.

### 9-5 Double Double Bonus Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Straight flush | 1000 | 36 | 0.000014 | 0.013852 |

4 aces + 2-4 | 2000 | 12 | 0.000005 | 0.009234 |

4 2-4 + A-4 | 800 | 36 | 0.000014 | 0.011081 |

4 aces + 5-K | 800 | 36 | 0.000014 | 0.011081 |

4 2-4 + 5-K | 500 | 108 | 0.000042 | 0.020778 |

4 5-K | 400 | 432 | 0.000166 | 0.066488 |

Full house | 45 | 3,744 | 0.001441 | 0.064826 |

Flush | 17 | 5,108 | 0.001965 | 0.033412 |

Straight | 14 | 10,200 | 0.003925 | 0.054945 |

3 of a kind | 8 | 54,912 | 0.021128 | 0.169028 |

Two pair | 2 | 123,552 | 0.047539 | 0.095078 |

Pair | 1 | 1,098,240 | 0.422569 | 0.422569 |

Nothing | 0 | 1,302,540 | 0.501177 | 0.000000 |

Total | 2,598,960 | 1.000000 | 0.980067 |

The probability of a winning stud poker hand is 0.498823. You can see from my Double Double Bonus page that the return for the draw poker hand is 0.978729. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 97.85%.

### 9-5 Double Double Bonus Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.980067 | 1.000000 | 0.098007 |

2 | 0.980067 | 1.498823 | 0.146895 |

3 | 0.980067 | 1.997645 | 0.195783 |

4 | 0.980067 | 2.496468 | 0.244671 |

5 | 0.978729 | 2.995290 | 0.293158 |

Total | 0.978513 |

## 20-12-10 Deuces Wild

The following table shows the probability and contribution to the return for each stud hand in 20-12-10 Deuces Wild.

### 20-12-10 Deuces Wild Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Natural royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Four deuces | 1000 | 48 | 0.000018 | 0.018469 |

Wild royal flush | 250 | 480 | 0.000185 | 0.046172 |

Five of a kind | 50 | 624 | 0.000240 | 0.012005 |

Straight flush | 38 | 2,068 | 0.000796 | 0.030237 |

Four of a kind | 10 | 31,552 | 0.012140 | 0.121402 |

Full house | 9 | 12,672 | 0.004876 | 0.043882 |

Flush | 8 | 14,472 | 0.005568 | 0.044547 |

Straight | 5 | 62,232 | 0.023945 | 0.119725 |

Three of a kind | 2 | 355,080 | 0.136624 | 0.273248 |

Two pair | 1 | 95,040 | 0.036568 | 0.036568 |

Jacks or better | 1 | 664,704 | 0.255758 | 0.255758 |

Nothing | 1,359,984 | 0.523280 | 0.000000 | |

Total | 2,598,960 | 1.000000 | 1.009708 |

The probability of a winning stud poker hand is 0.476720. You can see from my Deuces Wild page that the return for the draw poker hand is 0.975791. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 97.85%.

### 20-12-10 Deuces Wild Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 1.009708 | 1.000000 | 0.100971 |

2 | 1.009708 | 1.476720 | 0.149106 |

3 | 1.009708 | 1.953440 | 0.197240 |

4 | 1.009708 | 2.430160 | 0.245375 |

5 | 0.975791 | 2.906880 | 0.283651 |

Total | 0.976343 | ||

0.978513 |

## 13-4-3-3 Bonus Deuces Wild

The following table shows the probability and contribution to the return for each stud hand in 20-12-10 Deuces Wild.

### 13-4-3-3 Bonus Deuces Wild Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Natural royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Four deuces plus ace | 2000 | 4 | 0.000002 | 0.003078 |

Four deuces | 1000 | 44 | 0.000017 | 0.016930 |

Wild royal flush | 250 | 480 | 0.000185 | 0.046172 |

Five aces | 250 | 52 | 0.000020 | 0.005002 |

Five 3-5 | 100 | 156 | 0.000060 | 0.006002 |

Five 6-K | 50 | 416 | 0.000160 | 0.008003 |

Straight flush | 35 | 2,068 | 0.000796 | 0.027850 |

Four of a kind | 11 | 31,552 | 0.012140 | 0.133543 |

Full house | 8 | 12,672 | 0.004876 | 0.039006 |

Flush | 6 | 14,472 | 0.005568 | 0.033410 |

Straight | 4 | 62,232 | 0.023945 | 0.095780 |

Three of a kind | 2 | 355,080 | 0.136624 | 0.273248 |

Two pair | 1 | 95,040 | 0.036568 | 0.036568 |

Jacks or better | 1 | 664,704 | 0.255758 | 0.255758 |

Nothing | 0 | 1,359,984 | 0.523280 | 0.000000 |

Total | 2,598,960 | 1.000000 | 0.988046 |

The probability of a winning stud poker hand is 0.476720. You can see from my Bonus Deuces Wild page that the return for the draw poker hand is 0.988025. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 96.50%.

### 13-4-3-3 Bonus Deuces Wild Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.988046 | 1.000000 | 0.098805 |

2 | 0.988046 | 1.476720 | 0.145907 |

3 | 0.988046 | 1.953440 | 0.193009 |

4 | 0.988046 | 2.430160 | 0.240111 |

5 | 0.988025 | 2.906880 | 0.287207 |

Total | 0.965038 |

## 7-5 Super Aces

The following table shows the probability and contribution to the return for each stud hand in 7-5 Super Aces.

### 7-5 Super Aces Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal Flush | 5000 | 4 | 0.000002 | 0.007695 |

Straight Flush | 1000 | 36 | 0.000014 | 0.013852 |

4 of a kind A | 800 | 48 | 0.000018 | 0.014775 |

4 of a kind J-K | 600 | 144 | 0.000055 | 0.033244 |

4 of a Kind 2-4 | 500 | 144 | 0.000055 | 0.027703 |

4 of a Kind 5-10 | 400 | 288 | 0.000111 | 0.044325 |

Full House | 33 | 3,744 | 0.001441 | 0.047539 |

Flush | 25 | 5,108 | 0.001965 | 0.049135 |

Straight | 14 | 10,200 | 0.003925 | 0.054945 |

3 of a Kind | 8 | 54,912 | 0.021128 | 0.169028 |

Two Pair | 2 | 123,552 | 0.047539 | 0.095078 |

Pair | 1 | 1,098,240 | 0.422569 | 0.422569 |

Nothing | 1,302,540 | 0.501177 | 0.000000 |

The probability of a winning stud poker hand is 0.498823. You can see from my Super Aces page that the return for the draw poker hand is 0.975791. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 97.81%.

### 7-5 Super Aces Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.979889 | 1.000000 | 0.097989 |

2 | 0.979889 | 1.498823 | 0.146868 |

3 | 0.979889 | 1.997645 | 0.195747 |

4 | 0.979889 | 2.496468 | 0.244626 |

5 | 0.977710 | 2.995290 | 0.292853 |

Total | 0.978083 |

## 9-6 Triple Double Bonus

The following table shows the probability and contribution to the return for each stud hand in 9-6 Triple Double Bonus.

### 9-6 Triple Double Bonus Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Straight flush | 1000 | 36 | 0.000014 | 0.013852 |

4 aces + 2-4 | 5000 | 12 | 0.000005 | 0.023086 |

4 2-4 + A-4 | 1000 | 36 | 0.000014 | 0.013852 |

4 aces + 5-K | 800 | 36 | 0.000014 | 0.011081 |

4 2-4 + 5-K | 500 | 108 | 0.000042 | 0.020778 |

4 5-K | 400 | 432 | 0.000166 | 0.066488 |

Full house | 44 | 3,744 | 0.001441 | 0.063385 |

Flush | 19 | 5,108 | 0.001965 | 0.037343 |

Straight | 15 | 10,200 | 0.003925 | 0.058870 |

3 of a kind | 7 | 54,912 | 0.021128 | 0.147899 |

Two pair | 2 | 123,552 | 0.047539 | 0.095078 |

Pair | 1 | 1,098,240 | 0.422569 | 0.422569 |

Nothing | 0 | 1,302,540 | 0.501177 | 0.000000 |

Total | 2,598,960 | 1.000000 | 0.981976 |

The probability of a winning stud poker hand is 0.498823. You can see from my Triple Double Bonus page that the return for the draw poker hand is 0.975791. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 97.81%.

### 9-6 Triple Double Bonus Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.981976 | 1.000000 | 0.098198 |

2 | 0.981976 | 1.498823 | 0.147181 |

3 | 0.981976 | 1.997645 | 0.196164 |

4 | 0.981976 | 2.496468 | 0.245147 |

5 | 0.981540 | 2.995290 | 0.294000 |

Total | 0.980689 |

## 9-6-5 Double Bonus

The following table shows the probability and contribution to the return for each stud hand in 9-6 Triple Double Bonus.

### 9-6-5 Double Bonus Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Straight flush | 1000 | 36 | 0.000014 | 0.013852 |

4 aces | 800 | 48 | 0.000018 | 0.014775 |

4 2-4 | 500 | 144 | 0.000055 | 0.027703 |

4 5-K | 400 | 432 | 0.000166 | 0.066488 |

Full house | 45 | 3,744 | 0.001441 | 0.064826 |

Flush | 21 | 5,108 | 0.001965 | 0.041273 |

Straight | 14 | 10,200 | 0.003925 | 0.054945 |

3 of a kind | 8 | 54,912 | 0.021128 | 0.169028 |

Two pair | 2 | 123,552 | 0.047539 | 0.095078 |

Pair | 1 | 1,098,240 | 0.422569 | 0.422569 |

Nothing | 0 | 1,302,540 | 0.501177 | 0.000000 |

Total | 2,598,960 | 1.000000 | 0.978233 |

The probability of a winning stud poker hand is 0.498823. You can see from my Double Bonus page that the return for the draw poker hand is 0.980147. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 97.77%.

### 9-6-5 Double Bonus Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.978233 | 1.000000 | 0.097823 |

2 | 0.978233 | 1.498823 | 0.146620 |

3 | 0.978233 | 1.997645 | 0.195416 |

4 | 0.978233 | 2.496468 | 0.244213 |

5 | 0.980147 | 2.995290 | 0.293582 |

Total | 0.977654 |

## 8-6 Bonus Poker Deluxe

The following table shows the probability and contribution to the return for each stud hand in 8-6 Bonus Poker Deluxe.

### 9-6-5 Double Bonus Stud Hand Analysis

Event | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Royal flush | 5000 | 4 | 0.000002 | 0.007695 |

Straight flush | 1000 | 36 | 0.000014 | 0.013852 |

4 of a kind | 400 | 624 | 0.000240 | 0.096038 |

Full house | 40 | 3,744 | 0.001441 | 0.057623 |

Flush | 23 | 5,108 | 0.001965 | 0.045204 |

Straight | 15 | 10,200 | 0.003925 | 0.058870 |

3 of a kind | 9 | 54,912 | 0.021128 | 0.190156 |

Two pair | 2 | 123,552 | 0.047539 | 0.095078 |

Pair | 1 | 1,098,240 | 0.422569 | 0.422569 |

Nothing | 0 | 1,302,540 | 0.501177 | 0.000000 |

Total | 2,598,960 | 1.000000 | 0.987086 |

The probability of a winning stud poker hand is 0.498823. You can see from my Bonus Poker Deluxe page that the return for the draw poker hand is 0.980147. With this information, we can put together the total return of the game. The return column is the product of the base return in the second column, the average multiplier in the third column, and 0.1. The reason for multiplying by 0.1 is that the win is based off 10% of the total amount bet. The lower right cell shows a total return of 98.38%.

### 8-6 Bonus Poker Deluxe Analysis

Hand | Return | Average Multiplier |
Total Return |
---|---|---|---|

1 | 0.987086 | 1.000000 | 0.098709 |

2 | 0.987086 | 1.498823 | 0.147947 |

3 | 0.987086 | 1.997645 | 0.197185 |

4 | 0.987086 | 2.496468 | 0.246423 |

5 | 0.980147 | 2.995290 | 0.293582 |

Total | 0.983845 |