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Last Updated: July 24, 2016

# Lucky 8's

## Introduction

I first saw Lucky 8's in June 2016 at the Venetian. It is an innovative new table game, which is something I don't often say any more, in this era of copycat games. The betting structure of the game is similar to Three Card Poker, in that there is a raise or fold decision, and the dealer must have a certain hand to qualify. However, the scoring is based on the number of 8-point groupings that can be made with eight cards.

## Rules

Here are the rules to Lucky 8's.

1. The game is played with two modified decks of cards. Each deck uses only the aces to eights and one joker. The total cards is thus 66.
2. Aces count as one point and jokers count as 8 points. All other cards are scored according to pip value.
3. Play begins with the player making an Ante bet and optional Lucky 8 side bet.
4. The dealer shall then give the player and himself eight cards each.
5. The player shall examine his cards for the maximum number of sets of eight points he can created. A set can be of any number of cards, including one. If there are mutliple ways to create the same number of sets, then the player should go with the way using the greatest number of cards.
6. The player must either fold or raise with an In to Win bet. The In to Win bet must be equal exactly to the Ante bet.
7. If the player raised, then he should set his cards into two groups — One consisting of cards that are part of a group of eight and the other of the leftover cards, which are called the Side Cards. Otherwise, the dealer will collect the Ante bet.
8. After the players have made their decisions, unless all of them folded, then the dealer shall check his hand for at least one natural eight card or a joker. The dealer needs at least one eight or joker to qualify. If the dealer does not qualify, then the Ante is paid 1 to 1 and the In to Win bet shall push.
9. If the dealer does qualify, then he shall set his hand. As with the player, the dealer's objective is to maximize the number of sets of eight points. If this can be accomplished multiple ways, then the dealer will strive to minimize the number of Side Cards while still maximizing the number of sets.
10. The player and dealer hands shall then be compared, the one with the great number of sets of eight points shall win. In the event the number of sets is the same, then the one with the fewest Side Cards shall win.
11. If the player wins, then the Ante and In to Win bets shall pay 1 to 1.
12. If the dealer wins or ties, then the Ante and In to Win bets shall lose.
13. The Lucky 8's bet is adjudicated according to the number of natural 8's in the player's hand (eights or jokers). The dealer's hand does not matter and the Lucky 8's bet is adjudicated whether or not the player raises or folds.

### Lucky 8's Pay Table

Natural 8's Pays
8 1000
7 500
6 250
5 40
4 5
3 2
2 1
1 Loss
0 Loss

Here is the rack card. Click on either image for a larger version.

## Strategy

The strategy is based on the number of 8-point sets the player can make and Side Cards, as follows:

• 1 or less sets: Always fold.
• 2 sets: Raise with two or less Side Cards, otherwise fold.
• 3 or more sets: Always raise.

## Analysis

The following table shows the probability and return of all possible outcomes of the Ante bet. The lower right cell shows a house edge of 2.03%.

### Ante Analysis

Event Pays Probability Return
Player wins 2 0.292848 0.585696
Dealer doesn't qualify 1 0.205732 0.205732
Player folds -1 0.191118 -0.191118
Tie -2 0.064209 -0.128419
Dealer wins -2 0.246093 -0.492186
Total 1.000000 -0.020294

Under optimal strategy, the player will raise 80.9% of the time, for a total average bet of 1.809 units. That makes the Element of Risk, the ratio of the expected loss to average total bet, 2.03%/1.809 = 1.12%.

The next table shows the probability and contribution to the return for all possible outcomes of the Lucky 8 bet. The lower right cell shows a house edge of 10.66%.

### Lucky 8's Analysis

Natural 8's Pays Combinations Probability Return
8 1000 45 0.000000 0.000008
7 500 6,720 0.000001 0.000585
6 250 323,400 0.000056 0.014077
5 40 6,985,440 0.001216 0.048649
4 5 77,130,900 0.013429 0.067145
3 2 458,377,920 0.079807 0.159614
2 1 1,461,079,620 0.254385 0.254385
1 -1 2,319,174,000 0.403786 -0.403786
0 -1 1,420,494,075 0.247319 -0.247319
Total 0 5,743,572,120 1.000000 -0.106642

## Acknowledgement

I would like to thank Score Gaming for their cooperation in the making of this page by supplying to me the math report by GLI. This saved me a lot of time analyzing it myself.

Discussion of Lucky 8 in my forum at Wizard of Vegas.

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