Last Updated: January 11, 2015

# Lucky Draw Baccarat

## Introduction

Lucky Draw Baccarat (LDB) could be loosely described as a cross between baccarat and blackjack. The game features the scoring rules of baccarat and the options to stand or double of blackjack. It is created and owned by Mr. Casino Games. As of this writing (January, 2015), the game can be found at three casinos in the United Kingdom and the Treasury Casino & Hotel in Brisbane, Australia.

## Rules

1. The game uses eight ordinary 52-card decks.
2. Cards are scored as in conventional baccarat, as follows:
• Tens, face cards = 0 points.
• Aces = 1 point.
• 2-9 = Pip value.
3. Play starts with the player making an Enter bet. The player may also make an optional side bet called the Block Bonus.
4. The dealer will deal the player and himself two cards each.
5. Both player cards are dealt face up. One dealer card shall be face up and the other face down.
6. The player may either stand or make a Draw bet equal to his Enter bet.
7. If the player makes the Draw bet, then he will be dealt one more card.
8. The dealer will then expose his other card.
9. If the dealer has four or less points, then he will draw a third card.
10. The two hands are scored as in baccarat — adding the points and taking the terminal digit of the sum.
11. The higher score shall win.
12. If the player wins, then he shall win even money on the Enter bet and according to the pay table below on the Draw bet.
13. If there is a tie, then both the Enter and Draw bets shall push.
14. If the dealer wins, then the player shall lose both the Enter and Draw bets.

### Draw Bet Pay Table

Player Total Pays
9 3 to 1
8 2 to 1
7 3 to 2
1 to 6 1 to 1

## Strategy

The following image shows the strategy. To use the table, look up the player's total along the left column and the dealer's up card along the top row.

## Analysis

The following return table shows the probability and return from all possible events. The lower right cell shows a house edge of 3.34%.

### Lucky Draw Baccarat Return Table

Event Pays Permutations Probability Return
Three-card 9 win 4 198,673,673,889,792 0.039747 0.158990
Three-card 8 win 3 167,922,525,855,744 0.033595 0.100786
Three-card 7 win 2.5 137,012,025,251,840 0.027411 0.068528
Three-card 1-6 win 2 437,368,800,106,496 0.087502 0.175004
Two card win 1 1,283,922,912,731,140 0.256867 0.256867
Push 0 545,419,970,481,408 0.109119 0.000000
Two-card loss -1 489,318,928,551,936 0.097895 -0.097895
Three-card loss -2 1,738,759,438,635,000 0.347863 -0.695727
Total   4,998,398,275,503,350 1.000000 -0.033448

The player will make the Draw bet 59.193% of the time, for an average final wager of 1.59193 units. Thus, the element of risk, or expected loss to total amount bet, is 3.3448%/1.59193 = 2.10%.

## Block Bonus

The Block Bonus is based on the player's first two cards and the dealer's up card. It uses the following terminology:

• Ultimate Block = Both player cards greater in rank to the dealer's rank and equal to each other in both rank and suit.
• Pair Block = Both player cards greater in rank to the dealer's rank, equal to each other in rank, and one matches the dealer's suit.
• Flush Block = One or both player cards greater in rank to the dealer's rank and both equal to the dealer's card in suit.
• Normal Block = One card greater in rank to the dealer's rank and equal to the dealer's card in suit.

The following table shows the probability and return for all possible outcomes of the Block Bonus. The lower right cell shows a house edge of 4.96%.

### Block Bonus Return Table

Event Pays Permutations Probability Return
Ultimate Block 35 139,776 0.001956 0.068448
Pair Block 10 958,464 0.013410 0.134100
Flush Block 5 2,622,464 0.036692 0.183460
Normal Block 2 11,501,568 0.160922 0.321844
Push 0 2,114,112 0.029579 0.000000
Loser -1 54,136,576 0.757441 -0.757441
Total   71,472,960 1.000000 -0.049589

## Acknowledgement

I would like to thank the game inventor and owner, Mr. Casino Games, for the math report, by Cindy Liu, for the use on this page.