Last Updated: February 6, 2019

Lucky Cat Blackjack

Introduction

Lucky Cat Blackjack is a game by game inventor Geoff Hall. This one plays like conventional blackjack, except if the dealer gets a 22 (in version 1) or busts on any total (in version 2), then special Lucky Cat dice are rolled to determine the outcome.

As of June 2019, Lucky Cat Blackjack can be played at the Golden Nugget in Las Vegas and Internet casinos using Genesis Gaming software.

Version 1 Rules

1. Lucky Cat blackjack follows conventional blackjack rules, including all major rule variations, except as follows.
2. If the dealer draws to a total of 22, then four special Lucky Cat dice will be rolled.
3. Each Lucky Cat die has a picture of the Lucky Cat on one side and are blank on the other five.
4. Any player hands still standing, including after splitting, will pay according to the number of Lucky Cats appearing on the roll of the dice, according to one of the pay tables below.
5. As in conventional blackjack, if the player gets a blackjack, then he shall win immediately at the posted table odds and not be subject to the Lucky Cat roll if the dealer gets to 22.

According to the math report, there are two pay tables available the casino for outcome of a throw of the Lucky Cat dice.

Dealer 22 Pay Table

Hand Pay Table 1 Pay Table 2
4 100 to 1 50 to 1
3 10 to 1 10 to 1
2 3 to 1 2 to 1
1 1 to 1 1 to 1
0 Push Push

If these rules were confusing, perhaps this rack card will help. Click on it for a larger version.

Strategy

Following is the basic strategy for Lucky Cat Blackjack, assuming six or eight decks.

It should be noted the only differences compared to conventional blackjack are:

• Hit 11 against an aces, as opposed to doubling.
• Hit 3,3 against a 2, as opposed to splitting, assuming double after a split is allowed.

This basic strategy is for pay table 2. The only difference with pay table 1 is to stand on soft 19 against a 6, as opposed to doubling.

Version 1 Analysis

The following table shows the probability of 0 to 4 Lucky Cats per roll under Pay Table 1. The lower right cell shows an expected win of 0.964506 to 1. Compare to this the 1 to 1 win in conventional blackjack.

Expected Lucky Cat Win — Pay Table 1

Lucky
Cats
Pays Probability Expected
Cats
4 100 0.000772 0.077160
3 10 0.015432 0.154321
2 3 0.115741 0.347222
1 1 0.385802 0.385802
0 0 0.482253 0.000000
Total   1.000000 0.964506

The following table shows the probability of 0 to 4 Lucky Cats per roll under Pay Table 2. The lower right cell shows an expected win of 0.810185.

Expected Lucky Cat Win — Pay Table 2

Lucky
Cats
Pays Probability Return
4 50 0.000772 0.038580
3 10 0.015432 0.154321
2 2 0.115741 0.231481
1 1 0.385802 0.385802
0 0 0.482253 0.000000
Total   1.000000 0.810185

All things considered, for the same set of blackjack rules, I show the effect on the expected return of the Lucky Cat rule on a dealer 22 to be as follows. A negative number means a lower return for the player, thus a higher house edge.

• Pay Table 1: -0.34%.
• Pay Table 2: -1.44%.

Version 2

In Version 2, whenever the dealer busts on any total, three Lucky Cat dice are rolled. The version 2 dice have a white cat on one side, a gold cat on another, and the other four sides are blank. The win on a dealer bust is determined as follows:

• Three matching cats — 10 to 1
• Three mixed cats — 3 to 1
• Any two cats — 3 to 2
• Any one cat — 1 to 1
• No cats — Push

The following table shows the probability of each possible outcome with the dice on a dealer 22.

Version 2 Pay Table

Event Pays Combinations Probability Return
Three matching cats 10 2 0.009259 0.092593
Three mixed cats 3 6 0.027778 0.083333
Any two cats 1.5 48 0.222222 0.333333
Any one cat 1 96 0.444444 0.444444
No cats 0 64 0.296296 0.000000
Total   216 1.000000 0.953704

I show that given the same blackjack rules, the effect of the version 2 rules is an increase in the house edge of 1.29%. At the Golden Nugget, I believe they use six decks and do not allow re-splitting aces, for an overall house edge of 1.94%.

Following is the basic strategy for version 2. Click on the image for a larger version.

Acknowledgements

I would like to thank Geoff Hall for sharing the GLI math report, which I'm in agreement to within 0.03% on the house edge.