# Magic Jacks

## Introduction

Magic Jacks, also known as Jack Magic, is a blackjack side bet that has had two known placements in California. The bet pays according to the number of jacks, in particular one-eyed jacks, between the player's initial two cards and the dealer's up card.

## Rules

1. The side bet is based on the player's initial two cards and the dealer's up card.
2. Of the four jacks in each deck, two of them, the spade and the heart, the jack is shown in profile mode, with one eye only showing.
3. There are two known pay tables as shown below.

The following are the two known pay tables. Wins are on a "to one" basis.

### Pay Table — Version 1

Event Pays
Three one-eyed jacks 500
Three jacks 100
Two one-eyed jacks 30
Two jacks 10
One one-eyed jack 2
One jack 1

### Pay Table — Version 2

Event Pays
Three one-eyed jacks 500
Three jacks 100
Two one-eyed jacks 40
Two jacks, one with one eye 12
Two jacks 8
One one-eyed jack 3
One jack 1

## Analysis

The following table shows my analysis for version 1 with six decks. The lower right cell shows a house edge of 19.68% (ouch!).

### Version 1 Return Table — Six Decks

Event Pays Combinations Probability Return
Three one-eyed jacks 500 220 0.000044 0.021942
Three jacks 100 1,804 0.000360 0.035984
Two one-eyed jacks 30 19,008 0.003791 0.113745
Two jacks 10 60,480 0.012064 0.120639
One one-eyed jack 2 495,936 0.098924 0.197847
One jack 1 495,936 0.098924 0.098924
Zero jacks -1 3,939,936 0.785894 -0.785894
Total   5,013,320 1.000000 -0.196813

The following table shows the house edge under the version 1 rules for various numbers of decks.

### House Edge — Version 1

Decks House Edge
3 21.56%
4 20.63%
5 20.06%
6 19.68%
8 19.20%

The following table shows my analysis for version 2 with six decks. The lower right cell shows a house edge of 5.10%.

### Version 2 Return Table — Six Decks

Event Pays Combinations Probability Return
Three one-eyed jacks 500 220 0.000044 0.021942
Three jacks 100 1,804 0.000360 0.035984
Two one-eyed jacks 40 19,008 0.003791 0.151660
Two jacks, one with one eye 12 41,472 0.008272 0.099268
Two jacks 8 19,008 0.003791 0.030332
One one-eyed jack 3 495,936 0.098924 0.296771
One jack 1 495,936 0.098924 0.098924
Zero jacks -1 3,939,936 0.785894 -0.785894
Total   5,013,320 1.000000 -0.051013

The following table shows the house edge under the version 2 rules for various numbers of decks.

Decks House Edge
3 7.15%
4 6.13%
5 5.51%
6 5.10%
8 4.58%