Last Updated: July 23, 2017

# Blackjack 11's

## Introduction

I saw Blackjack 11's at the Grand Casino Brussels in Belgium on July 16, 2017. It is a 10 Euro bet that wins if the player gets 11 points in his first two cards, including a blackjack. The game uses some special equipment and has four progressive jackpots so read on to the rules for more information.

## Rules

1. The game is played with six decks of cards.
2. The bet amount, at least at the Grand Casino Brussels, is 10€
3. One of the six ace of spades is marked with the word "Jackpot." I shall refer to this as the Jackpot Ace.
4. Three dice are used. Each die has five blank sides and one side with an infinity symbol. I shall refer to these dice as Infinity Dice.
5. If the player gets a suited 11, other than the types that qualify for the top two progressive jackpots, then then the three Infinity Dice shall be tossed about in a dome at the player's touch of a red button. The player will qualify for progressive jackpots if at least two dice land on the infinity symbol.
6. The possible wins are as follows:
• Jackpot Ace and king of spades — Progressive (7,202€ on July 16, 2017)
• Jackpot Ace and any king not in spades — Progressive (1,318€ on July 16, 2017)
• Suited 11 and three infinities — Progressive (250€ on July 16, 2017)
• Suited 11 and two infinities — Progressive (165€ on July 16, 2017)
• Suited 11 and zero or one infinity — 15 for 1
• Colored 11 (cards in same color but different suits) — 10 for 1
• Mixed 11 (cards in opposite colors) — 3 for 1
• Mystery Jackpot — Progressive (3,900€ on July 16, 2017)

The Mystery Jackpot is awarded randomly, I presume by a random number generator. As usual, I have almost no idea the probability of winning. The odds must be pretty low given the high jackpot amount. I also have no idea about the seed amounts and progressive contribution rates of the jackpots based on the cards.

## Analysis

The following table shows the probability and contribution to the return for each event. Since four of the awards are progressive and I don't know how much they are seeded or the rate of increase, I don't know their value. The bottom right cell shows us that the fixed awards return 70.97%.

### Perfect 11's — General Case

Event Pays Combinations Probability Return
Jackpot ace and king of spades ? 1,296 0.000124 ?
Jackpot ace and king not in spades ? 3,888 0.000371 ?
Perfect 11 with three infinity dice ? 1,152 0.000110 ?
Perfect 11 with two infinity dice ? 17,280 0.001649 ?
Perfect 11 with one or zero infinity dice 15 230,400 0.021986 0.329788
Colored 11 10 248,832 0.023745 0.237447
Mixed 11 3 497,664 0.047489 0.142468
Loser 0 9,478,944 0.904526 0.000000
Total   10,479,456 1.000000 0.709704 + ?

The next table shows the analysis of the bet as of July 16, 2017 at the Grand Casino Brussels at about 9 PM. Progressive wins have been divided by 10, to put them in comparison to the 10€ required bet. This table does not factor in the value of the mystery jackpot. The lower right cell shows a return of 89.62%, not counting the Mystery Jackpot.

### Perfect 11's — July 16, 2017 Grand Casino Brussels

Event Pays Combinations Probability Return
Jackpot ace and king of spades 720.2 1,296 0.000124 0.089068
Jackpot ace and king not in spades 181.8 3,888 0.000371 0.067450
Perfect 11 with three infinity dice 25.0 1,152 0.000110 0.002748
Perfect 11 with two infinity dice 16.5 17,280 0.001649 0.027208
Perfect 11 with one or zero infinity dice 15 230,400 0.021986 0.329788
Colored 11 10 248,832 0.023745 0.237447
Mixed 11 3 497,664 0.047489 0.142468
Loser 0 9,478,944 0.904526 0.000000
Total   10,479,456 1.000000 0.896177

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