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Last Updated: December 8, 2016

Lucky Aces

Introduction

Lucky Aces is a blackjack side bet I noticed on an electronic blackjack game on October 13, 2016 at the Mirage. It based based on the number of aces between the player's and dealer's first two cards.

Rules

1. Eight decks of cards are used.
2. The Lucky Aces pays based on the four cards comprising the player's and dealer's initial two cards. The pay table is shown below. All wins are on a "to one" basis, meaning the original bet is returned on a win.

The following table shows two Lucky Aces pay tables I'm aware of.

Lucky Aces Pay Table

Event Pay Table 1 Pay Table 2
Four aces 500 500
Three suited aces 250 250
Three aces 30 20
Two suited aces 12 8
Two aces 5 5
One ace of diamonds 2 2
One ace 1 1

Analysis of Pay Table 1

The following table shows the probability and contribution to the return of all possible outcomes under pay table 1 and using eight decks. The lower right cell shows a house edge of 14.90%.

Lucky Aces Pay Table 1

Event Pays Combinations Probability Return
Four aces 500 35,960 0.000029 0.014619
Three suited aces 250 86,016 0.000070 0.017484
Three aces 30 1,818,624 0.001479 0.044359
Two suited aces 12 8,236,032 0.006696 0.080356
Two aces 5 28,237,824 0.022959 0.114794
One ace of diamonds 2 74,908,672 0.060905 0.121810
One ace 1 224,726,016 0.182714 0.182714
No aces -1 891,881,376 0.725148 -0.725148
Total   1,229,930,520 1.000000 -0.149012

The next table shows the house edge for 4, 5, 6, and 8 decks.

Decks House
Edge
8 14.90%
6 15.56%
5 16.08%
4 16.83%

Analysis of Pay Table 2

The following table shows the probability and contribution to the return of all possible outcomes under pay table 2 and eight decks. The lower right cell shows a house edge of 19.06%.

Lucky Aces Pay Table 2

Event Pays Combinations Probability Return
Four aces 500 35,960 0.000029 0.014619
Three suited aces 250 86,016 0.000070 0.017484
Three aces 20 1,818,624 0.001479 0.029573
Two suited aces 8 8,236,032 0.006696 0.053571
Two aces 5 28,237,824 0.022959 0.114794
One ace of diamonds 2 74,908,672 0.060905 0.121810
One ace 1 224,726,016 0.182714 0.182714
No aces -1 891,881,376 0.725148 -0.725148
Total   1,229,930,520 1.000000 -0.190583

The house edge under pay table 2 with six decks is 19.57%.

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