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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
- Eight decks of cards are used.
- 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.
House Edge by Number of 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%.