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Lucky Nines
Introduction
On October 13, 2019, I discovered the Lucky Nines side wager on a baccarat machine positioned on a bar top multi-game machine made by Interblock at Binion's in Las Vegas. Then, on June 26, 2023, I came across it again at Red Rock casino, which featured a more favorable payout structure. This bet rewards players based on the count of nines present between the initial cards of both the Player and the Banker, as well as their suits.
Rules
- Eight decks are used.
- Each hand of Player and Banker receives two cards.
- The Lucky Nines bet offers payouts according to a specific paytable, which is determined by the initial four cards dealt. These payouts are based on a ratio of 'to one'.
Lucky Nines Pay Table
Event Binion's
Pay TableRed Rock
Pay Table4 Nines 500 1,000 3 Nines, same suit 250 500 3 Nines, mixed suits 20 35 2 Nines, same suit 8 16 2 Nines, mixed suits 5 5 1 Nine of diamonds 2 2 1 Nine 1 1
Analysis
The table below illustrates the combinations, probabilities, and the potential return contribution of all outcomes as per Binion's payout structure. The bottom right corner indicates a house edge of 19.46%.
Binion's Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Four nines | 500 | 35,960 | 0.000029 | 0.014619 |
| Three suited nines | 250 | 64,512 | 0.000052 | 0.013113 |
| Three nines | 20 | 1,840,128 | 0.001496 | 0.029922 |
| Two suited nines | 8 | 8,236,032 | 0.006696 | 0.053571 |
| Two nines | 5 | 28,237,824 | 0.022959 | 0.114794 |
| One nine of diamonds | 2 | 74,908,672 | 0.060905 | 0.121810 |
| One nine | 1 | 224,726,016 | 0.182714 | 0.182714 |
| No nines | -1 | 891,881,376 | 0.725148 | -0.725148 |
| Total | 1,229,930,520 | 1.000000 | -0.194605 |
The subsequent table provides a breakdown of my findings regarding Lucky Nines using the Red Rock payout structure. The bottom right corner reveals a house edge of 8.27%.
Red Rock Return Table
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| 4 Nines | 1000 | 35,960 | 0.000029 | 0.029237 |
| 3 Nines, same suit | 500 | 86,016 | 0.000070 | 0.034968 |
| 3 Nines, mixed suits | 35 | 1,818,624 | 0.001479 | 0.051752 |
| 2 Nines, same suit | 16 | 8,236,032 | 0.006696 | 0.107141 |
| 2 Nines, mixed suits | 5 | 28,237,824 | 0.022959 | 0.114794 |
| 1 Nine of diamonds | 2 | 74,908,672 | 0.060905 | 0.121810 |
| 1 Nine | 1 | 224,726,016 | 0.182714 | 0.182714 |
| All other | -1 | 891,881,376 | 0.725148 | -0.725148 |
| Total | 1,229,930,520 | 1.000000 | -0.082730 |
Card Counting the Lucky Nines
The machine where I observed this side bet reshuffled the cards between rounds. If you encounter this side bet in a live dealer setting, it's likely to be susceptible to card counting (a point worth considering!).