Birthday Bets
Introduction
I noticed the "Birthday Bets" at the Downtown Grand casino in Las Vegas on March 28, 2024. They are a set of 12 bets in double-zero roulette, labeled with the 12 zodiac symbols. One bet for each row of three numbers on the layout.
Each bet pays as follows, based on the next two spins:
- Next two spins win — Pays 50 to 1
- Next one spin wins — Pays 6 to 1
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The following table shows my analysis. The lower right cell shows a house edge of 17.31%.
Birthday Bets Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Next two spins win | 50 | 9 | 0.006233 | 0.311634 |
| Next one spins win | 6 | 105 | 0.072715 | 0.436288 |
| Loss | -1 | 1330 | 0.921053 | -0.921053 |
| Total | 1444 | 1.000000 | -0.173130 |
The player could achieve a equal or better win by betting on the rows directly and parlaying part of the first win. To be specific, bet one unit on any row. If it wins, pocket the original wager and six units of the winnings. Then parlay five units of the winnings on the same row. If that second bet wins, you will get back 12*5=60 units on the second bet (including the 5 units bet) plus the 6 units in your pocket from the first win, for a total win of 6+60=66. That beats the 50 units you would have won on the Birthday Bet. The house edge with this parlay strategy is 7.34%.
Birthday Parlay Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Next two spins win | 66 | 9 | 0.006233 | 0.411357 |
| Next one spin wins | 6 | 105 | 0.072715 | 0.436288 |
| Loss | -1 | 1330 | 0.921053 | -0.921053 |
| Total | 1444 | 1.000000 | -0.073407 |
You might ask why is the house edge 7.34% with the parlay strategy? Isn't the house edge on the row bets 5.26%? It is. However, on average with this parlay you would be betting 1 + (3/38)*5 = 1.394737 units. The expected loss on that many units bet is 0.073407.
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