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Birthday Bets
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Introduction
On March 28, 2024, I came across the intriguing 'Birthday Bets' option at the Downtown Grand casino in Las Vegas. This unique feature allows players to place 12 distinct bets in double-zero roulette, each corresponding to one of the 12 zodiac signs. Essentially, there’s a separate bet for every trio of numbers laid out on the board.
The payout structure for each of these bets is determined by the results of the subsequent 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 illustrates my findings, with the bottom right cell indicating 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 |
A player could potentially secure a better outcome by directly betting on the rows and utilizing a portion of the initial winnings for further bets. For instance, by placing a bet of one unit on any row and winning, you could take back your original stake plus six units from your winnings. You could then roll over five units of your winnings on that same row. If this second wager proves successful, your payout would be 12 times 5, which equals 60 units, plus the six units you’ve already pocketed from your first win, totaling 66 units. This strategy exceeds the 50 units you would have earned with the Birthday Bet. The house edge using this parlay method 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 wonder why the house edge is 7.34% when using the parlay strategy, especially since the house edge for row bets stands at 5.26%. That is indeed correct; however, with this approach, your average bet would be approximately 1 + (3/38)*5, equating to around 1.394737 units. This leads to an expected loss corresponding to that number of units wagered, which is 0.073407.
