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Replay -- Craps Side Bet
Introduction
The Replay is a side bet in craps that I discovered at Boulder Station on September 16, 2010. This bet is successful if the shooter hits the same point at least three times before rolling a seven.
Rules
This wager starts with a fresh shooter and concludes when a seven is rolled. The table below outlines the payout structure, where winnings are calculated on a 'to one' basis.
Replay Pay Table
| Event | Pays |
|---|---|
| Achieving a point of 4 or 10 four or more times | 1000 |
| Achieving a point of 5 or 9 four or more times | 500 |
| Point of 4 or 10 achieved three times | 120 |
| Achieving a point of 6 or 8 four or more times | 100 |
| Point of 5 or 9 achieved three times | 95 |
| Point of 6 or 8 achieved three times | 70 |
Analysis
The table below presents my examination of the Replay bet, revealing a house edge of 24.81% in the lower right corner.
Replay Return Table
| Event | Pays | Probability | Return |
|---|---|---|---|
| Achieving a point of 4 or 10 four or more times | 1000 | 0.00003691863657 | 0.03691863656821 |
| Achieving a point of 5 or 9 four or more times | 500 | 0.00020671490002 | 0.10335745001061 |
| Point of 4 or 10 achieved three times | 120 | 0.00052298052124 | 0.06275766254895 |
| Achieving a point of 6 or 8 four or more times | 100 | 0.00069820960363 | 0.06982096036327 |
| Point of 5 or 9 achieved three times | 95 | 0.00179993294223 | 0.17099362951155 |
| Point of 6 or 8 achieved three times | 70 | 0.00429327448455 | 0.30052921391822 |
| Loser | -1 | 0.99244196891176 | -0.99244196891176 |
| Total | 1.00000000000000 | -0.24806441599095 |
Methodology
I employed integral calculus to investigate this wager, ensuring the results are accurate to the specified number of decimal places. Additionally, I ran a random simulation that confirmed these findings, aligning within 0.03% of the expected return.
I possess a detailed ten-page PDF document that outlines my analysis of the Replay bet .