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Xtra Roulette
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Introduction
Xtra Roulette is a roulette variant by wheel maker TCS John Huxley. It plays just like conventional roulette for all wagers except those on single numbers. For single number bets, the win can be anywhere from 30 to a maximum of 200 to 500 to 1, depending on the version used.
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Rules
- A single-, double-, or triple-zero wheel may be used.
- The wheel and betting layout are the same as conventional roulette.
- After betting is closed and before the ball lands determines the winning number, four random numbers on the wheel will be randomly and electronically chosen. Those numbers selected will be shown on a display.
- Each number from rule 3 will be assigned a multiplier of at least 50 to 1 according to a weighted table. I indicate my best estimate of such weights in a table below.
- If the ball does not land in one of the four numbers from rule 3, then winning single-number bets will pay 30 to 1.
- If the ball does land in one of the four numbers from rule 3, then wins will pay according to the multiplier shown for that number as explained in rule 4.
| Multipliers | ||
|---|---|---|
| Option 1 | Option 2 | Option 3 |
| 50 | 50 | 50 |
| 100 | 100 | 75 |
| 150 | 150 | 100 |
| 200 | 200 | 125 |
| 250 | 250 | 150 |
| 500 | 300 | 200 |
The following table shows my estimate of the weight of each multiplier under Option 1. The probability of each multiplier is proportional to its weight.
| Option 1 Weights | |
|---|---|
| Win | Weight |
| 50 | 410 |
| 100 | 30 |
| 150 | 20 |
| 200 | 15 |
| 250 | 12 |
| 500 | 6 |
The following table shows my estimate of the weight of each multiplier under Option 2. The probability of each multiplier is proportional to its weight.
| Option 2 Weights | |
|---|---|
| Win | Weight |
| 50 | 400 |
| 100 | 30 |
| 150 | 20 |
| 200 | 15 |
| 250 | 12 |
| 300 | 6 |
The following table shows my estimate of the weight of each multiplier under Option 3. The probability of each multiplier is proportional to its weight.
| Option 3 Weights | ||
|---|---|---|
| Win | Weight | |
| 50 | 403 | |
| 75 | 30 | |
| 100 | 20 | |
| 125 | 15 | |
| 150 | 12 | |
| 200 | 6 | |
If my rules were not clear, here are scans of both sides of the rack card. If the resolution is too low to read, I have links to the full size scans below the reduced images.
Full Size versions
Analysis
The following table shows the average multiplier for each of the three options.
| Average Multiplier | |
|---|---|
| Win | Weight |
| 1 | 72.008114 |
| 2 | 67.771639 |
| 3 | 60.236626 |
The next table shows the average win on single-number bets, including the possibility the ball lands in a number that doesn't have a multiplier, which always pays 30 to 1.
| Average Win | |||
|---|---|---|---|
| Zeroes | Option 1 | Option 2 | Option 3 |
| 1 | 34.541418 | 34.083420 | 33.268824 |
| 2 | 34.421907 | 33.975962 | 33.182803 |
| 3 | 34.308524 | 33.874014 | 33.101192 |
The next table shows the house edge on single-number bets according to the number of zeroes on the wheel and option chosen by the casino. My figures agree to those quoted on the rack card to within 0.01%.
| Average Win | |||
|---|---|---|---|
| Zeroes | Option 1 | Option 2 | Option 3 |
| 1 | 3.94% | 4.53% | 7.38% |
| 2 | 6.78% | 7.35% | 10.05% |
| 3 | 9.47% | 10.00% | 12.56% |
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