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Xtra Roulette
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Introduction
Xtra Roulette, created by the renowned wheel manufacturer TCS John Huxley, is a variation of traditional roulette. It operates similarly to regular roulette for all types of bets, except for those placed on single numbers. For bets made on a single digit, payouts can range significantly, from 30 to potentially as high as 200 or even 500 to 1, depending on the specific variant being played.
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Rules
- A wheel with a single, double, or triple zero may be utilized.
- The layout of the wheel and betting options remains identical to that of standard roulette.
- Once the betting phase concludes and before the ball settles, four numbers on the wheel are randomly selected and will be displayed electronically.
- Each number chosen as per rule 3 will be assigned a multiplier of at least 50 to 1, based on a weighted table. I have prepared a table below that outlines my best estimates for these weights.
- If the ball does not land on any of the four designated numbers from rule 3, then payouts for winning single-number bets will be at a rate of 30 to 1.
- When the ball does land on one of the four selected numbers from rule 3, the winnings will correspond to the assigned multiplier 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 subsequent table shows my estimate of the multiplier weights for Option 1. The probability of each multiplier is directly related to its weight.
| Option 1 Weights | |
|---|---|
| Win | Weight |
| 50 | 410 |
| 100 | 30 |
| 150 | 20 |
| 200 | 15 |
| 250 | 12 |
| 500 | 6 |
The following table provides my estimates for the weight of each multiplier under Option 2, where the probability corresponds proportionally to its weight.
| Option 2 Weights | |
|---|---|
| Win | Weight |
| 50 | 400 |
| 100 | 30 |
| 150 | 20 |
| 200 | 15 |
| 250 | 12 |
| 300 | 6 |
This table outlines my estimates for the weight of each multiplier for Option 3, again showing that the probability is proportional to its weight.
| Option 3 Weights | ||
|---|---|---|
| Win | Weight | |
| 50 | 403 | |
| 75 | 30 | |
| 100 | 20 | |
| 125 | 15 | |
| 150 | 12 | |
| 200 | 6 | |
If there’s any confusion regarding my rules, I’ve included scans of both sides of the rack card. If the images are not clear, links to the full-size scans can be found below the smaller versions.
Full Size versions
Analysis
The next table displays the average multiplier for each of the three options.
| Average Multiplier | |
|---|---|
| Win | Weight |
| 1 | 72.008114 |
| 2 | 67.771639 |
| 3 | 60.236626 |
Following that, a table presents the average payout for single-number bets, taking into account the scenario in which the ball lands on a number without a designated multiplier, which consistently 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 |
Another table outlines the house edge for single-number bets based on the quantity of zeros present on the wheel, as well as the casino's selected option. My calculations align closely with those presented on the rack card, differing by no more than 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% |
