Sic Bo Probabilities

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With three dice in play, there a great many possible outcomes on each spin at the Sic Bo table, all of which are available for wagering. Specifically, there are exactly six possible results for each die, so the total number of combinations that can occur is calculated by multiplying their possibilities together: 6 x 6 x 6 = 216.

The question a Sic Bo player must ask before betting is whether the payout anticipated for a particular wager warrants the risk involved. The answer can be found by comparing the odds offered to the probability of a win occurring.

Regrettably, owing to the differences in Sic Bo payout tables around the world, it is impossible to spell out the probabilities covering various bets with universal relevance. However, the mathematics used to compute those probabilities will be the same no matter what odds are offered, so taking one casino as an example may serve as an indicator of how the game can be expected to play out elsewhere.

At the Mirage Resort & Casino in Las Vegas, the Sic Bo payoffs are quite similar to those found at tables in Atlantic City. For example, Big and Small pay even money when they win, which happens for each of those bets on 105 out of 216 outcomes, or 48.61% of all possible spins, leaving a margin of 6 out of 216 or 2.78% for the House. This is almost exactly the same degree of risk encountered when betting at the European Roulette table.

The Mirage pays 10-to-1 for a successful Doubles wager, in which the selected number must come up on at least two faces of the three dice. No matter which number is chosen, there will be exactly 16 successes possible out of the 216 total combinations for a 7.4% chance of winning, which is roughly 1 in 13.5.

Since ten units will be won 7.4% of the time and one unit will be lost 92.6% of the time, the House Edge works out to (0.074 x 10) (0.926 x 1 ) = -0.185 or 18.5%. That is slightly worse than the worst possible wager at the Craps table, Prop 7, with a 16.67% House advantage.

The same approach can be used to determine the probabilities for other Sic Bo bets. The House edge for a specified Triple is 16.20% and for Any Triple it is 13.89%. The respective payouts for these wagers at the Mirage are 180-to-1 and 30-to-1. When betting on a single individual number, the House Edge is 7.87%, with payouts of 1-to-1, 2-to-1 or 3-to-1, depending on how many faces the number appears on.

Calculating the probability of any given total in the spin of three dice is a bit more complex. Each total has its own number of permutations available, from a total of 3, which can be spun in only one possible way (1-1-1) to totals of 10 or 11, each of which can be made by 27 combinations.

Suffice it to say, all of these are risky wagers. The best of them, 7 or 14, gives up a House Edge of 9.72% and pays out at 12-to-1 while occurring just 6.94% of the time or about 1 in 14.4 spins. The worst wager among them is the 6 or 15, paying 17-to-1 but giving away a House advantage of 16.67% and occurring just 4.63% of the time or about once every 21.6 spins. All of the other totals fall somewhere in between, on a risk level equivalent to playing very tight slot machines.

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