The pay structure of video craps reflects the pay structure of regular craps in most cases. That is, you are betting in relation to the seven's probability to show or, in the case of one-roll bets, the odds of that particular number being thrown in 36 trials. Thus, most craps bets are not even money affairs but offer interesting yet rarely generous odds.
But aren't the odds always fixed and based on pure mathematics?
Yes and no.
Unfortunately, as many of you know, there is a difference between "true odds" and "casino odds." In that difference lies the casinos' profits.
The true odds of a bet are based upon the probability of that particular event happening. For example, the number four can be made in three different ways with two dice—3:1; 2:2; 1:3—and thus it will theoretically come up once every 12 times because there are 36 possible combinations on two six-sided dice—6 x 6 = 36. So the true odds against a four coming up on the next roll are always 11 to one.
The true odds of the number seven coming up (and as you know the number seven is the single most significant number in the game) are five to one because the seven can be made six ways: 6:1; 5:2; 4:3; 3:4; 2:5; 6:1. Six goes into 36 six times and thus the odds are always 5 to one against a seven being the next number rolled.
You always get the true odds against something by figuring how many times an event won't occur as opposed to how many times the event will occur. (You get the odds for something the opposite way!) The seven won't be rolled 30 times in 36 rolls but it will be rolled six times. Thus, the odds against a seven are 30 to 6, or 5 to one! That's because six goes into six once and six goes into 30 five times.
Another thing to remember about probability and odds-making is this: we are only talking the theoretical likelihood of an event and not the predictive likelihood of an event. Theoretically, the seven will show six times for every 36 rolls but in actuality it might show ten times, or no times on the next 36 rolls. However, the longer the dice are rolled, as the total rolls approach the millions and billions, you will start to see numbers coming up with a frequency close to their probability. Probability theory is indicative and not predictive in the short run fluctuations of a game of chance.
Now, if the casinos were offering a fair game, theoretically at the end of an infinite number of rolls of the dice, neither the casino nor the player would be ahead. Everyone would be tied.
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