When you or I see an unusual streak at the gaming tables or on the machines, it strikes us as defying the odds. But from a casino standpoint, there are thousands of trials every day, millions over time, and unusual streaks are just part of normal probablility.
Not long ago, I received a note via email from a craps player who was taken aback when a shooter rolled five sevens in a row. “It would seem to me there has to be a makeup time to get the odds to come out right,” he wrote. “What’s the hidden factor that balances those five 7s in a row?”
There is no hidden factor, other than normal probability. Time, repetition and the odds of the game are all that are needed. Given large numbers of rolls, streaks like fade into statistical insignificance.
Let’s say that in the next 24 hours after that streak, there are 200 rolls per hour, or 4,800 rolls. There are 36 possible two-dice combinations, and six of them are 7s, so we expect an average of one 7 per 6 rolls, so that 16.67 percent of rolls are 7s. Of the 4,800 in our thought experiment, we’d expect 800 to be 7s.
Now add the five 7s in a row immediately prior to the 48, so we have 805 7s in 4,805 rolls. That’s 16.75 percent, just eight-hundredths of a percent above average – and that’s with just one day’s worth of average results.
Given enough time, streaks fade into statistical insignificance as the odds of the game inexorably drag the long-term results toward expected averages.
Casinos count on that. They need winners, otherwise no one would play. But casinos also need the odds of the game to pull the overall results toward a predictable percentage for the house. That’s how operators make their money.
