Those sevens just kept coming

2 November 2014

By John Grochowski

QUESTION: I was at a craps table where the shooter rolled five sevens in a row. They were all comeouts, so I won my pass bets, but didn’t get any odds.

I’ve read you and others say the dice have no memory, and that the odds stay the same after a streak like that. But I’ve also read that 7s will show up once per six rolls. How do you reconcile that? It would seem to me there has to be a makeup time to get the odds to come out right. What’s the hidden factor that balances those five 7s in a row.

ANSWER: Time, repetition and the odds of the game are all that are needed. Given large numbers of rolls, streaks like that 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.

Every game has streaks with results that happen more often or less often than their average expectation – periods of good luck and bad luck, if you will. It doesn’t matter if you’ve had a good run at blackjack, your number has hit several times in a row at roulette, you’ve had a big slot machine jackpot, or if you’ve drawn a royal flush or two at video poker. Those are all within the realm of normal probability, and given enough time they will 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 the fluctuations that will give some players winning sessions. If those hot streaks didn’t exist, no one would play. But casinos also need the odds of the game to drag the overall results toward a predictable percentage for the house. That’s how operators make their money.


QUESTION: Everything I've read about video poker says that in games that pay 800 or more on four Aces, you should break up an Aces up full house to hold the Aces alone. Is that true in all of those games? How close a call is it?

ANSWER: The closeness of the call depends on a couple of things: How much do full houses pay, and is there an extra jackpot if you draw a designated kicker to go with the Aces?

In 10-7-5 Double Bonus Poker, where full houses pay 10-for-1, your average return for a five-coin bet is 50.57 coins if you hold three Aces, compared to a flat 50-coin payoff if you hold the full house.

If you drop to a 9-6-5 or 9-6-4 pay table – all too common nowadays – the average return for holding three Aces dips slightly to 50.26 coins, but the reward for standing pat drops to 45 coins. This no longer is in the realm of close calls.

Make the game 9-6 Double Double Bonus, and the 2,000-coin bonanza for four Aces plus a low kicker takes the average return when holding Ace-Ace-Ace to 63.58 coins, and that towers over the 45-coin full house return.

In a non-kicker game with a high full house return such as 10-7-5 Double Bonus, it can be a close call, but in games with big payoffs for four Aces with a kicker, breaking up the Aces-up full house is a no-brainer.