Playing a "Hopping 7’s" Progression

by Jerry "Stickman"

Periodically people ask me about craps betting systems. Almost all of them rely on the premise that certain numbers are due because they haven’t appeared for a while. I normally tell them that in a random you cannot beat the math of the game. The house edge is the house edge. In the long term you will lose the amount of money played times the house edge.

For many that is enough, but every so often someone says they have won a lot of money on a particular system and want me to look further into it. So periodically I will devote an article to exploring some of these systems.

This article will look at a "Hopping 7’s" progression.

Here is the system as it was stated to me.

1. Start over with each new shooter.
2. Wait seven rolls before starting the progression
3. When the bet hits, take the bet down along with the win.
4. Start with a $3 bet. Starting with the first bet, the progression is: 3, 3, 6, 9, 15, 24, 39, etc. always adding the previous two bets together to determine the next bet in the progression.

Here is a table that shows the bet, amount invested, win amount (taking the bet down), and profit.

What we have here is a Fibonacci progression. This and the Martingale progression are well known in betting systems. In "up as you lose" progressions, the thought is that when your number hits you will recoup your losses and garner a little profit. The Fibonacci progression is the less aggressive of the two.

Either of these progressions works as long as two things are true. The first is you must have adequate bankroll to make it through the inevitable losing streaks you will encounter. The amount you require can be very substantial. The last row in the above table represents the 17^th roll without a 7. While 17 rolls without a 7 appearing may be somewhat unusual, it is not that uncommon.

If the shooter goes 20 rolls without a 7 appearing, the bankroll required is almost $2,000.

If the shooter rolls just five more numbers without throwing a 7, the total invested is over $20,000.

And what is the shooter is extremely lucky and throws just 5 more numbers without a 7? Our hapless system player will have just over $225,000 invested.

If he should win on the 30^th roll, he will win $233,000+, so maybe he thinks it is worth it.

If our lucky shooter goes five more rolls without a 7, however, the investment skyrockets to almost $2.5 million. I don’t know about you, but if I had that kind of money, I wouldn’t risk it on a craps game.

The second consideration before using this system is something called table maximum. Virtually every craps game has a maximum bet ranging from $2,000 and up. Most of them are $10,000 or less. That means in the unusual but very possible case of someone going 25 rolls without a 7, this player is out his entire investment of over $20,000 and he cannot continue.

The math of the hop bet says that a player will lose 11.11 percent of all money wagered on a random shooter. That is what the math says. Let’s see what some simulations say. I ran several simulations specifying a random shooter through an excellent software program called Smart Craps from DeepNet Technologies.

The first simulation did not put any limits on the maximum bet. It assumed an unlimited bankroll and no maximum bet limit at the craps table. It was very interesting watching the running edge percentage as the simulation progressed. For the first several seconds the expectation was a little over 103%. This means that if someone were playing this system and had the same results as the simulation, they would more than double their bets!

This came to an abrupt halt after about 96,000 rounds. At this point the simulation terminated because it couldn’t handle the size of the bet being placed – over 2.2 billion dollars. It may have taken a while, but the long term hit at about 96,000 player rounds.

Next I put some limits on maximum bet size. I started with 1.1 billion dollars. If the simulation hit the limit, it would restart the progression; that is, wait for seven rolls without a 7, then begin betting the progression. After 10 million rounds, the expectation was 59 percent for the house! During the 10 million rounds the $1.1 billion limit was reached 7 times. This was much worse than what the math would indicate, but with such a large limit, the long term had most likely not yet been reached.

Three more simulations were run with limits of $10,000, $3,000 and $2,000. The results more closely matched the mathematical expectations.

As you can see, all of these fell much closer to the calculated expectations.

So what does this show? You may be lucky and win for a period of time. You may even win for a long period of time. You could also be very unlucky and lose very big for a while. Eventually, however the math will catch up with you.

In the long run, you cannot beat the math of the game with random shooters. You will lose the house edge of your bets times the amount bet. Accept the fact and bet the low house edge bets. Your bankroll will thank you.

Jerry "Stickman" is an expert in craps, blackjack and video poker and advantage slot machine play. He is a regular contributor to top gaming magazines. The "Stickman" is also a certified instructor for Golden Touch™ Craps and Golden Touch™ Blackjack. For more information visit www.goldentouchcraps.com or www.goldentouchblackjack.com or call 1-800-944-0406. You can contact Jerry "Stickman" at stickmanGTC@aol.com