Playing a 'Hopping 7Â’s' Progression

By Jerry 'Stickman'

Because the 7 has the greatest number of combinations (six), it is the number that has the potential to come up most often, which is why 7 is the magic number in craps. There are 36 possible number combinations in craps. Here is a chart showing the possible combinations for each number using two die. A single round of craps is divided into two parts: the come-out roll and the point roll. A player known as the “shooter” rolls two dice to determine results. Each involves the placement of bets, though one is contingent on the other. If a player either rolls a “7” or craps out on the come-out roll, then that round of betting ends. This is convenient since seven is the most common number to be rolled in a game of craps, giving you a good chance of winning the bet. This wager is found in the middle of the table, though it is not placed. The probability of rolling a 7 would be 6/36 = 1/6 = 0.167 = 16.7%! Another way of thinking about the craps game is thinking that since there is a 1 in 6 chance that a 7 will be rolled, there is a 5 in 6 chance that a 7 will not be rolled. So betting on a point number in this case or betting for the shooter to not roll a 7 is a great bet as 5 out of 6 rolls will not be a lucky seven.

Periodically people ask me about craps betting systems. Almost all of them rely on the premise that certain numbers are due because they havenÂ’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 7Â’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 donÂ’t know about you, but if I had that kind of money, I wouldnÂ’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. LetÂ’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.

May all your wins be swift and large and all your losses slow and tiny.

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 1-886-738-3423. You can contact Jerry 'Stickman' at stickmanGTC@aol.com

Types of Craps Bets

Craps Seven

Craps Seven Count

Craps Seven Eleven

The any seven craps bet, also known as big red, is perhaps the most popular and well known wager in the game of craps. Basically all you are doing is betting that the shooter will roll a 7 on the next roll. Recall that the number 7 is the most frequent and probable number to appear when the dice are rolled so your odds of landing it are fairly nice.

The odds of actually rolling a 7 are 6 in 36 or 5:1. The house pays out 4:1 on a winning bet, which brings up an outrageous house edge of 16.67%. This is the absolute worst bet you can make in craps. This is actually one of the worst bets a player can make in any casino game at the casino. It is also the most profitable bet for the casino since a large house edge means that players will lose more money and quickly. Note that this rule depends on what casino you play at.

I added a picture below showing where the any seven bet is located on the table layout. This is a single roll bet so I would win only if the shooter rolls a 7 on the very next roll. I would lose if anything else is rolled. Note that 'any' seven means that any combination of numbers (such as 2 and 5, 1 and 6, 3 and 4) that add up to 7 will be acceptable for a win.

Carefully look at the image below. Notice that CasinoMax pays out 5 For 1. This does not mean 5:1 though, but 4:1. This is just an example and lesson of why it's important to understand the wording of what the odds mean! This can really benefit or hurt your game. An inexperienced player may assume 5 For 1 means 5:1 or paying out true odds, which is why some people will become obsessed with the number 7. Others will recognize that 5 For 1 means 4:1, which turns out to be the worst odds in the entire game. Just to appreciate how great true odds are though, there is usually no other bet in the casino (except a handful of other craps bets) that has no house edge. Card counters in blackjack would only dream to get near true odds in blackjack.

Craps Number Seven