February 27th, 2008

By Charles Jay

Were you ever wondering about this?

There is perhaps no bigger argument at a blackjack table than that which involves the player insuring a two-card natural (commonly known as a blackjack). The insurance rule says that when the dealer turns an Ace as the upcard, he will ask the players if they’d like to “insure” their hands. The player puts up one-half of his original bet, and if the insurance wager wins (if the dealer has blackjack), it pays off at two-to-one odds.

When the player is dealt, for example, a Jack and an Ace, which constitutes the aforementioned blackjack, and the dealer has an Ace showing, there is a great propensity on the part of the player to “protect” that hand by buying insurance. After all, the logic goes, the blackjack is a bonus hand, which pays off at three-to-two odds. The player doesn’t get a blackjack that often, so players feel they had better get something out of that situation. If they have a blackjack and the dealer also has one, it’s a push (a tie) and the player gets nothing.

Many supposed blackjack “experts” recommend strongly that their students always insure their blackjack in that situation. The rationale is that whatever happens, the player will always end up with a profit. And you know something? They’re right! The player will come out with a profit every time, if they insure a blackjack. But I’m telling you that insuring the blackjack is not the percentage play.

Let’s illustrate.

Take a 52-card deck. In this deck, there are 16 ten-value cards, and 36 non-tens, a ratio of 2.25-to-one. When we are faced with the situation in which we have a two-card blackjack and the dealer has an Ace showing, there are now 15 tens and 24 non-tens remaining. That’s a ratio of 2.27-to-one. Remember that insurance pays only two-to-one, so you’re sort of getting “the worst of it.”

But let’s get back to the illustration. Imagine that you’re laying out $10 bets in each of these situations. There are four different scenarios that can take place:






In scenario one and two – which we do not recommend for any player – the yield is $10 each for the player. If the player bets $10 and insures for $5, he’ll push the primary bet and win $10 on the insurance bet. If the dealer doesn’t have blackjack, the player wins $15 from the primary bet, but loses the $5 insurance bet, leaving a $10 profit.

In scenario three, we have not wagered on insurance, and tied the dealer on our blackjack. We retain our $10 bet, giving us a net gain of zero. In scenario four, we beat the dealer with our blackjack, giving us a gain of $15 on the hand.

As you can see, when you take insurance, you are guaranteed a return on investment, while in one of our scenarios you gain nothing.

Let’s take a look at probability for a moment: remember, we have 15 tens and 34 non-tens left, making a theoretical total of 49 cards remaining. Since the dealer has to have a ten in the hole to complete a two-card blackjack, let’s calculate the chance of that happening. Just divide 15 by 49, and you come up with a 30.6 percent chance of the dealer having blackjack. That leaves us with a 34/49, or 69.4 percent chance of the dealer not having blackjack. Clearly scenarios two and four are going to happen much more often than the first and the third, even in an online casino.

Now let’s look at what our expected gain is per 100 situations for each of our scenarios:





Just multiply it out.

Scenario #1 gives you an expected return of $306 for every 100 situations;

Scenario #2 yields $694 for that same duration. That’s a total of $1000 even.

Scenario #3, in which there is no insurance, offers an expected return of $0, since there was no protection for the blackjack. But in scenario #4, where the dealer doesn’t turn over a natural, we win $15 per play, or $1041 over the course of 100 situations ($15 x .694 x 100).

The difference, or gain, between the results when you TAKE insurance (Scenarios #1 and #2 added) and DON’T TAKE insurance (Scenarios #3 and #4 added) is $41 for every 100 situations, or $1000 wagered.

Our most profitable scenario, therefore, is the one that occurs the vast majority of the time. As this example illustrates, we are gaining 4.1 percent for every $1000 wagered by NOT insuring. The truth is, as we’ve stated before, it is not mathematically sound to exercise the insurance option if you’re a Basic Strategy player.

Tags: , , , , , , , ,


February 20th, 2008

General Gaming

As long as there has been gambling, there have been betting systems people have devised for the purpose of beating the game. Almost all of them that are no tied to some form of playing strategy are doomed to fail. In the interests of introduce you to some of these systems, perhaps more of an example of what not to do, we will discuss the Martingale.

The Martingale system (and there are different kinds of Martingales, as we’ll explore in future installments) involves doubling the bet after each loss until you win. That means if you’re at a $5 minimum table, your progression would go from $5 to $10 to $20 to $40 to $80 to $160 to $320. If you win sometime within that period, you are going to have a profit for that particular stretch. But obviously there is a flaw. As you’ve already guessed, if you have a $500 maximum at the table, there is only so far you can go with this system. In fact, you can go only seven levels (i.e., sustain seven straight losses) before the table limit renders the system useless.

Using the same $5 bet, you can go only six levels on a table with a $200 limit. And you can go only five levels with a $100 limit.

Proponents of the strategy (and I know plenty of them) will tell you that there is very little chance of losing six or seven hands in a row.

But you know that there are going to be losing streaks, regardless of the game you decide to play, and when you go on one of those streaks using a Martingale, it can kill you.

Let’s use an example of what can happen when you employ a Martingale system in your online casino:

Let’s say you have a $200 limit at the table (obviously not all of them are like this). If you experience a losing streak that takes you over the house limit, you are going to be betting not just the last bet, but everything before that: $5+$10+$20+$40+$80+$160 = $315

You have now lost $315 that is going to take you forever to get back, if it ever happens at all.

Conversely, if you get on a streak of six WINS in a row, you would win a grand total of $30, because remember, the only increases in bets happens when you LOSE. In a game like blackjack, for example, the chances of winning six hands in a row and losing six hands in a row is relatively the same. So you have a $30 win versus of $315 loss. That doesn’t look like a beneficial risk/reward scenario, does it?

Now, if you lose the first five bets and win the sixth, you’ll have lost $155 before winning the bet for $160, coming out $5 ahead. So you have put $315 on the table for a $5 profit that is in no way guaranteed.

You will find all the way through the Martingale system that when you DO win, it is an amount only equal to your single unit bet. In this case it is $5:

* If you win the third bet — $5+$10 = $15 in losses, $20 in wins = $5 profit
* If you win the fourth bet — $5+$10+$20 = $35 in losses, $40 in wins = $5 profit
* If you win the fifth bet — $5+$10+$20+$40 = $75 in losses, $80 in wins = $5 profit

This is a system that will look good, but only until the first protracted losing streak happens. Then it’s an uphill battle, to say the least.

There are other forms of the Martingale system. Let’s examine them, because we want you to know what you’re encountering in your online casino:

THE GRAND MARTINGALE — In the “regular” Martingale, you are going to double the bet each time you lose until you win, which then would yield a net profit. With the “Grand Martingale,” you are going to double the bet after losses, but this time you are going to add $1 to that bet. So instead of going from $5 to $10 to $20 to $40, etc., you are progressing from $5 to $11 to $23 to $47 and so on.

With the Grand Martingale, the losses you sustain if you lose six bets in a row are even greater than with the regular Martingale. In fact, when you look at that total:

$5+$11+$23+$47+$95+$191 = $372,

it is 18% more than if you used the regular Martingale:

$5+$10+20+$40+$80+$160 = $315

It is true that when you win on a series of hands with this system it will put you a little bit more ahead, but the basic principle still applies – you are potentially putting up a lot to earn just a little. In a game like blackjack, the risk-reward quotient is much greater than a player who would be employing Basic Strategy and card counting principles.

THE SHORT MARTINGALE — This is played just like the Grand Martingale, except here you are going to play up to four levels (in this case, $5+$11+$23+$47), then you’re going to quit. Obviously it doesn’t take much to send you back to the drawing board.

THE ROTATING MARTINGALE — This involves the same progression as the Grand Martingale (see above), except you are going to be doubling and adding one dollar if you WIN. For example, if you bet $5 and win, the next bet is $11. Then if you win again, the next bet is $23, and so on. When you lose, you take it down a level. So if you have won the $11 bet, put up $23 and lose, you go back down to $11 for the next bet. Your progression ends when you have gotten to the fourth level and won (meaning you have to win four hands in a row) or when you lose enough to have to regress to zero.

At that point, you’re finished.

And for this subject, so are we.

Tags: , , , , , , , ,


February 13th, 2008

By Charles Jay

One of the player’s most important options available is that of SOFT DOUBLING. This concept applies when the player holds a SOFT HAND, meaning a two-card hand which contains an ace. Of course, a hand with two aces is technically a soft hand, but the player would always split that hand, not double (If you were in a brick and mortar setting, however, and you doubled, you’d probably find pit bosses falling over each other to give you casino comps).

Another soft hand to which the doubling principle does not apply is the Ace-10 deal which naturally (pardon the pun) is a blackjack and constitutes a 3-2 payoff. That leaves us with the hands running from Ace-2 through Ace-9. By the way, an Ace-2 should be referred to by the player as “Ace-Two” and not as “3 or 13”. When this category of hand is dealt, it is the player’s option to take a one-card draw for twice the original bet, which of course is the concept of DOUBLING.

When you double soft hands, they differ from the process with hard hands since you can use either the soft or hard total of the original hand. With a hand like Ace-Five, you can improve your hand by a high card (Ace), bringing the total to 17, or by a low card (2, for example), which would bring the total to 18.

A potential danger to soft doubling as opposed to hard doubling has you making things worse for yourself by using the option. For instance, let’s say you held an Ace-7 which totals 18. The dealer holds a five, signaling the player to double. The player is dealt a six, producing a very weak total of 14. The dealer now has to bust for the player to win.

The soft doubling option does produce a tremendous potential opportunity for the player. Removing the option represents a disadvantage of approximately .14%. That figure at first glance may seem inconsequential but actually is very important, considering the maximum advantage a good card counter can procure, for example, is between 1.25% and 1.5%.

Put that in perspective, and it’s easy to see why the option can be critical.

The Basic Strategy decisions with soft doubling at first can seem a little confusing but become easy after familiarizing yourself with them. The hands are grouped in two — (A,2-A,3), (A,4-A,5), (A,6-A,7), and (A,8-A-9). In a multi-deck game, the Ace-2 and Ace-3 hands should be doubled when the dealer shows a 5 or 6 upcard. The Ace-4 and Ace-5 are doubled when the dealer has a 4,5, or 6 showing. The Ace-6 is doubled when the dealer is showing anything from a 3 through 6.

For all of the above hands, the player will hit on any other dealer’s upcard. The Ace-7 hand is similar to the Ace-6, with a double required when the dealer shows 3-6. But the Ace-7 differs from all other hands, because the player must stand with A-7 against the dealer’s 2,7, and 8 upcards. The two is never doubled upon, and the seven is already beat, for the most part, with a soft 18. A push (or tie) is very possible with the 8 showing. The only way to beat the dealer’s projected total of 18 is to draw an ace, 2, or 3, making it not a very strong option.

The Ace-8 and Ace-9 hands are already PAT, or standing, hands, and should be left alone. In all likelihood, these are winning hands.

All it takes is a little memorization of the basic rules to get yourself in tune to the correct plays. You might want to try a soft hand drill to facilitate learning. Just take one of the soft hands – Ace-4, for instance, and leave it as a constant. Then deal out samples of dealer’s upcards and practice making your decisions. Go through the deck a few times, keeping the rules handy for quick reference. It won’t be long before you know when to hit, stand, or double on soft hands.

Tags: , , , , , , , , ,


February 6th, 2008


By Charles Jay

What is important to know about craps is that there are two identical dice that are used in the play of the game. Each of these dice are six-sided, with values, naturally, of 1 through 6. When you look at the sides opposite each other in each die, you will find that the opposite sides add up to seven; for example, the 1 will be opposite the 6, the 2 will be opposite the 5, and the 3 will be opposite the 4. All of these combinations add up to 7.
On any one roll, there are thirty-six (36) different dice combinations that can come up.

* Of these combinations, there are going to be six of them that add up to seven (7), which makes 7 the key number in the game of craps, since it is the one most likely to occur. As we do our arithmetic, seven comes out to six combinations out of 36, which translates to a ratio of 6-to-30. Therefore, the odds against a seven being rolled are 5-1.
* Five of the dice combinations add up to six (the 4-2, 1-5 and their reverses, plus the 3-3 combination), and five of them also add up to eight (the 2-6, 3-5 and their reverses, plus 4-4); these constitute 5 out of 36, which comes out to a ratio of 5-to-31, so the odds against either of those totals being rolled are then 6.2 to 1.
* Four of the combinations add up to five (1-4, 2-3 and their reverse), and four of them also add up to nine (4-5, 3-6 and their reverse), making it 4 out of 36 combos, constituting a ratio of 4-to-32, which means there are 8 to 1 odds against a five or a nine being rolled.
* Three combinations add up to four (1-3 and its reverse, plus 2-2), and likewise three of them add up to ten (4-6 and its reverse, in addition to 5-5), bringing either of those totals to 3 out of 36, which is a 3-to-33 ratio, and 11 to 1 against either of those numbers being rolled.
* Two of the combinations add up to three (1-2, either way), and it is the same for eleven (6-5 either way). That translates to 2 out of 36 combinations, a 2-to-34 ratio, and 17 to 1 against either the three being rolled or the eleven being rolled.
* Only one of the combinations adds up to two (this is the 1-1, or “snake eyes”), and only one adds up to twelve (6-6, or “boxcars”). For both the 2 and 12 combination, it’s one combination out of 36, which translates to 35 to 1 odds against either of the combos being rolled.

The odds of rolling a seven before the combination of six is rolled comes out to 5 to 6 (representing the number of 7’s out of the 36 possible combos against the number of 6’s in the 36 combos). The odds of rolling a 6 before a 7 is 6 to 5. The odds of rolling the 5 before rolling the 7 is 6 to 4, which of course is then reduced to 3 to 2. The odds of a four being rolled before a 7 is rolled are 2 to 1. The odds of a 3 being rolled before a 7 is rolled are 3 to 1. And the odds of the 2 being rolled before a 7 is rolled are high – at 6 to 1. There is a lot of significance to these numbers, and they take on additional meaning as one progresses along the way to learning more and more about the way the game is played.

Tags: , , , , , , , , ,