OK, blackjack aficionados. Here’s your chance to find out how much you really know about the game of blackjack. Give yourself one point for every statement that you get right. Then subtract the number of wrong answers from the number of right answers for your final score.

The object of blackjack is to get the point total of your hand as close as possible to 21. 

False. The objective is to beat the dealer’s hand by either of two ways: Having your hand total higher than the dealer’s hand or not busting (i.e., going over 21) when the dealer busts. 

You will win 50% of the hands when you play blackjack.

False. On average, you will 43% of the hands, lose 48%, and tie 9%. If you discount ties, you will on average 47% of your hands and lose 53%.

The casino has the edge in blackjack because players act on their hand first, and if they bust, they automatically lose.

True. This “double bust” rule is what creates the casino’s inherent edge in the game. 

Clueless players on your table will cause you to lose.

False. How your fellow players decide to play their hands has no effect on your chances of winning or losing at blackjack in the long run. In fact, you could get the same long-term results playing on a table with six professional blackjack players as you would playing with six chimpanzees.

There is a mathematically optimal playing strategy for blackjack.

True. This strategy is known is the basic playing strategy and it shows you how best to play every hand dealt to you.

The most important card in blackjack is the dealer’s upcard.

True. That’s because the dealer’s upcard and the cards you hold in your hand determine how you should play your hand using the basic playing strategy.

It’s possible to make a living playing live blackjack.

True. In fact, many professional blackjack players, from all over the world, gather annually at a secret location in Las Vegas (this event is known as the “Blackjack Ball).

A player who enters a game in the middle of a shoe will change the flow of the subsequent cards that will be dealt, causing you to lose. 

False. Changing the order of the cards by creating another hand when a player jumps into a game in mid-shoe can help players as much as hurt them.

You should always split a pair of 8s.

True. Splitting a pair of 8s to play out two hands, each starting with an 8, is always the better play than hitting or standing on 16, regardless of what the dealer’s upcard happens to be.

Card counting is illegal.

False. Using your brains when you play blackjack is not illegal; therefore, card counting is not “illegal.”

You will be dealt a blackjack hand about once in every 30 hands.

False. It’s once in about every 21 hands. 

Progressive betting systems don’t work.

True. Progressive betting systems will not alter your long-term expectations; however, what they do in the short-term is increase the swings in your bankroll one way or the other compared to betting the same on every hand.

A basic strategy player will bust about 12% of the time.

False. A basic strategy player will bust about 16% on average. A clueless player who uses a seat-of-the-pants playing strategy will often bust more often.

Bringing a strategy card with when you play blackjack is perfectly legal.

True. There is nothing illegal about using a strategy card when you play. However, most casinos (for security reasons) prefer that you not place the card on the table. Therefore, you should hold the card in your hand.

The dealer busts about 2 out of every 7 hands.

True. On average the dealer will bust about 28% of the time (or about 2 out of every 7 hands).

Always stand with soft 18.

False. Most players mistakenly believe 18 is good enough to beat the dealer. Actually it’s not. When you are dealt a soft 18, the best strategy is to double down if the dealer shows a 3 through 6 upcard, hit if the dealer shows a 9, 10 or ace, and stand against a dealer’s 2, 7 and 8. (Note: Depending on the mix of playing rules and number of decks of cards, the above strategy may be slightly different; consult the strategy charts in the Ultimate Blackjack Strategy Guide for details.)

A single-deck game in which a blackjack pays 6-5 is one of the worst blackjack games.

True. The house edge increases by 1.4% when a blackjack pays 6-5 instead of the traditional 3-2. Avoid playing all 6-5 blackjack games.

The house edge decreases slightly when a casino uses a continuous shuffling machine (or CSM).

True. With a CSM, the discards from each round are randomly shuffled with the remaining unplayed decks of cards. The reason that the house edge decreases slightly with a CSM is because on average more tens and aces are dealt compared to a normally shuffled shoe with a fixed shuffle point. More large-value cards favor the player, which slightly decreases the house edge. However, with a CSM, casinos can deal roughly 20% more hands per hour, which results in a higher expected theoretical loss for players. The latter more than compensates for the slightly lower house edge. Bottom line: Avoid playing on any table that uses a CSM.

Because blackjack side-bets have high-payoff odds, they are a good bet.

False. Most blackjack side bets (e.g., 21 + 3, Royal Match, Pair Square, and others) have high house edges (greater than 2%). An enticing high payoff on a side bet does not make it a good bet. Bottom line: Avoid making side bets. (Note: Some, however, can be beaten by card counting. See Ultimate Blackjack Strategy Guide for details.)

You should always hit a hard 16 when the dealer’s upcard is a 10.

False. If your 16 comprises three or more cards, you are slightly better off standing.

Blackjack is the best casino game to play.

True. By selecting a blackjack game that has a good mix of player-favorable rules and using the basic blackjack playing strategy, it’s possible to reduce the house edge to about half a percent (even less, rule dependent). By learning a simple card-counting system, you can eliminate the house edge completely and swing the odds in your favor.

If you scored 17 or less, I would suggest you bone-up on your blackjack by reading my Ultimate Blackjack Strategy Guide before risking any more money in a casino.

Let’s face it. What all video poker players hope (and pray) for is that the next hand will give them a royal flush because that results in an immediate 4,000 coin payoff. But did you ever wonder what the chance that this will happen when you hold, say, four cards to a royal flush?  How about holding three cards to a royal?  And what is the chance of being dealt a royal flush on the initial deal? I’ve summarized the answers to these questions below and they may surprise you.

Note: There are many different video poker games but by way of example, I’m going to focus solely on Jacks or Better in this article. Also, keep in mind that a high card in video poker is a Jack, Queen, King, and Ace (a ten is considered a low card).

First off, it’s important that you understand how the cards are dealt in video poker. Even though there isn’t a casino dealer dealing the cards, a computer chip that resides inside the video poker machine simulates what a live dealer would do if she were dealing the cards. It works like this.

A standard 52-card deck is shuffled and when a player hits the deal button on the machine, the shuffling stops and five random cards are dealt to the player (i.e., these are the five cards that appear on the video poker screen on the initial deal.) While the player decides which cards he wants to keep (or hold), and which he wants to discard for replacement cards, the remaining 47 unplayed cards are shuffled. Let’s assume a player decides to hold the first four cards on the screen and discard the fifth card. He hits the hold button beneath each of the four cards that he wants to keep and then hits the draw button. The fifth card is removed and a single, randomly selected replacement card (from the shuffled 47 unplayed cards) is dealt to the player, which completes his hand. The key points to remember are this:

• Video poker plays like a five-card draw poker game. You get one opportunity to improve your poker hand.
• The card(s) in your initial hand that you discard can’t appear again on the secondary draw.
• Once the hand is completed, all the cards are reshuffled for the next hand.

OK, let’s now look at the facts on what your chances are to hit a royal flush depending upon how many cards to a royal flush you were dealt in your initial hand.

(Note: I’m going to assume a player is playing at a leisurely pace of 600 hands per hour for the examples that follow. Moreover, the data on the odds of hitting a royal came from Dan Paymar’s book, Video Poker – Optimum Play (second edition). 

ON THE INITIAL DEAL

Your chance of being dealt a five-card royal flush on the initial deal is a minuscule 0.00015 percent (or 1 chance in 649,740). You might think that with those long odds, you’ll never be lucky enough to be dealt a royal flush. However, never say never.

Once I was dealt a 10-J-Ace-Q-K in spades on the deal for an instant royal flush. It happened quickly because I was playing fast. (I had the speed of the cards being dealt on the screen on the fast setting). I knew something good happened when the machine locked up and music started playing. My second dealt royal flush was even more memorable. I was showing my father-in-law how to play a Triple Play game when I was dealt a royal flush on the bottom hand (and of course, I automatically wound up with a royal on the second and third hands). As I said earlier, never say never.

ON THE DRAW AFTER DISCARDING ALL FIVE CARDS

If you are holding five “garbage” cards and discard all of them for five new ones, the chance that it will result in a royal flush is 1 in 383,484. Although this has never happened to me, it happened once when my father-in-law tossed away all of his initial five cards and was dealt a royal flush. (Again, even though the odds are long, never say never!)

FOUR CARDS TO THE ROYAL FLUSH

Lucky you if you were dealt four cards to the royal flush right off the bat. This doesn’t occur very often: on average once every 2,777 hands (about once every 4.5 half hours of play). However, every time you are dealt four cards to the royal flush, the chance you will get the one card you need for a royal on the draw is a relatively measly 1 in 47.

 
Note: Coincidentally, during my last five-hour playing session prior to writing this article, I was dealt four cards to the royal flush a surprisingly five times. This is about six times more than what I should have statistically received during five hours of play.  Did I luck out and hit the royal flush at least once? Keep reading for the surprising result.

THREE CARDS TO THE ROYAL FLUSH

You’ll be dealt three cards to a royal flush once in every 92 hands, on average, (or about 13 times every two hours), Unlike the 1 in 47 chance above, now the chance of hitting a royal flush, when holding only three cards to the royal, is 1 in 1,081.

Note: Now for the rest of the story of my recent playing session, After being dealt four cards to the royal flush five times, and coming up empty handed each time, I was dealt (for the first time) three cards to the royal. And, as you probably guessed it, I held the three cards to the royal, hit the draw button, and up popped the two cards I needed for the royal flush. As I said earlier, never say never.

Sidebar: I wrote an article previously about my very long royal flush drought. The above royal flush finally ended my drought, which lasted 22 months and approximate 310,000 hands since my previous royal.  I’ll discuss how to survive long royal flush droughts in a future article.

TWO CARDS TO THE ROYAL FLUSH

You can expect to be dealt a two-card royal flush once in every 13 hands on average (or about 46 times per hour). Even though the frequency of being dealt a two-card royal is great, the odds of drawing a royal from it are long:  one in 16,215. (However, I remember twice in my playing career converting a hand containing two cards to the royal into a royal flush so I’ll say it again, never say never.)

ONE CARD TO THE ROYAL FLUSH

You’ll average being dealt only one high card on the deal about 100 times per hour. Far fetch as it may seem, it’s possible to hold one single high card, hit the draw button, and be dealt the other four cards you need for a royal flush. But don’t count on this happening very often because the odds are 1 in 178,365. (I can only recollect one-time holding a single high card and being dealt the other four cards I needed for a royal flush.)

The following table summarizes the above; namely, the odds and frequency of being dealt the cards you need for a royal flush on the initial deal, and what your chances are of converting the initial hand into that glorious royal flush. Good luck!

As casino axioms go, this one from roulette is a basic that everyone should know: The house edge at roulette is derived from the zeroes. Roulette odds are dependent on the zeroes.

Those devising roulette strategy need to be aware of the effect of the zeroes. What brings this to mind is a recent movement in Las Vegas toward offering wheels with three zeroes.

Most wheels in the United States have two zeroes. A few have one zero, a more common configuration in Europe than in the U.S. Those who search for an online casino can find either single- or double-zero wheels.

Triple zero is something new, at least in licensed, commercial casinos. Wheels with 0, 00 and 000 have sometimes been spotted at charity casino nights, where the odds are tilted toward earning money for the sponsoring charity.

But the Venetian in Las Vegas is no charity, and it added Sands Roulette in 2016. Others, including Excalibur, MGM Grand and Planet Hollywood, added triple-zero roulette in 2018 and 2019.

Sands Roulette substitutes a Sands logo for the third zero, but it does the same thing to the odds as if the space was labeled “000.”

Payoffs are the same as on single- or double-zero wheels: 35-1 on winning single-number bets; 17-1 on two-number splits; 11-1 on three number streets; 8-1 on four-number corners; 5-1 on six-number double streets; 2-1 on 12-number bets including columns and dozens; and even money on 18-number bets including red or black, odd or even and first 18 or last 18.

All those would be true odds with no house edge if there were 36 numbers on the wheel.

However, with the zeroes included, there are 37 numbers on a single-zero wheel, 38 with 0 and 00 or 39 on the new triple-zero games.

Instead of the true odds being 35-1 on a single number bet, they’re 36-1 with one zero, 37-1 with two zeroes and 38-1 with three. Instead of true odds being 18-18 on red or black, they’re 19-18, 20-18 or 21-18, depending on the number of zeroes.

Look at what that does to the house edge on a triple-zero wheel, starting with a single-number bet.

Imagine you’ve picked a number and bet $1 on it for 39 spins in which each number turns up once.

Your total risk is $39. On the one spin in which your number comes up, you win $35 and keep your $1. 

That means at the end of the trial you have $36 and the house has $3 of your $39 in wagers.

To calculate the house edge, divide that $3 by the $39, then multiply by 100 to convert to percent. 

The first part of the calculation comes to 0.0769. Multiplying that by 100 tells you the house edge on single-number bets on a triple-zero wheel is 7.69 percent.

We could go through the same exercise for single-zero and double-zero wheels, but to go straight to the answer, the house edge is 2.7 percent with one zero and 5.26 percent with 0 and 00.

Let’s try again, this time with even-money payoff bets such as red or black.

Imagine you bet $1 on black for 39 spins on a triple-zero wheel. Again, your total risk is $39.

You win on any of the 18 black numbers, lose on any of the 18 red numbers, and lose on the 0, 00 and 000 with their green backgrounds.

On each of the 18 wins, you collect $1 in winnings and get to keep your $1 bet. So at the end of the trial, you have $18 in winnings and $18 in bets retained for a total of $36.

Since you have $36 of your original $39, the house has the other $3. As we’ve already seen, the house edge is the $3 won by the house divided by the $39 you put at risk. When multiplied by the conversion factor of 100, that tells us the house has a 7.69 percent edge.

House edges on red/black bets are the same as on single-number bets on single- and double-zero wheels, too – 2.7 percent with one zero, or 5.26 with two.

In fact, you can apply those house edges to nearly every bet on the wheels. Regardless of whether you’re betting corners, columns, streets or almost anything else, the house edge is 2.7 percent with one zero, 5.26 percent on a double-zero wheel and 7.69 percent with 0, 00 and 000.

The exception is the five-number, or “basket,” bet on double-zero wheels. That’s  bet on 0, 00, 1, 2 and 3, and it has a house edge of 7.89 percent – even higher than the standard edge for all bets on a triple-zero wheel.

Best strategy for a double-zero wheel starts with avoiding the basket bet.

That’s not something you have to worry about on single- or triple-zero wheels. There is no five-number basket. If you want to bet the zeroes along with the 1-2-3 street, it’s a four-number bet on a single-zero roulette wheel with the same payoff and odds as a corner, and it’s a six-number bet on a triple-zero wheel with the same payoff and odds as a double street.

Some games have special conditions that can reduce the house edge on the even-money payoff bets. A common Atlantic City variation comes when you bet red or black, odd or even, or first 18 or last 18 and the ball lands in one of the zeroes. In that case, you lose only half your bet.

That reduces the house edge to 2.63 percent on the double-zero wheels common in A.C. If applied to other configurations, it would reduce the house edge on even-money bets to 1.35 percent with one zero or 3.85 percent on a triple-zero game.

Even with that in mind, the house edge on a triple-zero wheel is much higher than with fewer zeroes.

That leaves this basic strategy: If you want to play roulette and see a triple-zero game, your first move should be to look for a wheel with fewer zeroes.

By using the basic playing strategy, a player can reduce the house edge to less than 1% (rules dependent). Most blackjack players understand the logic behind the majority of the basic strategy plays; for example, why you shouldn’t hit a 16 when the dealer’s upcard is a 6 or why you should split a pair of 8s when the dealer’s upcard is a 6. However, some of the basic strategy is not so apparent: like hitting a 12 against a dealer’s 3, or splitting a pair of 9s against dealer’s 9. Below are four non-intuitive hands, with the justification for the correct play.

PLAYER’S 6-5 VS. A DEALER’S 10

Basic strategy says to double down on 11 against a dealer 10. However, many players chicken out and hit instead because they are afraid that the dealer might have a pat 20. Well, did you know that when the dealer has a 10 upcard (and doesn’t have a blackjack), he will wind up with a 20 roughly 33% of the time?

Meanwhile, a player holding an 11 and taking one card (i.e., doubling down), has roughly a 31% chance of getting a 21 (by drawing a 10) and an 8% chance of making a 20 (by drawing a nine). In other words, you are considerably more likely to make a 20 or 21 with a one-card draw than the dealer is to make a 20. Moreover, think about this: if you draw a 7, 8, 9, or 10, and the dealer has the same card in the hole, you still win! Even though doubling lowers slightly your chances of winning (because if you draw a small card, you can’t hit again to improve your total), your monetary gain is still greater by doubling because you bet twice as much money.

PLAYER’S 8-8 VS. DEALER’S 10

If I told you that playing an 8 twice, against a dealer 10, loses less money than playing a 16 once, would you believe me? Probably not, but guess what, it’s true.

When you hit 16 against a dealer 10, you’ll win only about 23% of the time and lose 77%, meaning you’ll win about four hands out of every 17. This is why holding a 16 against a 10 is the worst hand in blackjack. However, when your 16 is a pair of 8s, you have an out, namely splitting, because now your chances of winning when you start each hand with a single 8 against a 10 are 38%. In both cases (hitting and splitting), you are going to lose money, but it’s still cheaper to win 38 hands and lose 62 on each 8 (by splitting) than to win 23 hands and lose 77 once (by hitting). Still not convinced? Here’s the simple math to prove this point.

Hit: Bet $10 on the hand. Win 23 hands for a total win of $230. Lose 77 hands for a total loss of $770. After 100 hands (ties excluded), your net loss is $770 minus $230, or $540.

Split: Splitting 100 hands of 8s creates 200 hands, with each hand starting with an 8. If you bet $10 on each split 8, you’ll win 76 hands (38% of 200), for a total win of $760. You’ll lose 124 hands for a total loss of $1,240. Your net loss is $480. Therefore, losing $480 (by splitting) is, I’m sure you’ll agree, better than losing $540 by hitting.

PLAYER’S 9-9 VS. DEALER’S 9

It seems logical to split a pair of 9s when the dealer is showing a small card. However, it may not make sense to you to split 9s against a dealer 9, so you may stand with your “strong” 18. However, a hard 18 will beat a dealer’s 9 only eight times out of 20, while you’ll win almost half the time with a 9 facing a dealer 9 (actually, you’ll win 9.5 out of 20 hands). The bottom line is that even though you think an 18 is a strong hand, it isn’t against a dealer 9. To get close to break-even on this hand, you need to be aggressive and split. (Note, also, that when resplitting and doubling after splitting are permitted, there is the extra attraction of being able to double your 11, as per our first example, should you draw a deuce to any of your 9s.)

PLAYER’S 10-2 VS. DEALER’S 3

There is a “rule” in blackjack that says you should never risk busting your hand when the dealer shows a weak up card. That may be true for most stiff hands but it’s not the case when you are holding a 12 against a 3. When you think about it, there are only four cards that could bust your 12 — a ten, jack, queen, or king. On the other hand, five cards will get you to 17–21 (a five, six, seven, eight, or nine). Therefore, more cards will get you into the safe 17–21 zone than will break you. The other factor that works in your favor is the dealer’s 3 up card, which is not as weak as, say, a 4, 5, or 6 up card (she will bust less with a 3 up card compared to the 4, 5, or 6). The bottom line is that you will lose slightly less (about 2%) by hitting 12 against a 3 than by standing.

For more information on how to play every hand correctly when you play blackjack, consult Chapters 2 and 3 in my Ultimate Blackjack Strategy Guide.

For the most part, doubling down for less is not a smart play. Notice I said “for the most part.” There are exceptions, which I’ll explain shortly. But first, let me address the issue of doubling down for less in a traditional blackjack game.

A long time ago when I was playing blackjack, a fellow table player (who had been steadily losing) went ahead and unexpectedly placed four green chips (total of $100) in his betting spot.  The dealer dealt the cards, and I noticed the player cracked a smile as he stared at the good hand he was dealt — a 7-4. But his smile quickly turned to a frown when he glanced at the dealer’s upcard – a picture card.  When the dealer got to the player, he picked up four more green chips from his chip-stack as if he were going to double down. But instead, he hesitated and intensely stared at that dealer’s picture card. He probably knew that the basic strategy play for an 11 against a dealer ten was to double down; however, I could tell he was getting a little queasy about putting out another $100 and possibly losing $200 if the dealer were to beat him. It seemed like forever until he finally made a decision, which rather surprised everyone. Instead of doubling down for another $100, or possibly just hitting his hand, he instead took a middle-of-the-road approach and shoved out one green chip ($25),  nervously announcing to the dealer, “I’m going to double for less.”  

It turns out he pushed on his hand, and he quietly left the table with far fewer chips than he came with. Another player then made this comment to the dealer: “I didn’t know that you could double down for less.” The young dealer responded, “Yes, and that’s a pretty smart play when I’ve got a strong upcard.”

Let me say this as politically correctly as I can. Doubling for less is not a smart play, and any dealer who offers this advice to players needs to read a good book on blackjack. 

Let me pause for a second to ask you this question: Which of these betting propositions would you take?

1. Winning $100 56% of the time
2. Winning $200 54% of the time

While you ponder the answer to this question, let’s get back to this player who decided not to double for the full amount, but instead, creatively doubled for less. If you remember, he bet $100 on his 11 against a dealer’s 10 and then “doubled” for $25.  Let me show you what that play cost him, compared to doubling down for the full amount, or just hitting his hand.

OPTION #1. HIT

If you hit an 11 (potentially more than once) when the dealer shows a ten, you will win 56 percent of the time on average. This means that, for every hundred times you get this hand, with pushes excluded, you can expect to win 56 hands and lose 44 hands.

He wins $100 56 times for a total win of $5,600.
He loses $100 44 times for a total loss of $4,400.

His net expectation is the difference of his expected win minus his expected loss, which equals +$1,200. Not bad, and it’s obvious that hitting an 11 against a dealer’s 10 [aha!] is a profitable play. But, you can do even better when you double down.

OPTION #2. DOUBLING FOR THE FULL AMOUNT

Blackjack players have the option to double down on any two first cards. (Although some offline and online casinos will restrict players from doubling on some initial hands, the vast majority of casinos allow DOA or double on anything.) When you double down, the casinos will allow you to make a secondary bet up to the amount of your initial wager (meaning you can double your initial bet, which is why this rule is known as doubling down). 

In return for the casino’s allowing you to double your bet in beneficial situations, you are limited to only one draw card. Therefore, if you were to double down on 11 and drew a 3, you are stuck with a 14. Because you can’t draw more than one card when you double down, the percentage of the times that you win your hand is often less than for  hitting.  

Take the case of an 11 against the  10. If you hit 11 against the 10, you win 56% of time, but if you double down you win only 54% of the time, or 2% less.

You’re probably saying to yourself, “Wait a minute ... if I win fewer hands when I double down, how  can it be a better play than hitting?” Stay with me and I’ll explain.

In order to analyze the benefits of doubling down, we have to factor in the amount bet. In the above example, he could have doubled for the full amount of $100, which equals a total of $200 wagered on the hand. Therefore, his expectation, if he would have doubled for $200, is as follows:

Win $200 54 times = +$10,800
Lose $200 46 times = –$9,200.]

He would have had an expectation of winning $1,600 (over 100 hands). 

If you compare the expected win of $1,600 by doubling down for the full amount with the $1,200 if you hit instead, you can clearly see the answer to the question I posed to you earlier in this article, namely:

• You are better off winning $200 54% of the time, than winning $100 56% of the time.

OPTION #3. DOUBLING FOR LESS

Now let’s take a look at that doubling-for-less play, which the dealer praised.

Instead of doubling for $100, he “doubled” for $25. His expectation is:

Win $125 54 times = +$6,750
Lose $125 46 times = –$5,750 
Net expectation is +$1,000

The following table summarizes the expectation for the three possible choices he had on the hand. 

It turns out that his brilliant double-for-less play was the absolute worst of the possible three plays he could have made. He would be $200 better off hitting his 11 against the 10, or better yet, $600 better off if he doubled for the full amount. (I’m sure the casino bosses were thrilled when he decided to creatively double down for only $25!!) You’ve got the best of it when basic blackjack strategy says to double down, so always double for the full amount and never, never double for less.

Note: Of course, he could have doubled for all different amounts up to $200, and many of them would have had a higher Expected Value (i.e., EV) than hitting.

But wait, because there is more to this story. What if a player doesn’t have enough bankroll to make a full double down bet? Or how about a player that would have sleepless nights if he made the secondary $100 wager and lost $200 on the hand? My sage advice to these players is this: When you play live blackjack you need to have enough bankroll to support making occasionally large bets, including double downs and pair splits, and if you happen to be very risk averse, such that losing a big bet causes you emotional problems or sleepless nights, then you need to be betting at much lower stakes or to find a hobby other than blackjack.

There is one time where doubling for less can be a brilliant play and that’s when it’s crunch time (i.e., last hand) in a blackjack tournament.  I learned this ploy from my good friend and tournament expert Kenneth Smith (author of the books How to Win More Blackjack Tournaments, vols. 1 and 2.). In a future article on blackjack tournament strategies, I’ll explain how and when doubling down for less can be a very powerful strategy in a tournament.

Every video poker game has its strategy quirks dictated by their pay table. How to play video poker and get the most out of the game is different when you’re playing Jacks or Better, with a 2-for-1 payoff on two pairs, compared to Double Bonus Poker, with bigger pays on four of a kind but only 1-for-1 on two pairs.

And when you get to Double Double Bonus Poker and Triple Double Bonus Poker, that’s another thing altogether. They present special problems in video poker strategy.

What makes them different are the enhanced jackpots when your fifth card is a 2, 3 or 4 with four Aces or an Ace, 2, 3 or 4 with four 2s, 3s or 4s.

Assuming a five-coin bet in Double Double Bonus Poker, four Aces pay 800 coins without the fifth-card kicker, but 2,000 with it. Similarly, four 2s, 3s or 4s pay 400 without the kicker, but double to 800 with one.

Triple Double Bonus Poker takes that concept to an extreme. Four Aces usually are worth 800, but leap to 4,000 with a low-card kicker. That’s a bonanza equal to a royal flush.

With four 2s, 3s or 4s, payoffs are 400 without the kicker, but a whopping 2,000 with. That’s half a royal flush, or $500 on a 25-cent machine.

There are tradeoffs on the pay tables, of course. Two pairs just get you your money back, and on Triple Double Bonus three of a kind pays 2-for-1 instead of the 3-for-1 on most games.

More of the overall payback is tied up in the big-paying hands in most games. That makes it imperative to make the right plays in potential kicker situations.

The biggest dilemma comes when you’re dealt three Aces, 2s, 3s or 4s along with a kicker. Obviously, you should hold the three of a kind, but should you hold the kicker, too?

If you discard the kicker, you get a two-card draw and maximize chances at completing four of a kind. If you keep the kicker, you get only a one-card draw, but every time you complete four of a kind it will bring the kicker jackpot.

Let’s look at each situation in 9-6 and 8-5 Double Double Bonus Poker, then in 9-7 and 8-5 Triple Double Bonus Poker.

Overall, 9-6 Double Double Bonus returns 98.98% with expert play, while the 8-5 version returns 96.79%. In 9-7 Triple Double Bonus, the average return is 99.58%, while the 8-5 game returns only 95.97%. 

There are intermediate TDB pay tables at 9-6 (98.15%) and 9-5 (97.02), but strategy differences on three of a kind plus a kicker are influenced by the 9-for-1 vs. 8-for-1 payoffs on full houses. Flushes are not a possibility when you start with three of a kind, so flush payoffs don’t influence strategy on these hands.

DOUBLE DOUBLE BONUS POKER

Ace-Ace-Ace and a 2, 3 or 4: If you hold the kicker along with the Aces, there are 47 possible one-card draws.

Of the available cards, 43 will leave you with just your original three of a kind for a 15-coin payoff. Three will pair up the kicker for a full house, worth 45 coins on the 9-6 version or 40 on the 8-5 game.

One draw will be the fourth Ace, and keeping the kicker makes that worth 2,000 coins.

If you hold just the Aces and discard both of the other cards, including the kicker, there are 1,081 possible draws. 

Of those, 969 will not improve on three of a kind, leaving the 15-coin pay. You’ll pair up the kicker for full houses 66 times, worth 45 or 40 coins each, depending on the pay table. Thirty-five draws will bring the fourth Ace without a kicker for 800 coins, while 11 draws bring an Ace and a kicker for the 2,000-coin jackpot.

When all those payoffs are added and divided by the number of hands, the 9-6 pay table brings an average return of 62.45 coins if you hold just the three Aces, or 59.15 coins if you hold the Aces with a kicker.

With an 8-5 pay table, average payoffs are 62.14 coins on Ace-Ace-Ace, and 58.83 on Ace-Ace-Ace and a kicker.

So regardless of pay table, you’re better off maximizing your chances at drawing the fourth Ace rather than going all-out for the Aces-plus-kicker bonanza.

2-2-2, 3-3-3 or 4-4-4 and an Ace, 2, 3 or 4: Proportions are exactly the same with three low cards and a kicker as they are with four high cards and a kicker. Your possibilities are still 47 draws with 43 three of a kinds, three full houses and one four of a kind with kicker if you hold the kicker, and 969 three of a kinds, 66 full houses, 35 four of a kinds, and 11 four of a kinds with kicker if you don’t.

What’s different is the payback on the quads – 400 coins without a kicker, 800 with one.

When those lower four of a kind paybacks are plugged into calculations, the result on the 9-6 game is average returns of 37.28 coins if you discard the kicker and hold the three of a kind, and 33.62 if you hold the kicker along with the trips. On the 8-5 version, averages are 36.98 coins if you hold just the three of a kind, and 33.30 if you hold the kicker, too.

Just as with the Aces, you’re better off discarding the kicker on either pay table. Maximize your chance at four of a kind, and let the kickers take care of themselves.

TRIPLE DOUBLE BONUS POKER

The 4,000-coin jackpot on four Aces with a kicker is a game changer. On a 25-cent machine – the most popular coin denomination in video poker – that’s a $1,000 return, and it comes up more than three times as often as a royal flush.

With expert play, royals come up once per 45,358 hands in 9-7 TDB, while you’ll get four Aces with a kicker an average of once per 14,214 hands.

Draw possibilities and proportions of outcomes are the same as in Double Double Bonus Poker. The difference is in the huge four of a kind with kicker payoffs and in the reduced 2-for-1 payoff on three of a kind.

Given that, we can jump straight to the average returns.

• Ace-Ace-Ace with a 2, 3 or 4: In the 9-7 version, if you hold the kicker with the Aces, your average return per five coins wagered is 97.13 coins, and that beats the 78.32 if you hold just the Aces and discard the kicker.
  
  In the 8-5 version, average returns are 96.81 coins with the kicker and 78.01 without.
   
• 2-2-2, 3-3-3 or 4-4-4 with an Ace, 2, 3 or 4: In the 9-7 game, if you hold the kicker with the three of a kind, the average return is 54.57 coins, better than the 45.01 on the three of a kind by itself.
  
  With an 8-5 pay table, averages are 54.26 if you hold the kicker and 44.71 if you don’t.

That means in Triple Double Bonus Poker, the best video poker strategies are opposite those in Double Double Bonus Poker. Regardless of whether you have three Aces and a kicker or three 2s, 3s or 4s and a kicker on the initial deal, you hold the kicker along with the three of a kind in Triple Double Bonus, but discard the kicker in Double Double Bonus.

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What is a two-faced person? It is someone who is double-dealing and false. He is the opposite of what you think he is. He could be a friend or business partner who stabs you in the back. This type of person is also called Janus-faced, as a person with two characteristics modeled after the Roman god Janus. Think of those theatre faces with the smile and the frown connected together.

Table of Contents:

• Proposition Bets
• Quick Practice
• Double Zero Wheels
• Single Zero Wheels

This is at the root of my Big Number Two-Faced Roulette System. It contains the number and its opposite. I think you’ll find this a fun system to play, despite the fact that it is not an advantage-play method.

There are traditionally two types of “big number” roulette systems: The kind that can give you an edge over a land-based or an online casino because you have discovered a wheel that is biased or off balance (a very, very rare occasion today) or you’ve discovered a number that has been hitting more frequently than others simply due to the random nature of the game. This will happen a lot. In fact, this happens all the time.

Now, there is a third kind: A number that you choose as the “big number” and then decide to bet it, perhaps along with the numbers adjacent to it or to bet against it, perhaps along with the numbers adjacent to it. These are called “opposite numbers” as they are across the roulette wheel from the “big number” and its possible compadres. The opposite numbers are known as two-faced numbers as they go against the grain of the “big number” and its fellows. 

I recommend using the scoreboard to decide what your “big number” is. If the 4 has just hit, then your “big number” is a 4 and you work from there. You can bet the 4 and whatever adjacent numbers you wish or you can bet against the 4 and whatever adjacent numbers you wish. You can also bet proposition bets such as the red or black, high or low, even or odd.

[Please note: You can choose as many adjacent numbers as you wish. I have two on either side of the “big number” and two on either side of the Two-Faced number. That makes five numbers total. You can have more or fewer. This can be an expensive way to play so I would go for fewer and not more inside numbers.]

Using the proposition bets can save your bankroll some big hits if things are going the wrong way for you. I tend to always be cautious when betting my money.

[Please note: On the charts accompanying this article the designations for the “two-faced” propositions are not based on the second category of numbers; they are merely the reverse of the first category. So if the first category is odd, red, high; the “two-faced” category will be even, black, low. That second grouping of numbers is therefore irrelevant to the propositions.]

Let’s do a quick practice using the charts that accompany this article using the double-zero wheel. The scoreboard shows that the 11 has just hit. I now check out the number on the chart:

Going along with the “big number” we have these numbers: 26, 30, 11, 7, 20. If you bet these you are going with your “big number” of 11.

You can “two-face” that number by going with its opposite group of 25, 29, 12, 8, 19. Note that these numbers tend to be straight across the wheel from your “big number.” In single-zero roulette the zero does not have a “two-faced” number.

If you wish to bet the propositions you will see that the propositions that go along with 11 are odd, black and low. The propositions that “two-face” the 11 are the even, red and high.

All the best in and out of the casinos!

 

 

Should you play blackjack with one hand or two? I’ve been asked this question numerous times from blackjack players. My answer is this: “It depends on whether you have the edge or not.” Let me explain.

First let me focus on the majority of players who don’t have the edge when they play blackjack. (This includes blackjack basic strategy players.) 

Sometimes you’ll see a blackjack player playing two hands on every round. Other times a player may start a shoe playing one hand, and then suddenly, in the middle of the shoe, spread to two hands.  Why do some players do the latter? Mostly to “change the flow of the cards,” which they mistakenly believe will change their luck. (Because the house edge is the same on both hands, spreading to two hands will not guarantee that your luck will change.)

The one obvious thing that happens when you spread from one hand to two is that you will be dealt more hands per hour. For example, if you play with two other players, you can expect to be dealt roughly 100 rounds per hour. If, instead, you play two hands, you’ll get about 80 rounds dealt to you per hour, or a total of 160 hands per hour (that’s 60 more hands per hour). This isn’t a good idea because when the house has the edge and you play more hands per hour, you’re exposing more of your casino bankroll to that house edge, and you will lose more money.

But let’s say that instead of betting $20 on one hand, you split your bet evenly and wager $10 on each of two hands. Your theoretical hourly loss when you bet $20 on one hand is roughly $10 (assumes 100 hands per hour). Betting two hands of $10 each, your theoretical loss drops to $8 per hour (assumes 80 hands played per spot per hour, or 160 total). Therefore, you will decrease your hourly loss if instead of putting all your money on one hand, you bet half as much on each of two hands. (Note: The amount of the decrease of loss depends on how many other players are at the blackjack table with you.)

What if, instead of betting $20 on one hand, you bet $20 on each of two hands? Now you’ve increased the total amount bet in each round from $20 (one hand) to $40 (spread over two hands). In this scenario, the total amount that you wager per hour would be greater betting two hands than betting one, and your theoretical hourly loss will increase. Betting in this manner on two hands is, therefore, not recommended. 

On the surface you would think that the swings in your bankroll would be the same whether you bet, say, $50 on one hand or $25 on each of two hands, since the total amount wagered per round is the same ($50).  However, the two hands are really not independent because they are associated with the same dealer’s hand, so if the live casino dealer has a lousy hand, you are likely to win both hands (and vice versa if she has a strong hand). What this means in practical terms is that your bankroll will not fluctuate as much when you bet $25 on each of two hands compared to betting $50 on one hand.

Many blackjack players are happy if they can stretch their bankroll so it gives them a reasonable amount of time on the table (e.g., a three-hour session). Others are happy if they can achieve a predetermined win-goal (say, winning $150 with a $300 bankroll). Will betting more than one hand help you to achieve these objectives?

To answer this question, several years ago Norm Wattenberger, who is one of the foremost blackjack software developers, ran some computer simulations for different betting options (assuming the player started with a $300 bankroll) to determine what were the player’s chances of his bankroll’s surviving over a three-hour playing session (second column in table), and independently, the chances of a player’s winning $150 and quitting (third column). (Assumes100 hands per hour.)

What the data in the table show are:

1. For the same total amount wagered per round, betting two hands improves the chances of your bankroll’s lasting three hours but it also lowers the likelihood of winning $150.
2. Increasing the total amount wagered per round from $10 to $20 increases your chances of winning $150, but it also decreases the chances that your bankroll will last for three hours. Unfortunately, you can’t have it both ways.

The bottom line on playing two hands with half as much bet on each hand vs. betting it all on one hand is this: you will experience less fluctuation in your bankroll, and you are less likely to tap out during a session, but, you will have less chance of achieving a win goal. 

Now, what about a player who is card counting … is there an advantage to spreading to two hands? The answer is, yes, for several reasons.

1. Playing two hands is an excellent way of increasing your bet spread when the count is in your favor.
2. You can also bet 50% of what you would have bet on one hand, on each of two hands, with less risk and variance.
3. You can also keep your risk the same by betting 73% of what you would have bet on one hand on each of two hands instead. (For example, instead of betting, say, $50 on one hand, you could bet $35 on each of two spots with the same risk but greater expectation, assuming you are not playing alone.)
4. When the count is negative, you can spread to two hands with minimum bets to “eat” the small cards (i.e., by removing the small-value cards, the remaining unplayed cards become richer in the more player-favorable, high-value cards).
5. In a double-deck game, when the count is positive prior to the last round before the cut card appears, spreading to two hands will give a counter a slightly greater penetration (which increases his advantage).
6. If you are playing heads-up and spread to two hands, your chances of being dealt the high-value cards increase since you will be playing two hands against the dealer’s one hand.
7. Another way to camouflage your play and “eat” the small cards is to start a shoe betting two hands with minimum bets then reduce to one hand with larger bets when the count becomes favorable.

There are other reasons why spreading to two hands is advantageous to a card counter; if you want to learn more, I encourage you to consult Chapter 10 of my Ultimate Blackjack Strategy Guide. 

(Note: Most, but not all, casinos may have the requirement that when you spread to two (or more) hands, you must bet double the table minimum on each hand. Also, if you are card counting, spreading to two hands may bring attention your way from the pit. For details on this, see Chapter 10 of the Ultimate Blackjack Strategy Guide.)

Most land-based and online blackjack players have no idea of what taking “Even Money” means to their game. Yet, most players gladly take the even money when it’s offered. In fact, most dealers and fellow players, and sometimes even pit bosses, will encourage players to take the even money because "it’s a sure win." After all, a bird in the hand is worth two in the bush, right?

The even-money proposition comes into play whenever you’re dealt a blackjack hand and the dealer shows an Ace upcard. Say you bet $20 and you happily get a blackjack, but cringe when you see the dealer’s Ace upcard. You have the option to tell the dealer, before she peeks at her downcard, that you would like even money. She will pay you $20 and then remove your cards from the layout. You’ve won even money for your blackjack, even if the dealer subsequently flips over a blackjack of her own.

On the surface, taking even money looks like a “can’t lose” proposition, just as the dealers and pit bosses said. If you take even money, you'll be $20 richer regardless of what happens to the dealer’s hand. On the other hand, if you decline the even money, something very bad can happen; namely, the dealer could also have a blackjack, and you’d end up with nada for your beautiful blackjack. The choice looks clear: Take the sure money. 

But hold on, because there’s more to this story.

The problem here is what might happen if you decline the even money. What happens if the dealer doesn’t have a blackjack?

If you have a blackjack, decline the even money, and the dealer doesn't have blackjack, you are going to get paid $30 for your blackjack, which is 1.5 times your initial bet (equal to a 3-2 payout). That's something to consider before you take that “sure” even money.

So let’s review your choices when you get a blackjack and the dealer shows the Ace:

Choice #1: Take the even money and the sure twenty bucks.
Choice #2: Decline the even money and either:

• Win nothing, if the dealer has blackjack
• Win thirty bucks, if the dealer doesn't have blackjack.

It all boils down to this:

• Is it better to take the sure $20 by taking even money
• to decline even money and win $30, or get stuck with zilch? 

Most players don't want to risk getting nothing for their blackjack, so they opt for even money and the sure payoff. But guess what? That's the wrong play mathematically, and here’s why. 

 

 

Say you're sitting tight with your blackjack when the casino says it wants to pay you $20 for the hand. (That is, in fact, exactly what’s going on when the dealer asks you if you want “even money.”) Why, do you suppose, is the casino willing to give you $20 for your blackjack, right there and then, before the dealer peeks at the hole card? It’s certainly not because of your good looks. It’s definitely not because casino managers are being generous. 

No, the real reason that casinos are willing to give you twenty bucks for your blackjack is because they know that your hand is worth more than twenty bucks.

How? If you wager $20 and take even money, you'll win $20 one hundred percent of the time. But if you decline the even money, can you guess what percent of the time the dealer will have a blackjack (and you push) vs. the percent of the time she will not have a blackjack, and you joyously win thirty bucks? 

Check it out: A six-deck game contains 312 cards, of which 96 are ten-value cards (24 each of tens, jacks, queens, and kings). If you hold a blackjack and the dealer shows an Ace, there are 309 cards left, of which 95 are ten-value cards (remember that you're already holding one ten-value card in your blackjack hand). 

Therefore, the chance that the dealer has a ten in the hole is the ratio of 95 over 309, which is 30.7 percent. In other words, 30.7 percent of the time the dealer will get a blackjack and push your blackjack. 

It also means that a whopping 69.3 percent of the time, the dealer won't have the ten in the hole, and you'll be $30 richer!

With these percentages, you can easily compute the value of your blackjack hand. Here's how:

• 30.7 percent of the time you win 0 betting units
• 69.3 percent of the time you win 1.5 betting units.

If you average these numbers, you arrive at what many will find to be a surprising result—your blackjack hand is worth about 1.04 betting units. This means that for your $20 initial wager, your blackjack hand is actually worth about $20.80. No wonder the casinos are willing to pay you twenty bucks for your blackjack—they know it’s worth almost $20.80 (and they ain’t telling you). 

Here's another fact about even money that most players don't know: Taking even money when you have a blackjack and the dealer shows the Ace is the same as taking insurance on the blackjack. 

Suppose you bet $20 and get the blackjack, but the dealer happens to have an Ace upcard. If you want insurance, you make a $10 insurance wager (half your bet). What if the dealer checks her down card and she also has blackjack? Your blackjack ties hers and you push, but you get $20 for your winning $10 insurance wager (2 to 1 payoff), giving you a net profit of $20. 

If the dealer doesn't have the blackjack, you lose the $10 insurance bet, but you win $30 on your blackjack (3-2 payoff), for a net profit of—you guessed it—$20. Since insuring your blackjack yields a $20 profit whether the dealer has a blackjack or not, the casino offers players even money right up front. 

The bottom line with even money is this: If you always take it, in the long run you'll be giving away approximately four percent of your average profits on the hand. The casino is counting on you to take the even money; next time, surprise them and decline it. 

Note: There are three opportunities where it might sense to take even money. First is if a casino is paying 6-5 for a blackjack and offers even money, in which case you will have the advantage. (Don’t get too excited because firstly, you should never play in a 6-5 blackjack game, and secondly, most casinos are not that stupid to offer even money on their 6-5 tables.) The second time is to take even money as a strategic play on a last hand in a blackjack tournament to either overtake an opponent’s bankroll or preserve your bankroll from a potentially nasty negative swing. The third is if you are a card counter and know that there is a greater chance the dealer has a ten-value card in the hole. (I’ll cover these points in future articles.)